Examiner Tips

For time intervals crossing midnight, split into two parts: time until midnight + time after midnight. Remember an hour has 60 minutes, not 100.

CIE 0580 · Paper 1 · Feb/Mar 2024

For compound interest, the rate and the number of periods must MATCH. 0.25% per month over 5 years = 60 monthly periods (not 5). Don't silently convert to annual — apply the rate as given.

CIE 0580 · Paper 4 · Feb/Mar 2023

For compound interest equations, use TOTAL value in A = P(1 + r/100)ⁿ. If interest was $621.70 on $6000, then A = $6621.70 (principal + interest), not $621.70 alone.

CIE 0580 · Paper 4 · May/Jun 2023

When finding bounds, always give the final answer in the SAME UNITS as the variable in the question. If l is in metres, bounds must be in metres — convert at the end if your working was in cm.

CIE 0580 · Paper 1 · May/Jun 2023

To add/subtract numbers in standard form, convert to the SAME power first: 4 × 10¹⁰⁰ − 2 × 10⁹⁸ = 400 × 10⁹⁸ − 2 × 10⁹⁸ = 398 × 10⁹⁸. Then re-express in standard form.

CIE 0580 · Paper 4 · May/Jun 2022

In compound interest equations, the 'A' in A = P(1 + r/100)ⁿ is the TOTAL VALUE, not the interest. If interest is $1328.54 on $4540, then A = $5868.54 (add them). And keep 4+ sig figs when taking roots.

CIE 0580 · Paper 2 · May/Jun 2022

For speed = distance/time: LOWER bound of speed = min distance / max time. UPPER bound = max distance / min time. The division INVERTS the 'min/max' pattern for the denominator.

CIE 0580 · Paper 2 · May/Jun 2021

For 'given to 1 dp', bounds are ±0.05 (not ±0.1 and not ±0.005). So 8.2 → bounds 8.15 ≤ L < 8.25. Upper bound uses the 'less than' sign, not ≤.

CIE 0580 · Paper 1 · May/Jun 2019

'When do two repeating events next coincide?' is a classic LCM question. Find LCM of the two periods — e.g., LCM(90, 105) = 630 seconds. Don't subtract or add the periods.

CIE 0580 · Paper 2 · May/Jun 2019

When bounds are given 'to nearest centimetre' but the measurement is in metres, convert to cm first, apply ±0.5 cm, then convert back to metres. Or apply ±0.005 m directly. Mixing units is the most co

CIE 0580 · Paper 1 · May/Jun 2018

When rounded to nearest 0.5, the bounds are ±0.25 (half of 0.5). So 78.5 to nearest 0.5m gives bounds 78.25 to 78.75, NOT 78.45 to 78.55.

CIE 0580 · Paper 1 · Feb/Mar 2018

When an answer is exact (terminates), write every digit — rounding to 3 sig figs or truncating is NOT acceptable. The rounding rule only applies to non-exact answers.

CIE 0580 · Paper 2 · Feb/Mar 2024

2150 in 24-hour time is 9:50 pm, not 11:50 pm. When adding minutes that roll past 60, the hour advances — e.g., 2150 + 38 min = 2228, not 2188.

CIE 0580 · Paper 2 · Feb/Mar 2024

Product means multiplication. Negative × negative = positive, so the highest product of 2 numbers from a set may involve two negatives, not two positives.

CIE 0580 · Paper 1 · Feb/Mar 2024

Time does NOT convert as decimal: 3.6 hours is 3 hr 36 min (0.6 × 60), not 3 hr 60 min. And 3 hr 66 min is impossible — 66 min = 1 hr 6 min, so it should be 4 hr 6 min.

CIE 0580 · Paper 3 · Feb/Mar 2024

Simple interest I = PRT/100 gives ONLY the interest earned, not the total value. If $8000 grows to $12800 over 12 years, the interest is $4800 (total − principal), not $12800.

CIE 0580 · Paper 4 · Feb/Mar 2024

There are 60 minutes in an hour (never 100). When adding minutes across an hour boundary, carry 1 to the hour place. When adding across midnight, continue to the next day.

CIE 0580 · Paper 1 · May/Jun 2023

To find the original price BEFORE an 8.7% decrease, DIVIDE the current price by 0.913, don't multiply. Multiplying applies another decrease instead of reversing it.

CIE 0580 · Paper 3 · May/Jun 2023

To show a number is NOT prime, give a specific factor: 87 = 3 × 29, so 87 is not prime. Just stating 'a prime has only 2 factors' isn't enough — show the actual divisor.

CIE 0580 · Paper 3 · May/Jun 2023

For 'when do two buses next leave together', find LCM of the periods. Add that many minutes to the first common time. Listing is error-prone — LCM is safer.

CIE 0580 · Paper 2 · May/Jun 2023

'Estimate by rounding each number to 1 sf' — round FIRST, then compute with the rounded values. SHOW the rounding clearly. Rounding the exact answer at the end does NOT score.

CIE 0580 · Paper 1 · May/Jun 2023

When ordering numbers, convert them all to decimals with ENOUGH decimal places to distinguish them. And remember 7% = 0.07 (small), not 7 — don't confuse with percentages.

CIE 0580 · Paper 1 · May/Jun 2023

'Product' means multiplication, not addition. And when multiplying directed numbers, keep the signs: negative × positive = negative.

CIE 0580 · Paper 1 · Feb/Mar 2023

For minimum speed = min distance / max time. For maximum speed = max distance / min time. Mixing lower-bound distance with lower-bound time gives neither the min nor max — it's wrong.

CIE 0580 · Paper 2 · Feb/Mar 2023

Irrational numbers cannot be written as fractions — they include non-terminating, non-repeating decimals like π, √2, √5. But √16 = 4 and √256 = 16 are RATIONAL (they simplify to whole numbers).

CIE 0580 · Paper 3 · Feb/Mar 2023

Compound interest equation: A = P(1 + r/100)ⁿ. To find r: divide by P, take the nth root, subtract 1, multiply by 100. Don't forget the bracket around (1 + r/100).

CIE 0580 · Paper 2 · Feb/Mar 2022

When crossing midnight, compute: (24:00 − start) + end. So 2115 to 0433 next day = (24:00 − 21:15) + 04:33 = 2h45min + 4h33min = 7h18min. Don't simply subtract across the boundary.

CIE 0580 · Paper 2 · Feb/Mar 2022

If HCF(a,b) = 6 and LCM(a,b) = 90, then a × b = 6 × 90 = 540. Try a = 6m, b = 6n with HCF(m,n) = 1. Example: 18 × 30 = 540 (HCF 6, LCM 90).

CIE 0580 · Paper 1 · Feb/Mar 2022

'Nearest 5 mm' means bounds are ±2.5 mm (half of 5). So 15.0 cm to nearest 5 mm has bounds 14.75 cm ≤ L < 15.25 cm. Not ±0.5 cm and not ±0.05 cm.

CIE 0580 · Paper 4 · Feb/Mar 2022

Irrational = can't be written as a fraction. Examples: π, √2, √175. But √324 = 18 is rational (perfect square). For an irrational in a range, use √n where n is close to what you want but not a perfect square, or a multiple of π.

CIE 0580 · Paper 1 · May/Jun 2022

For time intervals crossing midnight: split into two parts (time to midnight + time from midnight). Adding minutes like 15+33 gives 48 but doesn't handle the carry when minutes > 60.

CIE 0580 · Paper 1 · Feb/Mar 2022

For a value 'correct to 1 dp', limits are ±0.05 (half of 0.1). So 30.7 has limits 30.65 ≤ x < 30.75, not 30.2 ≤ x ≤ 31.2.

CIE 0580 · Paper 2 · May/Jun 2022

'Power of 10' means just 10ⁿ (e.g., 10⁻⁴), not a × 10ⁿ. These are different forms. If the value is exactly 0.0001, write 10⁻⁴, not 1 × 10⁻⁴.

CIE 0580 · Paper 1 · Feb/Mar 2022

Simple interest I = PRT/100. Remember: (1) divide by 100, (2) 'value of investment' means principal + interest, not just interest. Read the question carefully.

CIE 0580 · Paper 1 · Feb/Mar 2022

A perfect cube has EVERY prime factor to a power that's a multiple of 3. To find the smallest value R that makes N × R a cube, find the prime factors of N and boost each exponent up to the next multiple of 3.

CIE 0580 · Paper 4 · May/Jun 2021

Any terminating decimal (like 31.5) is RATIONAL. To give an irrational example in a given range, use √n where n is not a perfect square — e.g., √1001 ≈ 31.6 is irrational.

CIE 0580 · Paper 1 · May/Jun 2021

For bounds, add and subtract HALF the unit of the last given digit. A length given as 567 cm has bounds 566.5 ≤ L < 567.5 — NOT 566 to 568, and NOT 566.05 to 567.95.

CIE 0580 · Paper 1 · May/Jun 2021

For 'how many days in a year are both schedules checked': find the LCM of the two periods, divide 365 by it, floor the result, and add 1 (to include day 1). LCM of 6 and 8 = 24.

CIE 0580 · Paper 3 · May/Jun 2021

Fractional and negative indices require careful application of index laws: x^(1/2) = √x, x^(−n) = 1/xⁿ. Confusing these leads to common wrong answers like 4 when evaluating 8^(2/3).

CIE 0580 · Paper 1 · Feb/Mar 2021

3 decimal places (e.g. 8.677) is NOT the same as 3 significant figures (e.g. 8.68). For d.p. count places after the decimal point; for s.f. count from the first non-zero digit.

CIE 0580 · Paper 1 · Feb/Mar 2021

For bounds involving a sum or difference of measurements: upper bound of total = upper + upper (or upper − lower for a difference). Simply adding or subtracting the rounding unit to both extremes is i

CIE 0580 · Paper 1 · Feb/Mar 2021

For a 34% decrease over 5 periods: use A × (1 − 0.34)^5 = A × (0.66)^5. Common errors: using + instead of −, using 66% (which gives (1−0.66) = 0.34), or using wrong index (1 or 6 instead of 5).

CIE 0580 · Paper 2 · Feb/Mar 2021

LCM (Lowest Common Multiple) is the smallest number both values divide into. HCF (Highest Common Factor) is the largest number that divides into both. These are frequently confused — read the question

CIE 0580 · Paper 1 · Feb/Mar 2021

For non-standard rounding intervals: 3m to nearest 20cm has bounds 2.9m and 3.1m (not 2.8 and 3.2). Also, when the final answer must be a whole number, apply the floor function — don't round to neares

CIE 0580 · Paper 2 · Feb/Mar 2021

When finding the product of numbers in standard form, give the exact unrounded answer in proper standard form (a × 10ⁿ where 1 ≤ a < 10). The word 'product' means multiply — not add or subtract.

CIE 0580 · Paper 1 · Feb/Mar 2021

Upper bound = halfway to the next unit above; lower bound = halfway below. For a value rounded to the nearest whole number, bounds are ±0.5. The bounds are not the same as rounding to a different degr

CIE 0580 · Paper 3 · Feb/Mar 2021

HCF (highest common factor) is usually SMALLER than the numbers. LCM (lowest common multiple) is usually BIGGER. Read the question — don't confuse them.

CIE 0580 · Paper 2 · May/Jun 2021

For 0.4̇7̇ (recurring 47): let x = 0.474747..., then 100x = 47.474747..., subtract: 99x = 47, so x = 47/99. Show this subtraction method — calculator answer alone may not score.

CIE 0580 · Paper 4 · May/Jun 2019

Apply upper/lower bounds to the ORIGINAL dimensions, then do calculations with the bound values. Don't compute first and then add 0.5 to the result — that gives wrong bounds.

CIE 0580 · Paper 4 · May/Jun 2019

To show no squares exist in a range, list integer squares: 7² = 49, 8² = 64. Since 49 < 50 < 60 < 64, no square lies in [50, 60]. Use integer squares, not roots of the range endpoints.

CIE 0580 · Paper 2 · May/Jun 2019

HCF = HIGHEST factor they share (smaller than both numbers). LCM = LOWEST multiple they share (bigger than both). They are different — always check you answered what was asked.

CIE 0580 · Paper 2 · May/Jun 2019

Decimal places count digits AFTER the decimal point. Significant figures count non-zero leading digits. 0.048 to 2 sf is 0.048 (or 0.048); to 2 dp it's 0.05. These are different!

CIE 0580 · Paper 2 · May/Jun 2019

For 'estimate' questions, ROUND each number to 1 sf FIRST, then compute with the rounded values. Rounding the final answer after exact calculation is not what the question wants.

CIE 0580 · Paper 1 · May/Jun 2019

−3 − 11 = −14, not 8. When subtracting from a negative, move further negative. A common error is treating −3 − 11 as 11 − 3 = 8.

CIE 0580 · Paper 1 · Feb/Mar 2019

Always work in the same unit as the variable. If w is in metres and the accuracy is 10 cm = 0.1 m, the bounds are ±0.05 m. So 4.2 m → bounds 4.15 m to 4.25 m, NOT 415 to 425.

CIE 0580 · Paper 1 · Feb/Mar 2019

Never add fractions by adding numerators and denominators separately. 5/6 + 2/3 needs a common denominator: 5/6 + 4/6 = 9/6 = 3/2.

CIE 0580 · Paper 1 · May/Jun 2019

Don't round calculator values mid-calculation. Keep full precision until the final answer, then round as required.

CIE 0580 · Paper 1 · Feb/Mar 2018

Always check if your answer makes sense in context. If the answer is a number of days or cakes, it should be a small whole number — not a decimal or huge value.

CIE 0580 · Paper 1 · Feb/Mar 2018

LCM (Lowest Common Multiple) is the smallest number in BOTH times tables. HCF (Highest Common Factor) is the largest number that divides BOTH. These are different — don't confuse them.

CIE 0580 · Paper 1 · Feb/Mar 2018

LCM and HCF are frequently confused. To find the LCM, break each number into prime factors and take the highest power of each prime. For 18 and 21: LCM = 2 × 3² × 7 = 126, not the HCF of 3.

