Question 1

What is a common maths exam mistake in Solving quadratic equations?

Accepted Answer

When using the quadratic formula, students frequently make sign errors by not correctly identifying a, b, and c before substituting. For example, in 2x² - 5x + 3 = 0, students write b = 5 instead of b = -5. How to avoid it: Before substituting into the formula, write out a, b, and c as a separate step. For 2x² - 5x + 3 = 0, write: a = 2, b = -5, c = 3. Include the sign as part of the value. Then substitute carefully. This one extra line of working protects the M1 method mark even if you make an arithmetic error later.

Question 2

What is a common maths exam mistake in Simultaneous equations?

Accepted Answer

When eliminating a variable, students forget to change the sign when subtracting equations. They subtract the left side but add the right side, leading to impossible or incorrect solutions. How to avoid it: After lining up the equations, underline the operation you are performing (add or subtract). Apply it to every term on both sides. Then check by substituting both values back into the original equations. If they do not satisfy both equations, you made a sign error.

Question 3

What is a common maths exam mistake in Rearranging formulae?

Accepted Answer

When the subject appears in more than one term, students try to simply "move terms" without factorising to isolate it. For example, rearranging ax + b = cx + d for x, they write x = (d - b) / a - c instead of x = (d - b) / (a - c). How to avoid it: Collect all terms containing the new subject on one side. Then factorise to take the subject out as a common factor. Only then divide by what remains in the bracket. Missing the bracket in the denominator loses the M1 method mark.

Question 4

What is a common maths exam mistake in Vectors?

Accepted Answer

Vector paths must follow a consistent direction, but students often write a + b when they should write a - b. Travelling against an arrow means the vector is negative, and this is frequently missed. How to avoid it: Trace the route on the diagram with your finger. Every time you travel in the same direction as the arrow, the vector is positive. Every time you travel against the arrow, negate it. Write out each leg of the journey separately before combining.

Question 5

What is a common maths exam mistake in Rounding and estimation?

Accepted Answer

Students round intermediate values too early in currency calculations, leading to a final answer that is off by several pence or cents. Examiners penalise premature rounding. How to avoid it: Keep at least 4 decimal places throughout all working. Only round the final answer to 2 decimal places for currency. If the question says "Give your answer to the nearest cent", this means round at the very end, not during working.

Question 6

What is a common maths exam mistake in Percentages?

Accepted Answer

For reverse percentage problems, students calculate a percentage of the given value instead of dividing. If an item costs $120 after a 20% increase, they calculate $120 × 0.8 = $96 instead of $120 ÷ 1.2 = $100. How to avoid it: Identify whether the given value is the original or the result. If it is the result after an increase, divide by (1 + rate). If it is the result after a decrease, divide by (1 - rate). Write the multiplier first, then divide.

Question 7

What is a common maths exam mistake in Indices and surds?

Accepted Answer

Students confuse negative and fractional indices. They think a negative index makes the answer negative (e.g., 2⁻³ = -8) rather than a reciprocal (2⁻³ = 1/8). Similarly, they confuse fractional indices with fractions of a number. How to avoid it: Write the rule before applying it: a⁻ⁿ = 1/aⁿ and a^(1/n) = the nth root of a. For combined indices like 8^(2/3), break it into two steps: find the root first, then raise to the power. Root first avoids large numbers.

Question 8

What is a common maths exam mistake in Ratio?

Accepted Answer

When sharing an amount in a ratio, students forget to find the total number of parts first. They divide by one of the ratio numbers instead of the sum, leading to a wrong answer. How to avoid it: Always write: total parts = sum of ratio parts. Then find the value of one part by dividing the total amount by the total parts. Finally, multiply one part by each ratio number. Check that your answers add up to the original amount.

Question 9

What is a common maths exam mistake in Direct and inverse proportion?

Accepted Answer

For inverse proportion, students write y = kx instead of y = k/x. They confuse direct and inverse proportion, setting up the equation the wrong way round. How to avoid it: Read the question carefully. "y is inversely proportional to x" means as x gets bigger, y gets smaller, so y = k/x. "y is directly proportional to x" means y = kx. Write the formula template first, then find k using given values.

Question 10

What is a common maths exam mistake in Ratio?

Accepted Answer

When simplifying ratios, students divide each side by different numbers. For example, simplifying 12:8 by dividing 12 by 2 and 8 by 4 to get 6:2 instead of 3:2. How to avoid it: Find the HCF of both numbers and divide both sides by it. For 12:8, the HCF is 4, so 12 ÷ 4 : 8 ÷ 4 = 3:2. Always divide both sides by the same number. Check that no common factor remains.