CIE 0580 · Paper 1 · May/Jun 2018

For maximum of a quotient (distance ÷ speed): use upper bound of numerator and lower bound of denominator. For minimum: use lower bound of numerator and upper bound of denominator. Using the same boun

CIE 0580 · Paper 4 · May/Jun 2018

Compound interest: A = P(1 + r/100)ⁿ. Common formula errors: adding P separately, using the rate as a percentage inside the bracket, or multiplying by n instead of using it as a power. Year-by-year ca

CIE 0580 · Paper 2 · May/Jun 2018

For a measurement of 6.2 correct to 1 d.p., the bounds are 6.15 and 6.25 (±0.05), NOT 6.2 ± 0.5. The bound is always ± half of the smallest unit of measurement. For 1 d.p., the unit is 0.1, so half is

CIE 0580 · Paper 3 · May/Jun 2018

For compound decrease use P×(1−r)^n. Don't use the growth formula then subtract, and don't apply simple (non-compound) decrease.

CIE 0580 · Paper 2 · Feb/Mar 2018

An irrational number cannot be written as a fraction — its decimal never ends or repeats. Between 6 and 7, examples include √37, √38, √39, √40, √41, √42, √43, √44, √45, √46, √47.

CIE 0580 · Paper 3 · Feb/Mar 2018

For maximum number of items, use maximum fabric length (602.5, not 605) divided by minimum dress length (8.5, not 9.5). Think: to fit the most, use the biggest fabric and smallest dress.

CIE 0580 · Paper 4 · Feb/Mar 2018

Convert all fractions, percentages and decimals to decimals before ordering. Don't guess which is smallest — calculate it.

CIE 0580 · Paper 1 · Feb/Mar 2018

Always check if your answer makes sense in context. If the answer is a number of days or cakes, it should be a small whole number — not a decimal or huge value.

CIE 0580 · Paper 1 · Feb/Mar 2018

Don't round calculator values mid-calculation. Keep full precision until the final answer, then round as required.

CIE 0580 · Paper 1 · Feb/Mar 2018

1 litre = 1000 cm³. This conversion factor must be memorised. To convert cm³ to litres, divide by 1000. Many students leave this type of question blank rather than attempt it.

CIE 0580 · Paper 1 · May/Jun 2018

When asked to write a fraction as a percentage, always include the % sign and at least 3 figures — '22' alone does not score, you must write '22.2%' or similar.

CIE 0580 · Paper 1 · Feb/Mar 2024

If the question asks for standard form, a whole number answer like 8400 is not complete — you must write 8.4 × 10³.

CIE 0580 · Paper 1 · Feb/Mar 2024

When subtracting fractions without a calculator, show the common denominator step. If the question asks for a fraction, a decimal answer (even the correct value) will not score.

CIE 0580 · Paper 1 · Feb/Mar 2024

For compound growth, when iterating years, keep at least 4-5 significant figures at each step. Rounding 30/26 = 1.15 instead of 1.154 can push the answer from 9 years down to 8 years.

CIE 0580 · Paper 4 · Feb/Mar 2024

Standard form is a × 10ⁿ where 1 ≤ a < 10. So 0.09 = 9 × 10⁻², not 0.09 or 0.9 × 10⁻¹. The coefficient must always start with a non-zero digit before the decimal point.

CIE 0580 · Paper 2 · Feb/Mar 2023

If the question asks for TOTAL value after n years, leave the compound interest formula answer as is. Subtracting the principal gives you only the interest earned — a different quantity.

CIE 0580 · Paper 1 · Feb/Mar 2023

91 is NOT a prime number — it equals 7 × 13. Other tricky composites: 51 = 3 × 17, 57 = 3 × 19, 87 = 3 × 29. Always check divisibility by 2, 3, 5, 7, 11, 13 for numbers under 200.

CIE 0580 · Paper 1 · Feb/Mar 2023

Working in 24-hour time avoids ambiguity. If you use 12-hour time, you MUST write 'am' or 'pm' — otherwise 2:15 could mean morning or afternoon and will lose the mark.

CIE 0580 · Paper 1 · Feb/Mar 2023

Divisibility by 3: if the digits sum to a multiple of 3, the number is divisible by 3. So 27 (2+7=9), 57 (5+7=12), 93 (9+3=12) are all divisible by 3 and NOT prime.

CIE 0580 · Paper 2 · May/Jun 2023

For compound interest, use the formula A = P(1 + r/100)ⁿ. Year-by-year calculations accumulate rounding errors. And round the final answer to the requested unit (e.g., nearest dollar).

CIE 0580 · Paper 3 · May/Jun 2023

For 'nearest 10', bounds are ±5 (half of 10). So 350 to nearest 10 → 345 ≤ x < 355. Not ±10 and not ±0.5.

CIE 0580 · Paper 2 · May/Jun 2023

If the question asks for standard form, you MUST convert. 15625 becomes 1.5625 × 10⁴. Keep all 5 figures, and ensure only ONE digit sits before the decimal point.

CIE 0580 · Paper 1 · May/Jun 2023

Simplest form means divide by the HIGHEST common factor in one step. Cancelling by a small factor and stopping doesn't give the simplest form — check your answer shares no common factor > 1.

CIE 0580 · Paper 1 · May/Jun 2023

Factors of N divide INTO N with no remainder (so they're ≤ N). Multiples are N × 1, N × 2, N × 3... (so they're ≥ N). 1 and N itself are always factors.

CIE 0580 · Paper 1 · Feb/Mar 2022

For significant figures, trailing zeros can be ambiguous. To 1 sf: 0.0483 → 0.05 (not 0.050). To 1 sf: 1.98 → 2 (not 2.0). Don't add zeros after rounding.

CIE 0580 · Paper 2 · May/Jun 2022

To convert seconds to hours, divide by 3600 (= 60 × 60). Dividing by 60 only gives you minutes, not hours. And never multiply — that gives a bigger unit from a smaller one.

CIE 0580 · Paper 1 · Feb/Mar 2022

x^(1/3) means CUBE ROOT of x, not x ÷ 3. On most calculators, use the ∛ button or type x ^ (1/3). Don't confuse the fractional exponent with division.

CIE 0580 · Paper 2 · May/Jun 2022

'Sixteen thousand and thirty-seven' = 16,037 (not 16,000,037). Join the thousands and the tens, not concatenate them as separate numbers.

CIE 0580 · Paper 1 · Feb/Mar 2022

When checking rounding, read carefully what unit is specified. Many students defaulted to nearest 1000, or confirmed the given rounding rather than finding an alternative to the nearest 100.

CIE 0580 · Paper 1 · Feb/Mar 2021

Small numbers (< 1) have NEGATIVE exponents in standard form: 0.00654 = 6.54 × 10⁻³. Large numbers have positive exponents. Count the decimal places carefully and get the sign right.

CIE 0580 · Paper 2 · May/Jun 2021

Follow BODMAS/BIDMAS: Brackets, Orders (powers), Division/Multiplication (left to right), Addition/Subtraction (left to right). Never evaluate left-to-right when a × or ÷ comes later.

CIE 0580 · Paper 2 · May/Jun 2021

Compound interest formula: A = P(1 + r/100)ⁿ. The bracket is (1 + 0.056), not just 0.056. And 'total value' ≠ 'interest' — the interest is A − P.

CIE 0580 · Paper 1 · May/Jun 2021

In the repeated division method for HCF, only divide by a prime factor if BOTH numbers are divisible by it. Dividing when only one is divisible corrupts the result. Factor trees are a safer alternativ

CIE 0580 · Paper 2 · Feb/Mar 2021

Identify which digits recur: 0.37̄ (only 7 repeats) = 34/90; 0.3̄7̄ (both 3 and 7 repeat) = 37/99. Place only the recurring digits over the appropriate number of 9s, subtract correctly for non-recurri

CIE 0580 · Paper 2 · Feb/Mar 2021

In estimation, round each value to 1 significant figure before calculating, not 1 d.p. or to nearest whole number. Also, never change the operation — subtraction in the denominator stays as subtractio

CIE 0580 · Paper 2 · Feb/Mar 2021

On 'show all your working' fraction questions: (1) convert mixed numbers to improper fractions, (2) use common denominators, (3) simplify the final fraction. Any answer not fully simplified loses marks.

CIE 0580 · Paper 1 · May/Jun 2021

1 m = 100 cm, so to convert metres TO centimetres, MULTIPLY by 100 (not divide, and not add zeros arbitrarily). 4.365 m = 436.5 cm.

CIE 0580 · Paper 2 · May/Jun 2019

For max/min products, apply bounds to EACH quantity first, then multiply. Max of 17.5 × 50.5 = 882.75 (not 17×50+0.5). The upper bound of each must be the one that maximises the product.

CIE 0580 · Paper 4 · Feb/Mar 2019

To divide fractions: convert mixed numbers to improper fractions, then flip the second fraction and multiply. The final answer must be a simplified mixed number — don't leave as an improper fraction.

CIE 0580 · Paper 1 · Feb/Mar 2019

For estimation questions, show the rounded values BEFORE the calculation: write '30 × 70 = 2100'. Rounding the answer after calculating is not estimation. Both numbers must be shown rounded.

CIE 0580 · Paper 4 · Feb/Mar 2019

Standard form a × 10ⁿ requires exactly ONE non-zero digit before the decimal point. So 640000 = 6.4 × 10⁵, not 64 × 10⁴ or 0.64 × 10⁶.

CIE 0580 · Paper 1 · May/Jun 2019

Estimation means round to 1 significant figure: 104.3 → 100, 8.72 → 9, 7.1 → 7. Then calculate with the rounded values. Never use exact values for estimation questions.

CIE 0580 · Paper 1 · Feb/Mar 2019

15 mm = 1.5 cm (divide by 10), NOT 150 cm. For volume: 1 cm³ = 1000 mm³, so divide mm³ by 1000 to get cm³. Track units carefully at every step in multi-unit problems.

CIE 0580 · Paper 4 · Feb/Mar 2019

Standard form requires exactly one non-zero digit before the decimal: 2,760,000 = 2.76 × 10⁶. Exact values must not be rounded — 2.7 × 10⁶ would lose the mark.

CIE 0580 · Paper 1 · Feb/Mar 2019

Significant figures always start at the first non-zero digit. To round 0.04762 to 2 s.f.: the first two sig figs are 4 and 7, and because the next digit is 6, round up to 0.047.

CIE 0580 · Paper 1 · Feb/Mar 2019

Speed = distance ÷ time. Time must be in HOURS for km/h. 10 minutes = 10/60 hours = 0.167 hours. Don't multiply distance by time or omit the unit conversion.

CIE 0580 · Paper 3 · Feb/Mar 2019

To find a fraction between 7/9 and 8/9: convert to equivalent fractions with larger denominators (14/18 and 16/18), then 15/18 fits between them. You cannot write 7.5/9 — fractions need whole number n

CIE 0580 · Paper 3 · Feb/Mar 2019

If the question asks for a mixed number, convert improper fractions (e.g., 7/4 → 1¾). Cancel before multiplying to keep numbers small. And always simplify the final fraction.

CIE 0580 · Paper 2 · May/Jun 2019

306 seconds ÷ 60 = 5.1 minutes = 5 minutes 6 seconds, NOT 5 minutes 10 seconds. The decimal 0.1 minutes = 0.1 × 60 = 6 seconds. Always multiply the decimal part by 60 to get seconds.

CIE 0580 · Paper 3 · Feb/Mar 2019

1 hour 43 minutes = 1 + 43/60 = 1.7167 hours, NOT 1.43 or 1.72. There are 60 minutes in one hour, not 100. Keep the full decimal — don't approximate 43/60.

CIE 0580 · Paper 4 · Feb/Mar 2019

Give answers to 3 significant figures unless told otherwise. Never round intermediate values — only round the final answer.

CIE 0580 · Paper 2 · Feb/Mar 2018

The compound interest formula P(1+r)^n gives the TOTAL amount, not just the interest. Only subtract the principal if the question asks for the interest earned.

CIE 0580 · Paper 1 · Feb/Mar 2018

When asked to write all digits on your calculator display, give at least 7 figures. Use brackets to ensure cube roots apply to the whole expression.

CIE 0580 · Paper 1 · Feb/Mar 2018

Estimation questions require rounding each number to 1 significant figure before calculating. Round 19.3 to 20 (not 19), 8.6 to 9 (not 8.6), 32.1 to 30 (not 32). The rounded calculation should be easy

CIE 0580 · Paper 4 · May/Jun 2018

Estimation questions require rounding each number to 1 significant figure before calculating. Round 19.3 to 20 (not 19), 8.6 to 9 (not 8.6), 32.1 to 30 (not 32). The rounded calculation should be easy

CIE 0580 · Paper 4 · May/Jun 2018

When a question asks for an exact answer, give a fraction (e.g. 4/7), NOT a rounded decimal (0.571...). A decimal that has been rounded or truncated is NOT exact.

CIE 0580 · Paper 2 · May/Jun 2018

To solve index equations like 3ˣ = 27 × 81, convert all terms to the same base: 3ˣ = 3³ × 3⁴ = 3⁷. Then x = 7 (or −7 if the equation has a negative exponent). Multiplying the numbers first (2187) make

CIE 0580 · Paper 2 · May/Jun 2018

1 litre = 1000 cm³. To convert cm³ to litres, divide by 1000 (not 100, not 10). This conversion must be memorised as it appears frequently.

CIE 0580 · Paper 2 · May/Jun 2018

Give answers to 3 significant figures unless told otherwise. Never round intermediate values — only round the final answer.

CIE 0580 · Paper 2 · Feb/Mar 2018

To multiply fractions: multiply numerators, multiply denominators. Do NOT invert any fraction (that's for division). Do NOT cross-multiply (that's for solving equations). Always simplify the final ans

CIE 0580 · Paper 1 · May/Jun 2018

When converting standard form to ordinary numbers with negative powers, count the decimal places carefully. 2.68 × 10⁻³ = 0.00268 — move the decimal point 3 places left, not right.

CIE 0580 · Paper 1 · May/Jun 2018

6.2 hours = 6 hours and 0.2×60 = 12 minutes, not 20 minutes. Multiply the decimal part by 60 to get minutes. Don't read 0.2 as '20 minutes'.

CIE 0580 · Paper 4 · Feb/Mar 2018

For train-crossing-bridge problems: (1) Total distance = train length + bridge length, (2) Convert all units to be consistent (all metres + seconds, or all km + hours) BEFORE calculating.

CIE 0580 · Paper 2 · Feb/Mar 2024

If 5/13 are sold, then 8/13 remain. Set the remainder (96) equal to the remaining fraction (8/13 of total), not the sold fraction. A decimal answer in a whole-number context should alert you to an err

CIE 0580 · Paper 1 · Feb/Mar 2021

Percentage profit = (profit / COST PRICE) × 100 — divide by COST, not selling price. Profit = selling − cost. This is the most-missed type of percentage question.

CIE 0580 · Paper 3 · May/Jun 2021

When a map scale is 1:25,000, that's a LENGTH ratio. For areas, you must use 25000² for the scale factor. Missing the squaring is the #1 map-scale mistake.

CIE 0580 · Paper 4 · May/Jun 2019

When working with exchange rates, keep full calculator precision until the final answer, then sanity-check: does the final amount look sensible compared to the starting amount?

CIE 0580 · Paper 1 · Feb/Mar 2024

Reverse percentage: if $1.15 is AFTER an 8% increase, divide by 1.08 to get the original (not multiply). Multiplying gives a further 8% increase instead of reversing it.

CIE 0580 · Paper 4 · Feb/Mar 2024

For 1 cm : 250,000 scale, 3.5 cm = 875,000 cm = 8,750 m = 8.75 km. Convert step by step: ÷ 100 to get m, ÷ 1000 to get km. Check: 1 cm should correspond to 2.5 km, so 3.5 cm ≈ 8.75 km — sanity check with scale.

CIE 0580 · Paper 2 · May/Jun 2023

For a map scale like 1:125,000, convert step-by-step: cm → m (÷ 100) → km (÷ 1000). Or simplify the scale first to '1 cm : 1.25 km' so one multiplication gives the real distance.

CIE 0580 · Paper 4 · May/Jun 2023

Two increases of 3% and 5% do NOT combine to 8%. Multiply the multipliers: 1.03 × 1.05 = 1.0815, an overall increase of 8.15%. Adding percentages ignores the compounding.

CIE 0580 · Paper 4 · Feb/Mar 2023

Average speed = TOTAL distance / TOTAL time. NOT the average of the segment speeds. Include ALL time (including stops) unless the question says 'average moving speed'.

CIE 0580 · Paper 4 · May/Jun 2022

To convert km/h to m/s: multiply by 1000 (km to m), divide by 3600 (hours to seconds). Shortcut: divide by 3.6. Example: 108 km/h ÷ 3.6 = 30 m/s.

CIE 0580 · Paper 4 · May/Jun 2022

A 15% increase followed by an 18% increase is NOT 33% overall. It's 1.15 × 1.18 − 1 = 0.357 = 35.7%. Multiply the multipliers, then subtract 1 for the percentage.

CIE 0580 · Paper 4 · Feb/Mar 2022

If a price has been INCREASED by a factor, get the original by DIVIDING. Multiplying by 1.142 again just adds another 14.2% increase, not reverses it.

CIE 0580 · Paper 4 · May/Jun 2021

Reverse percentage: if a price of $98.90 already includes 15% tax, the original = $98.90 ÷ 1.15 = $86. Finding 15% of $98.90 and subtracting is wrong because the tax was calculated on the original pri

CIE 0580 · Paper 4 · Feb/Mar 2021

Percentage profit = (profit ÷ cost price) × 100. If cost price = 41 and selling price = 65, profit = 24, so % profit = (24 ÷ 41) × 100. Never divide by the selling price.

CIE 0580 · Paper 3 · Feb/Mar 2021

Speed/distance/time: ensure units match. If speed is in m/s, distance must be in m and time comes out in seconds. 10 km = 10,000 m, not 10. Then convert seconds to min/sec if asked.

CIE 0580 · Paper 1 · May/Jun 2019

% increase = (increase ÷ ORIGINAL) × 100. If price went from 63 to 77, increase = 14, so % increase = 14/63 × 100 = 22.2%. Never divide by the new value (77).

CIE 0580 · Paper 1 · Feb/Mar 2019

To combine two ratios A:B = 7:10 and B:C = 4:3 into A:B:C, find a common value for B. LCM of 10 and 4 is 20, so A:B = 14:20 and B:C = 20:15, giving A:B:C = 14:20:15. The common term must be the same n

CIE 0580 · Paper 4 · May/Jun 2018

When a question says 'two-thirds of 600', use the original 600 — not the amount left after removing 18%. Apply each fraction/percentage to the quantity stated in the question.

CIE 0580 · Paper 2 · Feb/Mar 2018

If 3/7 of the total = 1248, then total = 1248 ÷ 3/7 = 1248 × 7/3 = 2912. Do NOT multiply 1248 by 3/7 (that gives 3/7 of 1248, which is a fraction of a fraction). Understand the difference between 'fra

CIE 0580 · Paper 4 · May/Jun 2018

In proportion questions, read the relationship precisely: 'y is proportional to (x−1)²' means y = k(x−1)², NOT y = kx², y = k/x², or y = k(x−1). Getting the initial relationship wrong invalidates all

CIE 0580 · Paper 2 · May/Jun 2018

Distance from a speed-time graph = area under the graph, NOT distance ÷ time. For a trapezium-shaped graph, use the trapezium area formula. Using d/t only works for constant speed.

CIE 0580 · Paper 2 · May/Jun 2018

Percentage increase = (increase ÷ original value) × 100. The denominator must be the ORIGINAL value, not the new value. Also, dividing the increase by 100 is not the same as finding a percentage — you

CIE 0580 · Paper 4 · May/Jun 2018

To write a map scale as 1:n, convert both distances to the same unit (cm). So 1 cm on map = 15 km = 1,500,000 cm, giving scale 1:1500000.

CIE 0580 · Paper 3 · Feb/Mar 2018

Read the question carefully — if it says two-thirds of 600, use 600, not the amount remaining after the percentage was removed. Each operation applies to the original amount unless stated otherwise.

CIE 0580 · Paper 1 · Feb/Mar 2018

Always simplify a ratio by dividing all parts by their HCF. 30:25:10 has common factor 5, so simplify to 6:5:2. 'Simplest form' means no common factor bigger than 1.

CIE 0580 · Paper 3 · Feb/Mar 2023

Use the FULL figures given. Don't round to 2 sf before starting — rounding-then-calculating loses accuracy. And for reverse percentage questions, DIVIDE by the multiplier, don't multiply.

CIE 0580 · Paper 1 · May/Jun 2022

For exchange rates, check which direction you're converting. If you get an exact decimal like 0.893, don't round it — write all the figures.

CIE 0580 · Paper 1 · May/Jun 2021

When T = D ÷ S gives a decimal in hours, convert carefully: 2.133… hours = 2 hours + 0.133… × 60 minutes = 2 hours 8 minutes. Do not read the decimal digits directly as minutes (e.g. 2.13 ≠ 2h 13min).

CIE 0580 · Paper 3 · Feb/Mar 2021

Never convert a fraction to a rounded percentage mid-calculation. Keep exact fractions or decimals with full precision throughout, and only round the final answer.

CIE 0580 · Paper 2 · Feb/Mar 2021

Inverse proportion means as one quantity increases, the other decreases proportionally. The precise terms accepted are 'inversely proportional' or 'indirect proportion' — vague terms like 'opposite' d

CIE 0580 · Paper 2 · Feb/Mar 2021

% increase = (increase/ORIGINAL) × 100 = 14/63 × 100 = 22.2%. Dividing by 77 (new value) gives a wrong answer. 122.2% means you divided the new value by the original — that's wrong.

CIE 0580 · Paper 2 · Feb/Mar 2019

When finding a proportionality equation: (1) write d = kt², (2) substitute known values to find k, (3) substitute k back to get the specific equation, e.g. d = 4.9t². Leaving the answer as d = kt² (wi

CIE 0580 · Paper 4 · May/Jun 2018

When converting minutes to hours for speed calculations, keep the exact fraction (50/60 = 5/6) rather than rounding to 0.83. The rounded decimal introduces enough error to give the wrong final answer.

CIE 0580 · Paper 4 · May/Jun 2018

Perpendicular bisector of AB requires TWO things: (1) the midpoint of AB (not A or B), (2) the negative reciprocal of the gradient of AB (flip and change sign — not 1 − gradient).

CIE 0580 · Paper 2 · Feb/Mar 2024

'Show that' requires explicit reasoning — you must show the perpendicular gradient is found by taking the negative reciprocal of the original (e.g., if m₁ = −1/2, then m₂ = 2). State this step.

CIE 0580 · Paper 4 · Feb/Mar 2023

If the question says the line passes through the origin, then c = 0 in y = mx + c. The equation is just y = mx — don't reuse an unrelated intercept from a previous part.

CIE 0580 · Paper 2 · Feb/Mar 2022

When finding gradient from a graph, use the SCALE on each axis, not the number of squares. If each y-square is 2 units but each x-square is 1 unit, gradient is doubled vs counting squares.

CIE 0580 · Paper 3 · May/Jun 2022

When the question says 'draw a suitable line to solve [equation]', you MUST (1) rearrange the equation to match one side = the existing curve, (2) draw the line, (3) read intersections. Using the quadratic formula ignores the method and scores partial.

CIE 0580 · Paper 4 · May/Jun 2021

After using Pythagoras to find the components (a = b = 2), use the direction of the vector and the starting point to find the endpoint coordinates. A clear diagram showing the vector components is ess

CIE 0580 · Paper 4 · Feb/Mar 2021

Gradient of perpendicular (normal) = −1 / (original gradient). Flip it AND change the sign. If the line has gradient −3/4, the perpendicular has gradient +4/3.

CIE 0580 · Paper 2 · May/Jun 2021

When subtracting a vector expression, bracket the whole thing and distribute the minus: OA − BA = (2x+3y) − (x−4y) = 2x+3y−x+4y = x+7y. Don't drop brackets and get −4y instead of +4y.

CIE 0580 · Paper 2 · Feb/Mar 2019

Gradient = rise/run = (y₂ − y₁)/(x₂ − x₁). Drawing a right-angled triangle on the graph and counting squares is often easier than the formula, especially with negative coordinates.

CIE 0580 · Paper 1 · May/Jun 2019

Distance on a speed-time graph = area under the curve. If the speed isn't constant, split into rectangles and triangles. Don't just use (max speed × total time) — that's the area of a rectangle only.

CIE 0580 · Paper 4 · May/Jun 2019

In y = mx + c, the gradient is m (the coefficient of x). For y = 5x + 12, the gradient is 5. Do not add the numbers together, divide them, or give '5x' — the gradient is a single number.

CIE 0580 · Paper 3 · May/Jun 2018

For perpendicular lines, the gradient of the perpendicular = −1/m (the negative reciprocal), NOT −m or 1/m. If the original gradient is 3, the perpendicular gradient is −1/3. Using just −3 or +1/3 is

CIE 0580 · Paper 2 · May/Jun 2018

To reverse a vector, negate it: BA = −AB. Break the path into known vectors and add/subtract carefully. Don't guess that a reversed vector equals p or q.

CIE 0580 · Paper 2 · Feb/Mar 2018

'Intersect' means where two lines cross (could be anywhere). 'Intercept' means where a line crosses an axis (at x=0 or y=0). These are different questions.

CIE 0580 · Paper 2 · Feb/Mar 2024

On a speed-time graph, the distance travelled equals the AREA under the curve — not time × maximum speed. Split into rectangles and triangles if the shape is complex.

CIE 0580 · Paper 2 · Feb/Mar 2024

For y = mx + c, if a graph is given, READ the y-intercept c directly from where the line crosses the y-axis — don't calculate it. Only calculate c if no graph is provided.

CIE 0580 · Paper 3 · Feb/Mar 2023

Gradient = (y₂ − y₁) / (x₂ − x₁). Watch for double negatives: −2 − (−6) = −2 + 6 = 4. Sanity-check against the diagram: if the line slopes down, the gradient must be negative.

CIE 0580 · Paper 2 · Feb/Mar 2022

Don't write '+ −1' — simplify to '− 1'. Final answers should have their signs properly resolved: y = 1.5x − 1, not y = 1.5x + −1.

CIE 0580 · Paper 1 · May/Jun 2019

When subtracting vectors, write out each component separately. Subtracting a negative: (3) − (−2) = 3 + 2 = 5. Setting out working clearly reduces sign errors.

CIE 0580 · Paper 1 · Feb/Mar 2019

Read carefully which point the perpendicular line must pass through. If asked for perpendicular through A, substitute point A's coordinates — not the midpoint — to find c in y = mx + c.

CIE 0580 · Paper 2 · Feb/Mar 2019

Perpendicular gradients multiply to −1. If gradient = 2, perpendicular gradient = −1/2 (flip and negate). Don't just negate (−2) or just flip (1/2).

CIE 0580 · Paper 4 · Feb/Mar 2018

Distance formula: √((x₂−x₁)²+(y₂−y₁)²). Bracket the whole subtraction before squaring: (4−(−2))²=36, not 4−(−2)²=4−4=0.

CIE 0580 · Paper 4 · Feb/Mar 2018

When squaring a negative component of a vector, always use brackets: (−1)²=1, not −1²= −1. Missing brackets on negative numbers is a very common error.

CIE 0580 · Paper 4 · Feb/Mar 2018

In probability without replacement, the denominator DECREASES by 1 for each subsequent pick (13 → 12 → 11...). Getting 104/169 instead of the correct answer usually means you forgot this.

CIE 0580 · Paper 2 · Feb/Mar 2024

For 'exactly one green button' out of two picks, there are TWO orderings: green-then-not OR not-then-green. Calculate one product and DOUBLE it (or add both products).

CIE 0580 · Paper 4 · May/Jun 2023

In a histogram, bar HEIGHT = frequency density (frequency ÷ class width). Find the scale using a bar whose frequency AND width you know, then apply it to the others.