Question 11

What is a common maths exam mistake in Histograms?

Accepted Answer

In histograms, students plot frequency on the y-axis instead of frequency density. With unequal class widths, this makes the bars visually misleading and loses all marks. How to avoid it: Always label the y-axis "Frequency density". Calculate it as frequency ÷ class width for each bar. Remember: in a histogram, area represents frequency, not height. If class widths are equal, frequency and frequency density are proportional, but you must still label the axis correctly.

Question 12

What is a common maths exam mistake in Probability?

Accepted Answer

For combined events, students add probabilities when they should multiply. They write P(A and B) = P(A) + P(B) instead of P(A and B) = P(A) × P(B). How to avoid it: Draw a tree diagram and multiply along branches for "AND". Add between branches for "OR". The key rule: "AND means multiply, OR means add." Check that all probabilities on any set of branches sum to 1.

Question 13

What is a common maths exam mistake in Averages and range?

Accepted Answer

When finding the mean from a frequency table, students divide the total of (value × frequency) by the number of rows in the table rather than by the total frequency. How to avoid it: Add a third column to the table: value × frequency. Sum this column for the numerator. Sum the frequency column for the denominator. Mean = sum of (value × frequency) ÷ total frequency. The number of rows is irrelevant.

Question 14

What is a common maths exam mistake in Trigonometry?

Accepted Answer

Students leave their calculator in radians mode instead of degrees when answering trigonometry questions. This produces completely wrong answers that make no sense in context. How to avoid it: At the start of every exam, check your calculator is in DEGREE mode (look for "D" or "DEG" on the display). If your answer to a trigonometry question seems unreasonable (e.g., an angle of 0.5 when you expect something between 0° and 180°), check your mode immediately.

Question 15

What is a common maths exam mistake in Pythagoras' theorem?

Accepted Answer

Students subtract when they should add (finding hypotenuse) or add when they should subtract (finding a shorter side). The confusion about which operation to use leads to impossible answers. How to avoid it: Draw and label the triangle. The hypotenuse is always the longest side and opposite the right angle. For the hypotenuse: c² = a² + b² (add). For a shorter side: a² = c² - b² (subtract the smaller square from the larger). If your answer is longer than the hypotenuse, something is wrong.

Question 16

What is a common maths exam mistake in Fractions?

Accepted Answer

Adding numerators and denominators separately without finding a common denominator. For example, writing 1/3 + 1/4 = 2/7. How to avoid it: Find the LCM of the denominators first, then convert both fractions. For 1/3 + 1/4: LCM of 3 and 4 is 12, so 4/12 + 3/12 = 7/12. Never add denominators together.

Question 17

What is a common maths exam mistake in Fractions?

Accepted Answer

Forgetting to flip the second fraction when dividing. Students write 2/3 ÷ 4/5 = 2/3 × 4/5 instead of 2/3 × 5/4. How to avoid it: Remember KFC: Keep the first fraction, Flip the second fraction, Change the operation to multiplication. Then multiply numerators together and denominators together.

Question 18

What is a common maths exam mistake in Decimals?

Accepted Answer

Assuming 0.45 is larger than 0.5 because 45 is bigger than 5. Students compare the digit strings rather than the decimal values. How to avoid it: Add trailing zeros to make the decimal places equal: 0.45 vs 0.50. Now it is clear that 50 hundredths is bigger than 45 hundredths. Alternatively, convert to fractions or percentages.

Question 19

What is a common maths exam mistake in Percentages?

Accepted Answer

Using additive rather than multiplicative methods for repeated percentage change. For example, a 10% increase followed by a 10% decrease does not return to the original value. How to avoid it: Use multipliers for repeated changes. A 10% increase is ×1.1, a 10% decrease is ×0.9. Combined: ×1.1 × 0.9 = ×0.99, which is a 1% decrease overall. Never assume percentage increases and decreases cancel out.

Question 20

What is a common maths exam mistake in Indices and Powers?

Accepted Answer

Multiplying the indices instead of adding them when multiplying powers with the same base. For example, writing x³ × x² = x⁶ instead of x⁵. How to avoid it: The rule is: when multiplying powers of the same base, ADD the indices. x³ × x² = x^(3+2) = x⁵. When dividing, subtract. Write the index law above your working as a reminder.

Question 21

What is a common maths exam mistake in Standard Form?