CIE 0580 · Paper 4 · Feb/Mar 2022

For 'picked from those wearing trainers', the denominator is the number wearing trainers (21), not the total (50). Read carefully — conditional probability restricts the sample space.

CIE 0580 · Paper 4 · Feb/Mar 2022

In a stem-and-leaf diagram, the full value is stem + leaf, not just the leaf. A leaf of '5' under a stem of '2' means 25, not 5. Apply this for median, mode, and range.

CIE 0580 · Paper 1 · May/Jun 2021

When there is an even number of values, the median is the average of the two middle values — it may not appear in the original list.

CIE 0580 · Paper 1 · Feb/Mar 2024

Estimated mean from grouped data: (sum of midpoint × frequency) / (total frequency). Sanity check: the mean must lie between the lowest and highest possible values.

CIE 0580 · Paper 2 · Feb/Mar 2024

Median from a frequency table: find the (n+1)/2 th VALUE using cumulative frequency. Don't use the raw column of marks and don't average the listed marks ignoring frequencies.

CIE 0580 · Paper 4 · Feb/Mar 2024

Frequency density = frequency ÷ class width (NOT class width ÷ frequency). The y-axis of a histogram shows frequency density, not frequency, for unequal class widths.

CIE 0580 · Paper 4 · Feb/Mar 2024

Median = middle value when the data is ordered. Mean = sum ÷ count. These are DIFFERENT — confusing them loses a whole question's worth of marks.

CIE 0580 · Paper 1 · Feb/Mar 2023

Mean from frequency table = (sum of fx) ÷ (total frequency), NOT ÷ number of groups. Sanity check: the mean must lie within the range of the actual data values.

CIE 0580 · Paper 1 · Feb/Mar 2023

For P(two students both satisfy X) without replacement, multiply (46/100) × (45/99) — numerator AND denominator both decrease by 1. Don't stop at just the first probability.

CIE 0580 · Paper 4 · Feb/Mar 2023

For median of n values from a frequency table, find the (n+1)/2 th position. If n = 80, that's the 40.5th value — average the 40th and 41st. Use the CUMULATIVE frequency column to locate which group it's in.

CIE 0580 · Paper 3 · Feb/Mar 2022

For P(A or B) where A and B are mutually exclusive, ADD the probabilities (3/n + 5/n = 8/n). Multiplication is for 'and' with independent events.

CIE 0580 · Paper 4 · May/Jun 2022

When drawing items without replacement, identical outcomes (like RRR) have only 1 arrangement, but mixed outcomes (like RRG) can occur in multiple orders. List all arrangements systematically before m

CIE 0580 · Paper 4 · Feb/Mar 2021

Comparing two distributions requires both a comparison ('the median increased from X to Y') AND an interpretation ('suggesting students scored higher on average in Test 2'). Describing that statistics

CIE 0580 · Paper 4 · Feb/Mar 2021

For qualitative (non-numerical categorical) data, only the mode is meaningful — not mean or median. The mode is the category appearing most frequently.

CIE 0580 · Paper 3 · Feb/Mar 2021

To compare likelihood between two bags, you must compare the PROBABILITIES (fractions), not the raw counts. More black marbles doesn't mean higher probability if the bag also has more total marbles.

CIE 0580 · Paper 3 · May/Jun 2021

When given a mean and count, always start by finding the total (mean × count = 9 × 17 = 153). Then use the total and additional constraints together — not separately — to find the missing values.

CIE 0580 · Paper 1 · Feb/Mar 2021

'Without replacement' means after picking once, the pool shrinks by 1. So P(event1) × P(event2 | event1 happened), with a smaller denominator for the second pick.

CIE 0580 · Paper 4 · May/Jun 2019

Mode = the value with the highest frequency, NOT the frequency itself. Mean from a frequency table = Σ(value × frequency) ÷ Σ(frequency). Do NOT add the values row or divide by the number of categorie

CIE 0580 · Paper 1 · May/Jun 2018

For 'at least one' probability problems without replacement: (1) denominators decrease each draw (15, then 14); (2) consider ALL valid combinations; (3) the most efficient method is often 1 − P(none),

CIE 0580 · Paper 2 · May/Jun 2018

In a grouped frequency table, the frequency for a group is not found by subtracting the group boundaries. Read the frequency column directly for each class interval.

CIE 0580 · Paper 3 · Feb/Mar 2018

Always read the question carefully — words like 'not' in bold mean you need the complement (1 − P). Missing this wastes an easy mark.

CIE 0580 · Paper 1 · Feb/Mar 2024

A line of best fit follows the shape of the data points — it does NOT need to pass through the origin. Draw so there's roughly equal data above and below the line.

CIE 0580 · Paper 3 · May/Jun 2023

Range = (largest VALUE in the data) − (smallest VALUE). Don't use the largest/smallest frequency, and don't use the number of groups — use the actual data values.

CIE 0580 · Paper 3 · Feb/Mar 2023

Check whether the problem says 'with replacement' or 'without replacement'. With replacement: probabilities on branches 2 match branches 1. Without replacement: denominators decrease.

CIE 0580 · Paper 4 · Feb/Mar 2022

For nth term n² + 12: first 3 terms are 1²+12 = 13, 2²+12 = 16, 3²+12 = 21. Substitute n = 1, 2, 3 and EVALUATE fully. Don't confuse n² with 2n.

CIE 0580 · Paper 2 · May/Jun 2022

For estimated mean from grouped data: use midpoints of each class interval (not class widths), calculate Σfx, then divide by Σf (total frequency, not number of classes). E.g. midpoint of 20 < x ≤ 30 i

CIE 0580 · Paper 4 · Feb/Mar 2021

The mean and median cannot be found for qualitative data because the categories are not numbers. The key explanation is: 'the data is qualitative (not numerical)', not 'there are only 3 values' or 'it

CIE 0580 · Paper 3 · Feb/Mar 2021

Range = largest value − smallest value. Do not confuse range with mean. Also check the required units — if the question asks for cm, give your answer in cm.

CIE 0580 · Paper 1 · Feb/Mar 2021

Multi-step questions: find what's asked at each stage. If asked for range but must first find a missing value: (1) total = mean × n, (2) missing value = total − known values, (3) range = max − min.

CIE 0580 · Paper 1 · Feb/Mar 2019

P(one red, one blue) = P(R then B) + P(B then R). Many only calculate one order. Add both orders. Also: without replacement means the denominator decreases by 1 for the second pick.

CIE 0580 · Paper 4 · Feb/Mar 2019

For P(one of each colour) without replacement, find P(A then B) and add P(B then A) — you must double or list all orders. Don't use 3-term products when only 2 picks are made.

CIE 0580 · Paper 2 · Feb/Mar 2018

Circle theorem reasons must be exact: 'opposite ANGLES of a cyclic quadrilateral add to 180°' (not 'sides'). Use the precise syllabus vocabulary — 'linear pair' is NOT the CIE phrase.

CIE 0580 · Paper 4 · Feb/Mar 2024

For similar shapes: area scale factor = (linear scale factor)², volume scale factor = (linear)³. If lengths are doubled, areas are × 4 and volumes are × 8 — not × 2.

CIE 0580 · Paper 4 · Feb/Mar 2024

At each vertex of a polygon, interior angle + exterior angle = 180° (they form a straight line). It's the SUM of all exterior angles that equals 360°, not one pair.

CIE 0580 · Paper 2 · Feb/Mar 2023

Official angle reasons: 'alternate angles' (Z-shape), 'corresponding angles' (F-shape), 'co-interior angles add to 180°' (C-shape). Learn the CORRECT VOCABULARY — 'Z angles' and 'parallel angles' are NOT accepted.

CIE 0580 · Paper 1 · May/Jun 2023

For similar solids: length ratio k, area ratio k², volume ratio k³. If you treat a volume ratio as a length ratio, you'll be off by a cube root. To go from volume ratio to length, take ∛.

CIE 0580 · Paper 2 · Feb/Mar 2023

Reverse bearing = original bearing ± 180°. If A→B is 59°, then B→A is 59° + 180° = 239°. Not 360° − 59°, not 180° − 59°.

CIE 0580 · Paper 2 · May/Jun 2022

For similar solids: if the linear scale factor is k, the VOLUME scale factor is k³ (not k or k²). To find the new volume, multiply old volume by k³.

CIE 0580 · Paper 4 · May/Jun 2022

Angle at centre = 2 × angle at circumference (subtended by the same arc). If AOB = 76° at the centre, then ACB = 38° at the circumference. This is a key circle theorem.

CIE 0580 · Paper 4 · Feb/Mar 2022

To go from AREA ratio to LENGTH ratio, take the square root. If area ratio is 9:4, length ratio is 3:2. Don't use the area ratio directly for lengths.

CIE 0580 · Paper 4 · Feb/Mar 2022

Hemisphere volume = (1/2) × (4/3)πr³ = (2/3)πr³. Halve the VOLUME formula, not the radius. To solve for r, take the cube root (it's r³, not r²).

CIE 0580 · Paper 4 · May/Jun 2022

A map scale like 1:50,000 is a LINEAR scale. For areas, you must square it: area scale = 1 : 50,000² = 1 : 2,500,000,000. Multiplying map area by the linear scale gives the wrong answer.

CIE 0580 · Paper 2 · May/Jun 2021

1 m = 100 cm, but 1 m³ = 100³ cm³ = 1,000,000 cm³. For VOLUME conversions you must CUBE the length conversion factor. Dividing by 100 only gives you 1/10,000 of the right answer.

CIE 0580 · Paper 1 · May/Jun 2021

Alternate segment theorem: the angle between a tangent and a chord equals the inscribed angle in the alternate segment. The most common error is applying it to the wrong angle — identify the correct c

CIE 0580 · Paper 2 · Feb/Mar 2021

To go from VOLUME ratio to LENGTH ratio, take the cube root: linear ratio = ∛(volume ratio). Don't use volume ratio directly as a linear scale — that's off by a cube factor.

CIE 0580 · Paper 4 · May/Jun 2021

If the bearing from K to R is 132°, the back bearing (R to K) is 132° + 180° = 312°. If > 360°, subtract 360°. The back bearing is always ±180° from the forward bearing, NOT 360° − bearing.

CIE 0580 · Paper 3 · May/Jun 2021

The centre of a circle is NOT a vertex of a cyclic quadrilateral. Cyclic quadrilateral theorems apply only to polygons with all vertices ON the circle. Use 'angle at centre = 2 × angle at circumference' instead.

CIE 0580 · Paper 4 · May/Jun 2019

Length scale k → area scale k² → volume scale k³. To find a volume ratio from a length ratio, cube it. Using the linear factor directly on volume is the #1 mistake.

CIE 0580 · Paper 4 · May/Jun 2019

The angle in a semicircle theorem: any angle inscribed in a semicircle (i.e. subtended by a diameter at the circumference) is 90°. You must state the full reason — just saying 'it's a right angle' wit

CIE 0580 · Paper 4 · May/Jun 2018

For vector AB, compute (coordinates of B) − (coordinates of A). Reversing gives BA which is the negative — about 1 in 5 candidates lost the mark this way.

CIE 0580 · Paper 2 · Feb/Mar 2024

Perimeter of a sector = arc length + 2 × radius (because the perimeter includes the two straight edges back to the centre). Don't stop after finding just the arc.

CIE 0580 · Paper 4 · Feb/Mar 2024

Circumference (2πr) and area (πr²) are different formulas — don't mix them up. Always sanity-check: if the answer is a length, should it be larger or smaller than the radius?

CIE 0580 · Paper 1 · Feb/Mar 2024

If the question says 'describe the single transformation', give exactly one (rotation OR translation OR reflection). Listing two will lose marks even if both are individually correct.

CIE 0580 · Paper 1 · Feb/Mar 2024

A vector from A to B is written with tail at A and head at B. Reversing the direction gives the negative. Always check the starting point matches the question.

CIE 0580 · Paper 1 · Feb/Mar 2024

Surface area and volume are different — read carefully which part asks for which. A cuboid's faces come in 3 pairs of different-sized rectangles, not all the same.

CIE 0580 · Paper 1 · Feb/Mar 2024

For bearing questions, always sketch the situation first. Don't blindly subtract from 360° or 180° — the back-bearing from B to A is (A→B bearing) ± 180°.

CIE 0580 · Paper 2 · Feb/Mar 2024

When giving a geometric reason, state it fully: 'angles on a straight line add to 180°' (not 'a line is 180'). Partial reasons don't score. Memorise the exact phrases from the syllabus.

CIE 0580 · Paper 3 · Feb/Mar 2024

1 m³ = 1000 litres (and 1 litre = 1000 cm³). This conversion is not on the formula sheet — you must memorise it. Many students leave these questions blank.

CIE 0580 · Paper 3 · Feb/Mar 2024

Bearings are always measured clockwise from the North direction. Practise measuring with a protractor from North — not from the line you're drawing.

CIE 0580 · Paper 3 · Feb/Mar 2024

A full sphere has surface area 4πr². A hemisphere's CURVED surface is half that: 2πr². Add πr² for the flat circular base only if the question includes it (e.g., a bowl).

CIE 0580 · Paper 4 · Feb/Mar 2024

For trapezium area, the formula (1/2)(a+b)h is more efficient than splitting into triangles + rectangle. If you do split, keep full calculator precision — don't round mid-calculation.

CIE 0580 · Paper 2 · Feb/Mar 2024

Enlargement description: SCALE FACTOR (from original to image, e.g., 2 if image is bigger), and CENTRE as coordinates (not a vector). Always include all three: 'enlargement', SF, and centre.

CIE 0580 · Paper 2 · May/Jun 2023

Alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment. Know this as a circle theorem — faster than multi-step triangle calculations.

CIE 0580 · Paper 2 · May/Jun 2023

For bearing problems involving non-right triangles: (1) find the unknown angle using sine or cosine rule, (2) combine it with the NORTH direction at the point of interest to get the bearing.

CIE 0580 · Paper 4 · May/Jun 2023

Magnitude of a vector (x, y) = √(x² + y²). Use BRACKETS around negative numbers before squaring: (−4)² = 16, not −4² = −16. And magnitude is always positive.

CIE 0580 · Paper 4 · May/Jun 2023

When an angle is formed at the circumference by a diameter, state the reason: 'angle in a semicircle is 90°'. Knowing it's a right angle isn't enough — you must cite the theorem.

CIE 0580 · Paper 3 · May/Jun 2023

Pythagoras: if you're finding a leg (not the hypotenuse), SUBTRACT the squares: a² = c² − b². Check: any leg must be SHORTER than the hypotenuse. If your answer is bigger, you added when you should have subtracted.

CIE 0580 · Paper 2 · May/Jun 2023

For similar triangles, use PROPORTIONS of corresponding sides, not subtraction. Sanity check: the unknown side must lie between the known corresponding sides of the triangles.

CIE 0580 · Paper 1 · May/Jun 2023

Volume of sphere = (4/3)πr³. If given the diameter d, use r = d/2 — don't use d directly. And keep 4/3 as a fraction in your calculator, don't round to 1.3.

CIE 0580 · Paper 1 · May/Jun 2023

Volume of a hemisphere = (1/2) × (4/3)πr³ = (2/3)πr³. Don't use the full sphere formula — always halve it. Similarly, a hemisphere's curved surface is 2πr² (half of 4πr²).

CIE 0580 · Paper 4 · Feb/Mar 2023

Sum of interior angles of an n-sided polygon = (n − 2) × 180°, NOT (n − 1) × 180°. Divide by n to get one interior angle of a regular polygon.

CIE 0580 · Paper 1 · Feb/Mar 2023

The reason for right angle in semicircle is 'angle in a semicircle is 90°' — NOT 'triangle in a semicircle'. You must mention the 90° or 'right angle'.

CIE 0580 · Paper 1 · Feb/Mar 2023

Pythagoras: c² = a² + b² means ADD when finding the hypotenuse, SUBTRACT when finding a leg. If you're looking for the longest side, you must add — check your answer against the diagram.

CIE 0580 · Paper 1 · Feb/Mar 2023

Total surface area of a closed cylinder = 2πrh + 2πr² = 2πr(r + h). You need BOTH the curved part AND the two circular ends. Memorise this — it's not on the formula sheet.

CIE 0580 · Paper 1 · Feb/Mar 2023

For similar triangles, set up ratios of CORRESPONDING sides — the shortest of one triangle matches the shortest of the other. Don't subtract lengths: similarity is about proportion, not difference.

CIE 0580 · Paper 2 · Feb/Mar 2023

Rule of thumb: for a 3-sig-fig final answer, keep at least 4 sig figs at every intermediate step. Rounding mid-calculation gives the 'almost right but not accepted' kind of answer.

CIE 0580 · Paper 2 · Feb/Mar 2023

Area of a triangle = ½ × base × perpendicular height. Don't measure all 3 sides. 'Base' and 'height' must be perpendicular to each other.

CIE 0580 · Paper 3 · Feb/Mar 2023

To describe an enlargement fully, state THREE things: (1) 'Enlargement', (2) scale factor, (3) centre as a coordinate. Missing the centre loses a mark.

CIE 0580 · Paper 3 · Feb/Mar 2023

For a cone + hemisphere shape: curved hemisphere = 2πr², curved cone = πrl. If they're joined at the base, DON'T include the flat circle (it's inside). Check if the shape is sealed or open before deciding which areas to include.

CIE 0580 · Paper 2 · May/Jun 2022

Reasons in geometry must be complete statements: 'angles in a triangle sum to 180°' — not 'a triangle is 180'. And 'base angles of an isosceles triangle are equal' — not 'two angles are equal'.

CIE 0580 · Paper 3 · Feb/Mar 2022

Reverse bearing from B→A = (A→B bearing) + 180° (subtract 360° if > 360°). It's NOT (360° − bearing) or (180° − bearing).

CIE 0580 · Paper 3 · Feb/Mar 2022

To find how many small boxes fit in a big container, divide the volumes (assuming perfect packing). Convert units first: if container is 1m³ and box is 2×4×5 cm, then container = 100³ cm³, so boxes = 1,000,000 / 40.

CIE 0580 · Paper 3 · Feb/Mar 2022

For back-bearing problems: (1) draw the North line at BOTH points, (2) use co-interior angles (sum to 180°) between parallel North lines to find the angle at the second point. A clear diagram is essential.

CIE 0580 · Paper 4 · May/Jun 2022

For the height of an isosceles triangle, use HALF the base in Pythagoras: h² = slant² − (base/2)². SUBTRACT the squared values (you're finding a leg, not the hypotenuse).

CIE 0580 · Paper 3 · May/Jun 2022

For a 3sf final answer, keep interim values to at least 4-5 sf (or use calculator memory). Rounding to 3 sf mid-calculation is the #1 cause of answers that are 'almost right but outside tolerance'.

CIE 0580 · Paper 2 · Feb/Mar 2022

If a shape is explicitly called a trapezium, USE the formula A = (1/2)(a + b)h. It's faster than splitting. And find the perpendicular height (not a slant side) — you may need Pythagoras.

CIE 0580 · Paper 1 · May/Jun 2022

For similar triangles, DIVIDE by the scale factor to go from larger to smaller. If the scale factor (larger/smaller) is 4/3, then smaller side = larger side × 3/4. Sanity check: the answer should be smaller.

CIE 0580 · Paper 1 · May/Jun 2022

For composite length problems, expect multi-step: find an intermediate length first (e.g., a shared side), then use Pythagoras/trig on a second triangle. A 4-mark question usually means 2+ stages.

CIE 0580 · Paper 2 · May/Jun 2022

Angle sum of n-sided polygon = (n − 2) × 180°. Pentagon: (5 − 2) × 180° = 540°, not 360°. Each interior angle of a regular pentagon = 540/5 = 108°.

CIE 0580 · Paper 4 · May/Jun 2022

The formula (1/2)ab sin C requires C to be the angle BETWEEN sides a and b (the 'included' angle). Using the wrong angle gives the wrong answer. Label your triangle carefully.

CIE 0580 · Paper 4 · Feb/Mar 2022

For vector questions, START by writing a clear route: e.g., PQ = PO + OR + RQ. This earns the method mark even if the algebra after is wrong. Without a stated route, method marks are lost.

CIE 0580 · Paper 2 · Feb/Mar 2022

Alternate segment theorem: the angle between a tangent and a chord at the point of contact = angle in the alternate segment. Learn this — it's a quick shortcut to tricky circle problems.

CIE 0580 · Paper 4 · May/Jun 2022

3D diagonal (vertex to opposite vertex, NOT sharing a face): d² = l² + w² + h². Work it in ONE step to avoid rounding errors. d = √(l² + w² + h²).

CIE 0580 · Paper 4 · May/Jun 2022

For composite shapes: (1) triangle area = ½ × base × height — don't forget to halve; (2) use sector area = (θ/360)πr², not full circle area; (3) use the calculator's π key, not 3.14 or 22/7.

CIE 0580 · Paper 1 · Feb/Mar 2021

Properties of a rhombus must be specific enough to distinguish it from other quadrilaterals. 'Opposite sides equal' is true for parallelograms too. Give properties from two different categories: sides

CIE 0580 · Paper 1 · Feb/Mar 2021

The reason is 'angle in a semicircle is 90°' (or 'angle subtended by diameter is 90°'). Saying 'it's a right-angled triangle' just restates — it's not a REASON.

CIE 0580 · Paper 3 · May/Jun 2021

In bearing problems with regular polygons, always use the interior angles of the shape. For an equilateral triangle, each interior angle is 60°. Ignoring this property is the most common error.

CIE 0580 · Paper 2 · Feb/Mar 2021

To describe an enlargement: (1) say 'enlargement', (2) scale factor, (3) centre as a coordinate. All three. Omitting any one loses a mark.

CIE 0580 · Paper 3 · May/Jun 2021

For similar 3D shapes: if the linear scale factor is k, the volume scale factor is k³. To compare volumes, set up (V₁/V₂) = (l₁/l₂)³. Using the linear or area ratio for volumes gives the wrong answer.

CIE 0580 · Paper 2 · Feb/Mar 2021

For a cone with top removed, the small cone is similar — its radius scales by the same ratio as its height. If height ratio is 1:4, radius ratio is also 1:4.

CIE 0580 · Paper 4 · May/Jun 2021

In similar shapes, corresponding lengths are in a constant ratio — use multiplication/division, never addition or subtraction. Also, do not round the scale factor before applying it to other lengths.

CIE 0580 · Paper 1 · Feb/Mar 2021

An enlargement is a single transformation — never describe it as two. Verify the scale factor by dividing any image length by the corresponding original length. Negative scale factors indicate the ima

CIE 0580 · Paper 4 · Feb/Mar 2021

'Total surface area' of a cone includes the curved part (πrl) AND the circular base (πr²). Of a hemisphere: 2πr² curved + πr² flat. Don't skip the flat faces.

CIE 0580 · Paper 4 · May/Jun 2021

Every step in a geometric proof needs its own reason, using precise terminology: 'alternate angles' (not 'alternative'), 'angle in a semicircle = 90°', 'angles in the same segment are equal'. Missing

CIE 0580 · Paper 4 · Feb/Mar 2021

Exterior angle method: exterior angle = 180° − interior angle; number of sides = 360° ÷ exterior angle. For interior 162°: exterior = 18°, sides = 360 ÷ 18 = 20. This method is easier and less error-p

CIE 0580 · Paper 3 · Feb/Mar 2019

Always calculate the sector angle from the given geometry — don't assume 45° or use the wrong arc. Check whether you need the minor or major sector angle for the required area/perimeter.

CIE 0580 · Paper 4 · Feb/Mar 2019

Volume of a cuboid = length × width × height. If a cuboid is made of unit cubes, count the cubes along each edge and multiply. Volume ≠ surface area — different concepts.

CIE 0580 · Paper 2 · May/Jun 2019

For similar triangles, use a SCALE FACTOR (divide corresponding sides), not subtraction. If one side is 12 and its pair is 18, the scale factor is 18/12 = 1.5, not '+6'.

CIE 0580 · Paper 1 · May/Jun 2019

For similar triangles, say 'corresponding angles are equal' (or 'all 3 pairs of angles are equal'). 'Congruent' means identical — different from similar. 'All angles are the same' is too vague.

CIE 0580 · Paper 1 · May/Jun 2019

Volume = base area × height. To find height, divide volume by the BASE AREA (e.g., 6 × 6 = 36 for a square base with side 6), not just one side length.

CIE 0580 · Paper 1 · May/Jun 2019

Surface area of a cuboid = 2(lw + lh + wh) — there are 6 faces in 3 PAIRS. Don't calculate volume by mistake. A cuboid has only 3 different face shapes, each repeated twice.

CIE 0580 · Paper 1 · Feb/Mar 2019

For back bearings: if bearing A to B is less than 180°, bearing B to A = bearing + 180°. Don't subtract from 360 or 180 directly without a clear diagram sketch.

CIE 0580 · Paper 2 · Feb/Mar 2019

The angle at the centre is twice the angle at the circumference in the same segment. Don't assume a triangle is isosceles without proof. Check which circle theorem applies at each step.

CIE 0580 · Paper 2 · Feb/Mar 2019

Volume per hour = (cross-section area) × (length of water per hour). Convert 12 cm/s to cm/hour: × 60 × 60 = 43,200 cm/h. Then convert cm³ to litres: ÷ 1000. Keep track of units at every step.

CIE 0580 · Paper 2 · Feb/Mar 2019

A POSITION vector is from the origin O to a point (e.g., OP). A DISPLACEMENT vector is between two other points (e.g., AB). These are different — position vectors always start at O.

CIE 0580 · Paper 4 · May/Jun 2019

To find a reverse (back) bearing: if original is ≥ 180°, subtract 180°; if < 180°, add 180°. Always draw a sketch with north arrows at both points. 360 − bearing gives the wrong answer.

CIE 0580 · Paper 3 · Feb/Mar 2019

To estimate the area of an irregular shape on a grid, count all full squares plus approximately half the partial squares. Don't use circle formulas for non-circular shapes.

CIE 0580 · Paper 1 · Feb/Mar 2018

For similar 3D shapes: if linear ratio is k, volume ratio is k³. When working backwards from volume ratio to linear: take the CUBE root. Using the ratio directly, squaring it, or taking the square roo

CIE 0580 · Paper 4 · May/Jun 2018

Back bearing = bearing ± 180°. If bearing < 180°, add 180°. If bearing ≥ 180°, subtract 180°. Do NOT subtract from 360°. Drawing a diagram with north lines at both points helps visualise this.

CIE 0580 · Paper 2 · May/Jun 2018

When enlarging, draw ray lines FROM the centre of enlargement THROUGH each vertex of the original shape. The image vertex lies on the ray at (scale factor × distance from centre). Starting from the sh

CIE 0580 · Paper 1 · May/Jun 2018

The volume of a hemisphere is HALF the volume of a sphere: V = (2/3)πr³, not (4/3)πr³. When a question involves a hemisphere, always halve the sphere formula. Forgetting to halve is a very common erro

CIE 0580 · Paper 4 · May/Jun 2018

For similar solids, volume ratio = (linear ratio)³. So to go from volume ratio back to linear ratio, take the CUBE ROOT. If volume ratio = 64, the linear scale factor = ³√64 = 4, not 64 × (some length

CIE 0580 · Paper 4 · May/Jun 2018

The angle at the centre is TWICE the angle at the circumference (subtended by the same arc). If the circumference angle is 48°, the centre angle is 96° — not the other way round. Getting this reversed

CIE 0580 · Paper 4 · May/Jun 2018

Circle theorem reasons must use precise mathematical vocabulary: 'centre' (not 'middle' or 'origin'), 'circumference' (not 'edge' or 'perimeter'), 'angle at centre is twice angle at circumference'. In

CIE 0580 · Paper 4 · May/Jun 2018

In a right-angled triangle, to find a shorter side: c² = a² + b² rearranges to a² = c² − b². Subtracting the sides directly (without squaring) is wrong. Also, the hypotenuse is always the longest side

CIE 0580 · Paper 2 · May/Jun 2018

If the linear scale factor between similar shapes is k, the area scale factor is k² (not k). For a base ratio of 12:3 = 4:1, the area ratio is 4² : 1² = 16:1. Applying the linear scale factor directly

CIE 0580 · Paper 4 · May/Jun 2018

Read the question carefully: volume and surface area are different. Volume = space inside (measured in cm³). Surface area = total area of all faces (measured in cm²). Calculating the wrong one earns z

CIE 0580 · Paper 3 · May/Jun 2018

If the linear scale factor of an enlargement is k, the area scale factor is k². For a scale factor of 1/3: area factor = (1/3)² = 1/9, NOT 1/3. Calculate actual areas to verify if unsure.