Accepted Answer

Writing 32 × 10⁵ instead of 3.2 × 10⁶. Students forget that the coefficient a must satisfy 1 ≤ a < 10. How to avoid it: After writing a number in standard form, check: is the first part between 1 and 10? If not, adjust by moving the decimal point and changing the power accordingly. 32 × 10⁵ = 3.2 × 10⁶.

Question 22

What is a common maths exam mistake in Surds?

Accepted Answer

Thinking the square root of (a + b) equals the square root of a plus the square root of b. For example, √(9 + 16) = √9 + √16 = 3 + 4 = 7. But √25 = 5, not 7. How to avoid it: Square roots do NOT distribute over addition or subtraction. Work out the expression inside the root first, then take the root. √(9 + 16) = √25 = 5. Only multiplication and division distribute: √(a×b) = √a × √b.

Question 23

What is a common maths exam mistake in Estimation and Bounds?

Accepted Answer

Forgetting that to maximise a division you use the upper bound of the numerator and lower bound of the denominator. How to avoid it: For maximum of A/B: use upper bound of A and lower bound of B. For minimum of A/B: use lower bound of A and upper bound of B. Think about it logically: biggest top and smallest bottom gives the biggest fraction.

Question 24

What is a common maths exam mistake in Prime Factors, LCM & HCF?

Accepted Answer

Confusing HCF and LCM. Students mix up which is bigger. The HCF is always smaller than or equal to both numbers; the LCM is always bigger than or equal to both numbers. How to avoid it: HCF = Highest Common Factor (the biggest number that divides into both). LCM = Lowest Common Multiple (the smallest number both divide into). HCF ≤ both numbers ≤ LCM. Use a Venn diagram with prime factors: HCF is the intersection, LCM is the union.

Question 25

What is a common maths exam mistake in Solving Linear Equations?

Accepted Answer

Performing an operation on one side of the equation without doing the same to the other. Students subtract 3 from the left but forget to subtract 3 from the right. How to avoid it: Think of the equation as a balance. Whatever you do to one side, you must do to the other. Write each step on a new line and apply the operation to both sides simultaneously.

Question 26

What is a common maths exam mistake in Quadratic Equations?

Accepted Answer

Forgetting that x² = 9 gives two solutions: x = 3 and x = -3. Students only write the positive root. How to avoid it: Every time you take a square root, write ±. If x² = 9, then x = ±√9 = ±3. In the quadratic formula, the ± symbol gives you both solutions. Always check you have two answers (or explain why there is only one).

Question 27

What is a common maths exam mistake in Quadratic Equations?

Accepted Answer

Failing to rearrange the equation to equal zero before factorising. Students try to factorise x² + 3x = 10 directly without subtracting 10 from both sides first. How to avoid it: Factorising only works when one side is zero. Rearrange first: x² + 3x - 10 = 0, then factorise: (x + 5)(x - 2) = 0. The zero product rule says if ab = 0, then a = 0 or b = 0.

Question 28

What is a common maths exam mistake in Inequalities?

Accepted Answer

Forgetting to reverse the inequality sign when multiplying or dividing by a negative number. For example, -2x > 6 becomes x > -3 instead of x < -3. How to avoid it: When you multiply or divide both sides by a negative number, flip the inequality sign. Write a reminder note next to the step. Test your answer: if x < -3, try x = -4: -2(-4) = 8 > 6. Correct.

Question 29

What is a common maths exam mistake in Sequences?

Accepted Answer

Confusing the common difference with the first term when writing the nth-term formula. For the sequence 5, 8, 11, 14..., students write the nth term as 5n + 3 instead of 3n + 2. How to avoid it: Step 1: Find the common difference d (here, d = 3). Step 2: Write dn = 3n. Step 3: Adjust by comparing with the first term: when n = 1, 3(1) = 3 but the first term is 5, so add 2. nth term = 3n + 2. Always check: does n = 1 give the first term?

Question 30

What is a common maths exam mistake in Algebraic Fractions?

Accepted Answer

Cancelling individual terms instead of factors. For example, cancelling x from (x + 1)/x to get 1/1 = 1 instead of recognising that (x + 1)/x cannot be simplified. How to avoid it: You can only cancel factors (things multiplied together), not terms (things added together). Factorise the numerator and denominator first, then cancel common factors. (x + 1)/x has no common factor to cancel.

Common Maths Exam Mistakes

Found Your Weak Spots?

Common Maths Exam Mistakes

Found Your Weak Spots?