CIE 0580 · Paper 4 · May/Jun 2018

Area scale factor = (linear scale factor)². To find the linear scale factor from areas, you must SQUARE ROOT the area ratio. Forgetting the square root is the most common error.

CIE 0580 · Paper 2 · Feb/Mar 2018

To find a back bearing (return direction): if bearing < 180°, add 180°; if bearing > 180°, subtract 180°. Draw a sketch showing north lines at both points — this makes it visual.

CIE 0580 · Paper 3 · Feb/Mar 2018

Interior angle = 180° − exterior angle. Always check: if the polygon is regular and the question asks for interior angles, don't stop at the exterior.

CIE 0580 · Paper 2 · May/Jun 2023

Arc length = (angle / 360) × circumference = (θ/360) × 2πr. Use your calculator's π button for accuracy, not 3.14 or 22/7.

CIE 0580 · Paper 2 · May/Jun 2021

Read the question carefully. If the cross-section area = 12 × side², then side = √(area/12) — square root, not cube root. Don't automatically cube-root because it's a volume context.

CIE 0580 · Paper 2 · May/Jun 2021

In 'show that' questions, you must show at least 4 significant figures of working before rounding to the given value. Writing 41.7 = 41.7 is circular — you must show the full unrounded value first.

CIE 0580 · Paper 4 · Feb/Mar 2021

Geometric reasons must use precise, complete mathematical language: e.g. 'angles on a straight line sum to 180°', 'alternate angles are equal (parallel lines)', 'co-interior angles sum to 180°'. Vague

CIE 0580 · Paper 3 · Feb/Mar 2021

A complete description of an enlargement requires three things: the word 'enlargement', the scale factor (check it carefully — not a nearby integer), and the coordinates of the centre of enlargement.

CIE 0580 · Paper 3 · Feb/Mar 2021

Do not round the scale factor before applying it. Calculate 3.2 ÷ 2.8 exactly, keep full precision, then multiply — rounding to 1.14 introduces enough error to lose the accuracy mark.

CIE 0580 · Paper 2 · Feb/Mar 2021

Students confuse the angle of rotation with the order of rotational symmetry. The order is how many times the shape maps onto itself in one full turn — not the angle turned each time.

CIE 0580 · Paper 1 · Feb/Mar 2021

For Pythagoras with a shorter side: subtract the squares, don't add. Give at least 3 significant figures — answers of 2.9 or 3 lose the accuracy mark. Show intermediate values to full precision.

CIE 0580 · Paper 1 · Feb/Mar 2019

For enlargement scale factor −2 from centre (3,0): each vertex goes THROUGH the centre and the image vertex is twice as far on the OTHER SIDE. Draw rays through the centre and measure distance careful

CIE 0580 · Paper 4 · Feb/Mar 2019

A running track has two straight sides and TWO SEMICIRCLES (not two full circles). The semicircles combine to make one circle. Perimeter = 2 × straight + π × diameter.

CIE 0580 · Paper 3 · Feb/Mar 2019

Locus of points a fixed distance r from a point P is an ARC (or circle) centred at P with radius r. Use compasses set to the correct radius — don't freehand.

CIE 0580 · Paper 2 · May/Jun 2019

Always sanity-check geometric answers against the diagram. If the answer can't physically be bigger than a given length, it's wrong — rework it.

CIE 0580 · Paper 3 · May/Jun 2019

Area of semicircular annulus = ½π(R² − r²). You cannot add/subtract the radii first then square. The correct formula uses the DIFFERENCE OF THE SQUARES: R² − r² = 49 − 9 = 40.

CIE 0580 · Paper 3 · Feb/Mar 2019

Rotational symmetry order = how many times the shape looks the same in one full rotation. A regular pentagon has order 5; a kite has order 1.

CIE 0580 · Paper 1 · Feb/Mar 2018

Use precise terminology: 'corresponding angles in parallel lines are equal', not just 'parallel lines'. Alternate, corresponding, and co-interior angles are different — don't confuse them.

CIE 0580 · Paper 2 · Feb/Mar 2018

For the hypotenuse (longest side) always ADD the squares: c² = a² + b². If your answer is smaller than the two shorter sides, you subtracted instead — check your working.

CIE 0580 · Paper 1 · Feb/Mar 2018

Geometry reasons must be complete: say 'corresponding angles in parallel lines are equal' not just 'parallel lines'. For angle sum say 'angles in a triangle add up to 180°' with all key words.

CIE 0580 · Paper 1 · Feb/Mar 2018

Arc length = (θ/360) × 2πr. Sector area = (θ/360) × πr². These are different formulas — one gives a length, the other gives an area. Also check which arc is required: minor (< 180°) or major (> 180°).

CIE 0580 · Paper 4 · May/Jun 2018

For exterior angle of a regular polygon: exterior = 360 ÷ n. For an octagon: 360 ÷ 8 = 45°. This IS the answer — do not subtract from 180° (that gives the interior angle) or from 360°.

CIE 0580 · Paper 1 · May/Jun 2018

When finding surface area from a net or given volume and base area, determine ALL three distinct dimensions carefully. Do not assume faces are square unless proven. A cuboid typically has three differ

CIE 0580 · Paper 4 · May/Jun 2018

Known weak areas for extended candidates: error bounds, circle geometry, reading inequalities from graphs, 3D problems, vector magnitude, time conversions, and distance formula.

CIE 0580 · Paper 4 · Feb/Mar 2018

Always use the π key on your calculator, not 3.14 or 22/7 — these approximations lose the accuracy mark. Also, do not round intermediate values (like πr²) before completing the full calculation.

CIE 0580 · Paper 2 · May/Jun 2018

Diagonals of a square intersect at 90°, not 60° or 120°. Segment area = (sector area) − (triangle area). Divide by 4 only if you computed the whole difference then split into quadrants.

CIE 0580 · Paper 4 · Feb/Mar 2018

When a square is inscribed in a circle of radius 8, the diagonal = 16, so side = √128. To find the area, use side² = 128 directly — don't square root then square again as this loses accuracy.

CIE 0580 · Paper 4 · Feb/Mar 2018

Known weak areas for extended candidates: error bounds, circle geometry, reading inequalities from graphs, 3D problems, vector magnitude, time conversions, and distance formula.

CIE 0580 · Paper 4 · Feb/Mar 2018

For an enlargement, always give THREE things: (1) it is an enlargement, (2) the scale factor, (3) the centre of enlargement as coordinates. Missing the centre loses a mark.

CIE 0580 · Paper 3 · Feb/Mar 2018

For a rotation, always give THREE things: (1) it is a rotation, (2) the angle and direction (e.g. 90° clockwise), (3) the centre of rotation as coordinates.

CIE 0580 · Paper 3 · Feb/Mar 2018

To find the area scale factor, divide the two areas. Don't subtract them. Then check: area scale factor = (linear scale factor)².

CIE 0580 · Paper 3 · Feb/Mar 2018

Say 'an enlargement with scale factor −2', not 'a negative enlargement of scale factor 2'. The −2 must be the scale factor, not an adjective describing the enlargement.

CIE 0580 · Paper 2 · Feb/Mar 2018

A regular polygon has the same number of lines of symmetry as it has sides. A regular pentagon has 5 lines of symmetry.

CIE 0580 · Paper 1 · Feb/Mar 2018

For 'show that' questions, compute with full calculator precision and give AT LEAST one more decimal place than the target. Don't start from the target — that's circular reasoning and scores zero.

CIE 0580 · Paper 1 · Feb/Mar 2023

For cos(x) = k in 0° ≤ x ≤ 360°, the two solutions are θ and (360 − θ). For sin(x) = k, they are θ and (180 − θ). Learn which formula goes with which trig function.

CIE 0580 · Paper 2 · Feb/Mar 2024

y = cos(x) starts at (0, 1), crosses x-axis at 90°, reaches (180°, −1), crosses x-axis at 270°, reaches (360°, 1). SMOOTH curve, wave shape. Don't make it parabolic or linear.

CIE 0580 · Paper 4 · May/Jun 2023

Use tan(angle) = opposite / adjacent when you have those two sides and need the third. Pythagoras works too but takes extra steps. Pick the most direct method.

CIE 0580 · Paper 1 · May/Jun 2023

For cos(x) = k with x in 0°–360°, the two solutions are x = arccos(k) and 360° − arccos(k). Use the symmetry of the cosine curve around 180° (or the y-axis).

CIE 0580 · Paper 4 · May/Jun 2023

When 'show that' gives you a target rounded to e.g. 2dp, you must compute to at least ONE more dp (here 3dp) and then state it rounds to the target. Writing only the rounded target does not score.

CIE 0580 · Paper 4 · Feb/Mar 2023

Don't assume a triangle is right-angled unless it says so or there's a right-angle mark. If the given angle is 149°, use the COSINE rule — not Pythagoras (which only applies to 90° triangles).

CIE 0580 · Paper 4 · Feb/Mar 2023

y = tan(x) has period 180°, and VERTICAL ASYMPTOTES at x = 90°, 270° (where cos = 0). The curve rises from −∞ to +∞ in each branch. It's NOT the same shape as sin or cos.

CIE 0580 · Paper 4 · Feb/Mar 2023

For tan(x) = k in 0° ≤ x ≤ 360°, solutions come in pairs 180° apart: θ and θ + 180°. If tan(x) = √3/3 and x = 30°, the other solution is 30° + 180° = 210°.

CIE 0580 · Paper 4 · Feb/Mar 2023

For sin x = k in 0°–360°, the two solutions are arcsin(k) and 180° − arcsin(k). Don't stop at the first calculator answer. If the calculator gives a negative angle, adjust to the range 0°–360°.

CIE 0580 · Paper 2 · May/Jun 2022

SOH CAH TOA — label opp, adj, hyp first, then pick sin (opp/hyp), cos (adj/hyp), or tan (opp/adj). Rearranging depends on what you're solving for: BC = 15 × sin 38 or 15 / sin 38 depending on context.

CIE 0580 · Paper 1 · May/Jun 2022

For 3D angle problems, (1) find the relevant 2D diagonal on the base first with Pythagoras, (2) then use tan(θ) = opposite/adjacent with the vertical height. The angle is in a 2D right-angled triangle — not 3D.

CIE 0580 · Paper 2 · Feb/Mar 2022

The shortest distance from a point to a line is the perpendicular distance. The foot of the perpendicular is NOT necessarily the midpoint of the line — assuming it bisects the line segment is a very c

CIE 0580 · Paper 4 · Feb/Mar 2021

For 'show that angle = 36.9°', compute to at least 1 more decimal place (e.g., 36.87°) and then say it rounds to 36.9. Don't start from 36.9 — that's circular and scores zero.

CIE 0580 · Paper 2 · May/Jun 2021

y = tan(x) has period 180° (not 360° like sin and cos). It has vertical asymptotes every 180° starting at 90°. It's NOT the same shape as sin or cos.

CIE 0580 · Paper 2 · May/Jun 2021

For 'show that the angle is 63.4° correct to 1dp', write the calculator display (e.g., 63.4349...) FIRST, then state it rounds to 63.4. One dp alone is not enough.

CIE 0580 · Paper 3 · May/Jun 2021

For 3D angles (like a diagonal to a base), first SKETCH the right-angled triangle you need — one side is the diagonal, another is the relevant 2D length on the base. Then use tan/sin/cos.

CIE 0580 · Paper 4 · May/Jun 2021

Give inexact answers to 3 significant figures (e.g., 6.90, not 6.9). Always show working — 'just the answer' is risky because if it's wrong, you get zero instead of method marks.

CIE 0580 · Paper 1 · May/Jun 2019

For 3D trig: DRAW OUT the 2D right-angled triangle you're using, label all vertices, mark the angle you want to find. Ambiguous working can't be credited even if the method is correct.

CIE 0580 · Paper 4 · May/Jun 2019

In the cosine rule a² = b² + c² − 2bc·cos A, the '−2bc·cos A' means only the 2bc term is multiplied by cos A. A common error is to subtract 2bc from (b² + c²) first and then multiply the result by cos

CIE 0580 · Paper 2 · May/Jun 2018

The graph of y = cos(x) is a smooth curve (not straight lines). Key points: (0,1), (90,0), (180,-1), (270,0), (360,1). It starts at 1 when x=0, NOT at 0.

CIE 0580 · Paper 2 · Feb/Mar 2024

Always check your calculator is in DEG (degrees) mode before a trigonometry question — look for 'DEG' on the screen. GRAD and RAD give different (wrong) answers for CIE 0580.

CIE 0580 · Paper 4 · Feb/Mar 2024

For the cosine rule a² = b² + c² − 2bc·cos(A), type the whole right-hand side into your calculator in ONE go and take the square root last. Breaking it into stages introduces rounding and sign errors.

CIE 0580 · Paper 4 · Feb/Mar 2024

y = sin(x) starts at (0, 0), rises to (90°, 1), crosses (180°, 0), drops to (270°, −1), returns to (360°, 0). Smooth wave shape. Don't confuse with cos (which starts at (0, 1)).

CIE 0580 · Paper 2 · May/Jun 2022

When a final answer requires rounding, show a more accurate intermediate value (at least 4 significant figures) before stating the rounded answer. Writing only the rounded value means the accuracy of

CIE 0580 · Paper 4 · Feb/Mar 2021

Truncating (dropping digits) is not rounding. 26.97 truncated is 26.9, but correctly rounded to 3 s.f. is 27.0. Always round, never truncate, when giving a final answer.

CIE 0580 · Paper 4 · Feb/Mar 2021

In multi-step trigonometry, keep at least 4 significant figures in intermediate values. Rounding too early compounds errors and can cost the accuracy mark even when the method is correct.

CIE 0580 · Paper 2 · Feb/Mar 2021

Always check whether a triangle is right-angled before assuming trig ratios apply. For oblique triangles, use sine or cosine rule. For the cosine rule: after finding RQ², take the square root to get R

CIE 0580 · Paper 2 · Feb/Mar 2019

Never round the trig ratio before applying inverse trig. Use the full decimal from your calculator in sin⁻¹, cos⁻¹, or tan⁻¹. Rounding 0.649 to 0.65 then taking sin⁻¹ gives a wrong final angle.

CIE 0580 · Paper 1 · Feb/Mar 2019

Always read which angle or vertex is required before applying trig ratios. Don't assume the angle is at the base — check the diagram and question carefully.

CIE 0580 · Paper 1 · Feb/Mar 2018

When finding an obtuse angle, prefer the cosine rule — it gives the correct obtuse value directly. The sine rule has ambiguity (sin gives the same value for θ and 180°−θ), so using it for the largest

CIE 0580 · Paper 4 · May/Jun 2018

In trig calculations, keep the fraction (e.g. 20/52) or full calculator value throughout. Rounding 20/52 to 0.38 before taking cos⁻¹ loses enough accuracy to give the wrong answer. Use the fraction di

CIE 0580 · Paper 4 · May/Jun 2018

cos θ = adjacent/hypotenuse. Getting the fraction upside down (hyp/adj) gives the wrong angle. Also, use the simplest trig ratio directly — don't find a third side first then use a different ratio, as

CIE 0580 · Paper 2 · May/Jun 2018

To find turning points: (1) find dy/dx, (2) set dy/dx = 0, (3) solve for x, (4) substitute each x back into the ORIGINAL y equation. Guess-and-check with tables is risky.

CIE 0580 · Paper 4 · May/Jun 2023

To determine max vs min: (1) find d²y/dx², (2) substitute the x-value of the turning point, (3) state whether the result is positive (min) or negative (max). All 3 steps must be shown.

CIE 0580 · Paper 4 · Feb/Mar 2024

Gradient of a CURVE at a point requires differentiation. Find dy/dx, then substitute the x-value. Linear gradient calculations (rise/run with 2 points) only work for straight lines.

CIE 0580 · Paper 4 · May/Jun 2023

The gradient of a curve y = f(x) at a point is dy/dx evaluated at that x-value. Substituting x = 1 into f(x) gives you y — that's the y-coordinate, not the gradient.

CIE 0580 · Paper 4 · Feb/Mar 2023

For stationary points: (1) compute dy/dx, (2) set dy/dx = 0 (NOT y = 0), (3) solve for x, (4) substitute x into original y to get the y-coordinate.

CIE 0580 · Paper 4 · Feb/Mar 2022

Stationary/turning points are where dy/dx = 0, NOT where y = 0. After solving dy/dx = 0 for x, substitute back into the ORIGINAL curve to find y.

CIE 0580 · Paper 4 · May/Jun 2021

To find stationary points: differentiate (multiply coefficient by index, reduce power by 1; constants vanish), then set dy/dx = 0 — NOT d²y/dx² = 0. The second derivative is used only to classify the

CIE 0580 · Paper 2 · Feb/Mar 2021

To find the gradient of a curve at a given x: differentiate to get dy/dx, then substitute x into dy/dx. Substituting into the original equation gives a y-coordinate, not a gradient.

CIE 0580 · Paper 4 · Feb/Mar 2021

You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.

CIE 0580 · Paper 4 · May/Jun 2021

In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.

CIE 0580 · Paper 3 · May/Jun 2021

When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.

CIE 0580 · Paper 2 · Feb/Mar 2024

Completing the square rewrites x² + bx + c as (x + b/2)² + constant. It is NOT the same as difference of two squares a² − b² = (a+b)(a−b). Different techniques for different tasks.

CIE 0580 · Paper 2 · Feb/Mar 2024

The line of symmetry of a parabola is a VERTICAL line, so its equation is x = [number] (not y = ... or just a number alone). For y = ax² + bx + c, it is x = −b/(2a).

CIE 0580 · Paper 3 · Feb/Mar 2024

−(x + 1)² means you square FIRST, then negate: −(x² + 2x + 1) = −x² − 2x − 1. And (x + 1)² ≠ x² + 1 — you need the cross term 2x.

CIE 0580 · Paper 4 · Feb/Mar 2024

When the question says 'write down an equation', you MUST state it explicitly (e.g., '5x + 2x + 90 = 180'). Trial-and-error without a clear equation loses method marks even if the answer is right.

CIE 0580 · Paper 1 · May/Jun 2023

To solve a new equation using an existing graph, rearrange it to match '(existing curve expression) = (something linear)'. Then plot that linear part and find intersections. Using the quadratic formula ignores the method.

CIE 0580 · Paper 4 · May/Jun 2023

(81x¹²)^(3/4) = 81^(3/4) × x^(12 × 3/4) = 27x⁹. Apply the power to BOTH the coefficient (81^(3/4) = 27) and the variable (x^9). Don't multiply 3/4 × 81.

CIE 0580 · Paper 4 · May/Jun 2023

Read proportion wording precisely: 'proportional to the square' → y = kx²; 'proportional to the square root' → y = k√x; 'inversely proportional' → y = k/x. Always include the constant k.

CIE 0580 · Paper 4 · May/Jun 2023

For a triangle with angles 10x − 12, 2x + 3, and some third: sum them and set equal to 180°. Form ONE equation, not two to solve simultaneously. Trial and error rarely scores full marks.

CIE 0580 · Paper 2 · May/Jun 2023

In 5a + 7b − 11b − 6a, the minus sign belongs to 11b only. When collecting like terms: 7b − 11b = −4b, not +4b. Circle each term WITH its sign before combining.

CIE 0580 · Paper 1 · May/Jun 2023

When factorising 5x² − 19x + 12: the constant (+12) tells you both brackets need the SAME sign, and the middle term (−19x) tells you both are NEGATIVE. Answer: (5x − 4)(x − 3).

CIE 0580 · Paper 2 · Feb/Mar 2023

nth term = a + (n − 1)d. If d is negative, write (n − 1)(−6) or (n − 1) × (−6) — the bracket is essential. Writing '(n − 1) − 6' means subtract 6, which is different.

CIE 0580 · Paper 2 · Feb/Mar 2023

x² + 3x = 0 has no constant term — factor out the common x: x(x + 3) = 0, giving x = 0 or x = −3. You do NOT need the quadratic formula here.

CIE 0580 · Paper 2 · Feb/Mar 2023

When you halve (or multiply by a constant ratio) each term, you have a GEOMETRIC sequence. The nth term is a × r^(n−1), not 24/n or 24 − 12(n−1).

CIE 0580 · Paper 2 · Feb/Mar 2023

2y + 3y = 5y (addition) but 2y × 3y = 6y² (multiplication — multiply coefficients AND the variables). These are completely different.

CIE 0580 · Paper 3 · Feb/Mar 2023

When expanding, (−a)(−b) = +ab (positive). Also remember 2p² × 3p² = 6p⁴ (multiply coefficients, ADD the exponents). And −9p² − 4p² = −13p² (both negative: add them, keep the minus).

CIE 0580 · Paper 4 · Feb/Mar 2023

In factor-by-grouping, the two brackets after grouping MUST be identical (not just close). Rewrite (3 − 2q) as −(2q − 3) to flip the sign — that's how you make the brackets match.

CIE 0580 · Paper 4 · Feb/Mar 2023

a² − b² = (a − b)(a + b) — NOT (a − b)². And (x² − 5²) factorises as (x − 5)(x + 5), not (x² − 5)(x + 5) — you take the square root of EACH term.

CIE 0580 · Paper 4 · Feb/Mar 2023

√(16x²) = 4x (square root each factor — both the number and the variable). And y⁰ = 1 exactly, so 5y⁰ = 5, not y or 0.

CIE 0580 · Paper 1 · Feb/Mar 2022

For joint proportion, COMBINE relationships into one: if y ∝ x and y ∝ 1/z², then y = kx/z². Use ONE constant k for the combined relationship, not different k's for each.

CIE 0580 · Paper 4 · May/Jun 2022

To find where a line meets a curve: set the two y-equations equal, move everything to one side (= 0), and solve the resulting quadratic. Don't set the curve to some arbitrary constant.

CIE 0580 · Paper 4 · May/Jun 2022

If y ∝ 1/x² and x is halved, then y is multiplied by 4 (because 1/(x/2)² = 4/x²). Inverse square: halving x quadruples y. 'Doubles' is wrong — work it out algebraically.

CIE 0580 · Paper 2 · May/Jun 2022

When factoring by grouping, watch for signs inside brackets. (1 − 4k) is not (−4k). Check the brackets match exactly — sign errors cost marks.

CIE 0580 · Paper 2 · May/Jun 2022

For a quadratic sequence an² + bn + c: substitute n = 1, 2, 3 (the position numbers) to get term 1, term 2, term 3. Don't substitute the term VALUES — substitute the n-positions.

CIE 0580 · Paper 2 · May/Jun 2022

For 5x² − 20y²: first factor out 5 → 5(x² − 4y²), THEN recognise 4y² as (2y)² so x² − 4y² = (x − 2y)(x + 2y). Final: 5(x − 2y)(x + 2y), not 5(x − 4y)(x + 4y).

CIE 0580 · Paper 2 · May/Jun 2022

n/5 + n/2 = 2n/10 + 5n/10 = 7n/10. Use LCM (10) as denominator. Then n − 7n/10 = 3n/10.

CIE 0580 · Paper 1 · Feb/Mar 2022

The line of symmetry of a parabola y = ax² + bx + c is x = −b/(2a). It's a vertical line, so always of the form x = [a number]. Not 'y = ...', not a number alone.

CIE 0580 · Paper 3 · Feb/Mar 2022

Positive cubic: comes from bottom-left, up through a max, down through a min, up to top-right. For y = x(x − a)(x − b), roots are 0, a, b. Don't try to plot points — use the shape and roots.

CIE 0580 · Paper 4 · Feb/Mar 2022

Apply fractional powers to EVERY part inside. (x³/343)^(1/3) = x^(3×1/3) / 343^(1/3) = x / 7. Both the numerator AND denominator get the power.

CIE 0580 · Paper 2 · Feb/Mar 2022

Recognise the pattern a² − b² = (a − b)(a + b). So 4x² − 16 = (2x − 4)(2x + 4). Check each expression carefully — not every expression is a difference of squares.

CIE 0580 · Paper 4 · Feb/Mar 2022

When multiplying both sides by (g − c), distribute: M(g − c) = Mg − Mc, not Mg − c. Then collect all g-terms on one side, factor out g, and divide.

CIE 0580 · Paper 4 · Feb/Mar 2022

In the quadratic formula x = (−b ± √(b² − 4ac))/(2a), use brackets for b when it's negative: −(−5) = +5 and (−5)² = +25. Use long division and square root lines that cover everything.

CIE 0580 · Paper 4 · Feb/Mar 2022

Time = distance ÷ speed. Convert 'hours and minutes' to DECIMAL hours (2h 48min = 2.8 h, not 2.48 h). And if cycling at (x+10) km/h, the time is distance/(x+10), not distance/(10x).

CIE 0580 · Paper 4 · Feb/Mar 2022

When forming equations, re-read the problem and check: (1) how many of each item, (2) exact wording of 'less than' or 'more than'. '$24 less than a book' means (book − 24), and 2 of them is 2(book − 24), not (book − 48).

CIE 0580 · Paper 2 · Feb/Mar 2022

'y is inversely proportional to the square root of (x + 4)' means y = k / √(x + 4). Not (x + 4)², not (x + 4), not direct. Read the exact wording and match every piece.

CIE 0580 · Paper 2 · Feb/Mar 2022

Rearranging formulas: work STEP BY STEP and finish the simplification. s/(0.5a) should be simplified to 2s/a. Don't leave fractions unresolved.

CIE 0580 · Paper 4 · May/Jun 2022

HCF of algebraic terms: take the LOWEST power of each common variable. HCF(12a³b², 20a²b) = 4a²b (lowest powers). Not the highest — that would be the LCM.

CIE 0580 · Paper 4 · May/Jun 2022

1/64 = 1/4³ = 4⁻³. So if 4ˣ = 1/64, then x = −3. Answer x (the exponent only), not the whole expression.

CIE 0580 · Paper 4 · May/Jun 2022

When one equation is linear and the other is quadratic, substitute the linear one INTO the quadratic. Rearrange the linear to x = ... (or y = ...) and substitute. Make the substitution from the simpler variable.

CIE 0580 · Paper 2 · Feb/Mar 2022

For completing the square x² + bx + c = (x + b/2)² + (c − b²/4). The 'a' in (x + a)² is always HALF the coefficient of x. Then adjust the constant.

CIE 0580 · Paper 4 · May/Jun 2022

3 − 2(3 − 2x): expand the bracket FIRST: 3 − (6 − 4x) = 3 − 6 + 4x = −3 + 4x. Don't evaluate 3 − 2 first. And the negative distributes over both terms inside.

CIE 0580 · Paper 4 · May/Jun 2021

If the new subject appears in TWO places, (1) move all terms containing that subject to one side, (2) factor the subject out, (3) divide. This ALWAYS comes up when the subject appears twice.

CIE 0580 · Paper 2 · May/Jun 2021

Look for compound common factors: if two terms both contain 5(k + g), take it out as a single factor. Expanding the brackets to avoid the challenge and then failing to simplify earns no marks.

CIE 0580 · Paper 4 · Feb/Mar 2021

When eliminating fractions, use brackets correctly: 48/(x+2) multiplied by (x+2) simplifies to 48 — not 48x + 2. Forgetting the bracket around the denominator is the most common algebraic slip in rati

CIE 0580 · Paper 4 · Feb/Mar 2021

To find an unknown in an identity, match coefficients: if x³ − 4x² + 4x ≡ x³ − 2ax² + a²x, then −2a = −4 and a² = 4, giving a = 2.

CIE 0580 · Paper 4 · May/Jun 2021

For proportion questions: (1) write y = k × (the correct function), (2) substitute the given pair to find k, (3) substitute back. Always include k — don't skip it.

CIE 0580 · Paper 2 · May/Jun 2021

Geometric nth term = a × r^(n−1). The base is the COMMON RATIO r (e.g., 2 if you double each time), not the first term. 0.25 × 2^(n−1) ≠ 0.5^(n−1).

CIE 0580 · Paper 4 · May/Jun 2021

From A = πr², divide by π first to get r² = A/π, then square root BOTH together: r = √(A/π). Write the vinculum (top bar) long enough to cover the whole fraction — √A/π means √A ÷ π which is different.

CIE 0580 · Paper 3 · May/Jun 2021

After eliminating one variable, divide carefully. From 28y = 7, y = 7 ÷ 28 = 0.25, not 4. Students often invert the division when the coefficient is larger than the constant.

CIE 0580 · Paper 1 · Feb/Mar 2021

To add algebraic fractions, find a common denominator (multiply the two denominators if they share no factors). NEVER add numerators and denominators separately — that's not how fractions work.

CIE 0580 · Paper 4 · May/Jun 2021

For decreasing arithmetic sequences, the common difference d is negative. Using the positive difference gives an increasing formula (wrong). For d = −7, the nth term contains −7n, giving a formula lik

CIE 0580 · Paper 1 · Feb/Mar 2021

When substituting into a quadratic equation, you cannot take square roots of individual terms: √(149 − y) ≠ √149 − √y. Rearrange the linear equation first, substitute entirely, then solve the resultin

CIE 0580 · Paper 2 · Feb/Mar 2021

The axis of symmetry of a parabola is a vertical line, so its equation must be x = (value), never y = something. Find it by halving the sum of the x-intercepts, or by completing the square.

CIE 0580 · Paper 3 · Feb/Mar 2021

When a word problem mixes dollars and cents, convert everything to ONE unit before writing the expression. $y = 100y cents — multiply by 100 to convert dollars to cents.

CIE 0580 · Paper 2 · May/Jun 2021

When subtracting algebraic fractions, bracket the second numerator before subtracting. a/x − b/y = (ay − bx)/(xy). Remember the negative distributes over EVERY term in b.

CIE 0580 · Paper 4 · May/Jun 2019

When raising a product to a power, EVERY factor gets the power: (81y¹²)^(3/4) = 81^(3/4) × y^(9) = 27y⁹. Don't leave 81 alone.

CIE 0580 · Paper 4 · May/Jun 2019

p² − q² = (p − q)(p + q), NOT (p + q)(p + q). The difference of two squares always gives ONE bracket with minus and ONE bracket with plus.

CIE 0580 · Paper 4 · May/Jun 2019

For proportion, match the wording exactly: 'y proportional to √(x+1)' means y = k√(x+1). Not y = k(x+1), not y = k/(x+1). Set up the relationship correctly before finding k.

CIE 0580 · Paper 4 · May/Jun 2019

(x + a)² = x² + 2ax + a² (not x² + a²). For x² + 4x − 9 in the form (x + a)² + b: compare → 2a = 4 so a = 2, then a² + b = −9 so b = −13.

CIE 0580 · Paper 4 · May/Jun 2019

When dividing or multiplying BOTH sides of an inequality by a NEGATIVE number, the inequality sign REVERSES. −4x < 20 → x > −5. Forgetting to flip the sign is the most common error.

CIE 0580 · Paper 4 · Feb/Mar 2019

From 2w + 2h = P, isolate w: 2w = P − 2h, then w = (P − 2h)/2. Don't drop coefficients: 'w + h = P/2' forgets the 2 in front of h.

CIE 0580 · Paper 3 · May/Jun 2019

When rearranging terms, KEEP their signs. 5x − 3y + 9x + 10y ≠ 5x + 3y + 9x + 10y. Underline or box the sign attached to each term before reordering.

CIE 0580 · Paper 3 · May/Jun 2019

When solving 5x² = k, divide by 5 FIRST (x² = k/5), then square root. Make the √ sign cover the whole expression underneath — √(k/5), not √k/5.

CIE 0580 · Paper 2 · May/Jun 2019

For double factorisation: first spot the common factor (m+p), then factorise again. 4(m+p)(3+2m+2p) — if you see the same bracket appearing twice, factor it out as a bracket.

CIE 0580 · Paper 2 · Feb/Mar 2019

Factorising means rewriting as a product: 10 + 16w = 2(5 + 8w). It does NOT mean adding (26w), solving as an equation (w = −6), or dividing each term by the factor (5 + 8w).

CIE 0580 · Paper 1 · May/Jun 2018

In vector geometry, direction matters. CD = CO + OD = −OC + OD. Ignoring the arrows and just adding OC + OD gives the wrong vector. When reversing direction, negate ALL components of the vector, not j

CIE 0580 · Paper 4 · May/Jun 2018

When expanding –(5y – 5), the minus sign applies to BOTH terms: –5y + 5, not –5y – 5. The sign error in the second term is the most common mistake in bracket expansion.

CIE 0580 · Paper 1 · May/Jun 2018

From 1 − p = 12: subtract 1 from both sides to get −p = 11, then multiply by −1 to get p = −11. Many students cannot handle the −p step and give a positive answer instead.

CIE 0580 · Paper 3 · May/Jun 2018

When writing inequalities from a graph: (1) find the equation of each boundary line (gradient and intercept); (2) test a point inside the region to determine the correct inequality direction; (3) use

CIE 0580 · Paper 2 · May/Jun 2018

To use a graph to solve an equation, rearrange it so that one side matches the graph's equation. The other side gives the line to draw. Aim for y = (something without the graph variable).

CIE 0580 · Paper 4 · Feb/Mar 2018

Simplify means collect like terms and write the shortest equivalent expression. Don't factorise unless the question asks. 3m + 10k is simplified; (m + k)(...) is not.

CIE 0580 · Paper 2 · Feb/Mar 2024

When generating terms from an nth term formula, the first term uses n = 1 (not n = 0). Starting at n = 0 gives an extra 'zeroth' term that doesn't belong.

CIE 0580 · Paper 2 · Feb/Mar 2024

For simultaneous equations, look at the coefficients. If they match (or are opposite) you can add or subtract directly to eliminate a variable — no need to multiply through first.

CIE 0580 · Paper 3 · Feb/Mar 2024

When rearranging formulas, do ONE operation at a time and write each step. Trying to skip steps is where mistakes happen: u + v = 2s/t ⇒ v = 2s/t − u (subtract u, don't multiply).

CIE 0580 · Paper 4 · Feb/Mar 2023

If 3rd differences are constant, the sequence is cubic (n³ form). Try comparing to 1, 8, 27, 64... — a shift like (n − 1)³ − 1 is often simpler than expanding to n³ − 3n² + 3n − 2.

CIE 0580 · Paper 2 · Feb/Mar 2023

From 16t = −4, divide both sides by 16 (the coefficient): t = −4/16 = −0.25. Don't accidentally flip the division — dividing 16 by −4 gives −4, not −0.25.

CIE 0580 · Paper 2 · Feb/Mar 2023

After factorising, ALWAYS expand your answer to check it equals the original expression. This catches partial-factorising errors in seconds.

CIE 0580 · Paper 2 · Feb/Mar 2023

When factorising, take out EVERY common factor in one go. 6g³ − 4g² factorises to 2g²(3g − 2), not g(6g² − 4g) or 2(3g³ − 2g²).

CIE 0580 · Paper 1 · Feb/Mar 2023

When solving an inequality, KEEP the inequality sign throughout. The answer is x > 3 (or x < 3), not x = 3 or '3'. Never swap to equals.

CIE 0580 · Paper 2 · May/Jun 2023

To list the first three terms from an nth term formula, substitute n = 1, 2, 3 (not 0, 1, 2). The first term always uses n = 1.

CIE 0580 · Paper 1 · May/Jun 2023

nth term of an arithmetic sequence is dn + (a − d), where d is the common difference. The common difference becomes the COEFFICIENT of n, not the constant.

CIE 0580 · Paper 1 · Feb/Mar 2022

A compound inequality like −1 < n < 1 MUST include n in the middle — '−1 < 1' is not an inequality for n, it's just a (true) fact. Always place the variable between the two bounds.

CIE 0580 · Paper 2 · Feb/Mar 2022

'Treble' a number means ×3, not ^3. So 'treble n, then subtract 5 equals 22' → 3n − 5 = 22.

CIE 0580 · Paper 3 · May/Jun 2022

Sector angle = (fraction of total) × 360°, not × 100 or × 180. A full circle is 360°.

CIE 0580 · Paper 2 · May/Jun 2022

When subtracting expressions like a² − b², evaluate each FULLY first (e.g., 36 − 25 = 11), not just the exponents. Indices aren't collected across subtraction.

CIE 0580 · Paper 1 · May/Jun 2022

When substituting into a formula like F = 9C/5 + 32, replace only the named variable (C) with the given value. Don't overwrite the constants 9, 5, or 32.

CIE 0580 · Paper 2 · May/Jun 2021

When asked to write an answer as a 'power of 2', the expected form is 2ⁿ (e.g., 2⁻³ or 2⁵). Don't evaluate it as a decimal or give a different base like 25.

CIE 0580 · Paper 1 · May/Jun 2021

When a term is completely absorbed into the common factor, a '1' must remain inside the bracket. E.g. factorising t² + t gives t(t + 1), not t(t).

CIE 0580 · Paper 1 · Feb/Mar 2021

In the identity (x + a)² = x² + 2ax + a²: the constant term b = a², NOT 2a. If a = 11, then b = 121 (not 22). The coefficient 2a appears in the middle term, not as the constant.

CIE 0580 · Paper 4 · Feb/Mar 2021

Column vectors are NOT fractions. The top number is the x-component (horizontal movement) and the bottom is the y-component (vertical movement). Writing a fraction line between them shows a fundamenta

CIE 0580 · Paper 1 · Feb/Mar 2021

Strict inequalities (< or >) use a dashed boundary line; ≤ or ≥ use a solid line. Also check carefully: y = 1 is a horizontal line; x = 1 is vertical. Reading the wrong variable is a common error.

CIE 0580 · Paper 2 · Feb/Mar 2021

For quadratic sequences: (1) find first differences, (2) find second differences, (3) halve the second difference to get the n² coefficient, (4) subtract the n² sequence from the original to find any

CIE 0580 · Paper 2 · Feb/Mar 2021

If the second differences are constant (not the first), the sequence is QUADRATIC, not linear. A quadratic nth term has an n² term. Check: if second differences = 4, the coefficient of n² is 4÷2 = 2.

CIE 0580 · Paper 4 · Feb/Mar 2019

For aᵐ ÷ aⁿ = aᵐ⁻ⁿ, SUBTRACT the indices. Don't divide them. Example: t⁶/t² = t⁴, not t³.

CIE 0580 · Paper 1 · May/Jun 2019

When adding equations to eliminate a variable, add ALL terms including the x terms. Don't subtract just some terms. Check: if the y's are +3y and −3y, adding gives 0y — and the x terms must also be ad

CIE 0580 · Paper 1 · Feb/Mar 2019

Always find the HIGHEST common factor. For 8g² − 4g: HCF is 4g, giving 4g(2g − 1), not 2g(4g − 2). Check by expanding — the bracket should have no remaining common factors.

CIE 0580 · Paper 1 · Feb/Mar 2019

When dividing powers: w⁷ ÷ w⁻² = w^(7−(−2)) = w⁹. Subtracting a negative gives a bigger positive index — don't get 5 or −9.

CIE 0580 · Paper 1 · Feb/Mar 2019

When multiplying powers with the same base: (y⁵)³ = y^(5×3) = y¹⁵, not y⁸. The index outside means you MULTIPLY the powers, not add.

CIE 0580 · Paper 1 · Feb/Mar 2019

When factorising, don't leave decimal coefficients inside brackets — rewrite with fractions or clear the decimal by adjusting the common factor.

CIE 0580 · Paper 1 · May/Jun 2019

Distance = speed × time ONLY works for constant speed. For a velocity-time graph, distance = AREA UNDER THE GRAPH. Use triangles and rectangles to find each section's area.

CIE 0580 · Paper 2 · Feb/Mar 2019

Geometric sequences (multiplied by the same ratio each time) cannot be solved using differences. Identify the common ratio and use the form a × r^(n−1). Powers of 3: 3, 9, 27, 81, 243, … → nth term =

CIE 0580 · Paper 4 · Feb/Mar 2019

Acceleration = gradient of velocity-time graph. 25÷15 = 1.666... = 1.67 to 3 s.f. (recurring). 1.6 or 1.66 is insufficient precision — give 1.67 or write as 5/3.

CIE 0580 · Paper 2 · Feb/Mar 2019

To find gradient at a point: draw a tangent to the curve at that point, then find gradient of the TANGENT LINE using two clearly-separated points ON THE TANGENT, not on the curve.

CIE 0580 · Paper 2 · Feb/Mar 2019

After writing y = k(x−4) and substituting x=16, y=3: 3 = k(16−4) = 12k, so k = 3/12 = 1/4, not 4. Divide y by the bracket value to find k.

CIE 0580 · Paper 2 · Feb/Mar 2019

In the quadratic formula, the whole of (−b ± √(b²−4ac)) is divided by 2a. Draw the fraction line under everything. Use brackets when typing to avoid sign errors.

CIE 0580 · Paper 2 · Feb/Mar 2018

The axis of symmetry of a parabola is a vertical line, so its equation is x = (value). Writing y = 2.5 describes a horizontal line, not a vertical one. Do not use y = mx + c format for a vertical line

CIE 0580 · Paper 4 · May/Jun 2018