How Examiners Mark Your IGCSE Maths Paper

In questions requiring standard formulae — such as the sine rule (a/sinA = b/sinB), the cosine rule (a^2 = b^2 + c^2 - 2bc cosA), the quadratic formula, or the area formula (Area = 1/2 ab sinC) — the first method mark (M1) is awarded for writing the correct formula BEFORE substituting any values. This is one of the most misunderstood mark scheme conventions. Many students jump straight to substitution, writing something like "x^2 = 7^2 + 9^2 - 2(7)(9)cos54" without first stating the cosine rule. If the substitution is perfect, they will still earn the marks. But here is the critical problem: if they make ANY error in substitution (wrong value, wrong sign, calculator slip), they lose BOTH the M1 and the subsequent A1 because the examiner cannot see which formula they intended to use. By writing the formula first, you "bank" the M1 regardless of what happens next. This is especially important in multi-step problems where errors compound. The pattern applies to approximately 15-20% of all Paper 4 marks across trigonometry, mensuration, and algebra topics. Examiners consistently report that candidates who write formulae first score 2-4 marks higher on average in these question types. Think of the formula as your insurance policy: it costs you 10 seconds of writing but protects 2-3 marks every time.

When solving linear equations, examiners award two method marks (M2) plus one accuracy mark (A1) for more complex equations, or one method mark (M1) plus one accuracy mark (A1) for simpler ones. The key principle is that method marks are earned by demonstrating valid algebraic steps — such as correctly expanding brackets, collecting like terms, or isolating the variable — even if an arithmetic error leads to an incorrect final answer. For example, solving 3(2x + 1) = 15: expanding to get 6x + 3 = 15 earns M1, then correctly rearranging to 6x = 12 earns the second M1, and x = 2 earns A1. If a student makes an arithmetic slip at the rearrangement step but the method is clearly shown, they can still earn both M marks. On simpler two-step equations (e.g., 4x − 3 = 9), just one method mark is available for the rearrangement step. The accuracy mark is 'correct answer only' relative to the method shown — it is lost if the final answer is wrong, even if the process was valid. Students must show working clearly; a bare incorrect answer with no working scores zero.

Factorisation questions consistently use an M2 A1 mark structure across all 30 sampled questions, indicating that examiners split the factorisation process into two method stages before awarding the accuracy mark. For simple factorising (e.g., taking out a common factor like 6x² + 9x = 3x(2x + 3)), the first M mark is typically for identifying the correct common factor and the second for correctly writing the remaining bracket. For quadratic factorisation (e.g., x² + 5x + 6 = (x + 2)(x + 3)), M1 may be awarded for finding a pair of numbers that multiply to the constant term, and M2 for forming the correct bracket structure, with A1 for the fully correct factorised form. Critically, if a student partially factors — say, taking out only part of the common factor — they may still earn M1 but not M2. The final A1 is awarded only when the factorisation is completely correct and fully factorised. Writing an expression that is only partially factorised (e.g., 2(3x² + 4.5x) instead of 3x(2x + 3)) will lose both M2 and A1.

Sequence questions use three distinct mark structures: M1 A1 (2 marks), M1 A1 A1 (3 marks), and M2 A1 (3 marks), each appearing equally across the data. For finding the nth term of a linear sequence, the M1 is typically earned by identifying the common difference (which becomes the coefficient of n), and A1 for the correct full expression. In the M1 A1 A1 structure — common in longer paper questions — the first A1 may be for the correct coefficient of n and the second A1 for the correct constant term. The M2 A1 structure (common on Paper 1) rewards a two-step method: one mark for setting up the arithmetic correctly and a second for carrying it through, with A1 for the final answer. For example, for the sequence 5, 8, 11, 14…: identifying d = 3 earns M1, writing 3n + c earns partial credit, and the correct 3n + 2 earns A1. A student who writes only '3n + 2' with no working on a 3-mark question risks losing method marks entirely.

Simplification questions involving laws of indices are marked M1 A1 (2 marks), where the method mark is awarded for demonstrating a correct application of at least one index law in the working, even if the final simplified form contains an error. The accuracy mark requires the fully correct simplified expression. The examiners look for evidence of applying rules such as a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), or handling negative and fractional indices correctly. For example, simplifying (x³y²)² ÷ x⁴: M1 for correctly expanding the bracket to x⁶y⁴, A1 for the final answer x²y⁴. A student who writes x⁵y⁴ (adding instead of multiplying the power of x in the bracket) loses A1 but may retain M1 if the division step is handled correctly in their working. Students who attempt to substitute numbers to check their answer risk the examiner not awarding M1 if no algebraic law is shown.

When solving equations involving indices or logarithms, examiners award between two and three method marks (M2 or M3) before a single accuracy mark (A1), reflecting the multi-stage nature of these solutions. Each method mark corresponds to a key algebraic manipulation: for example, taking logarithms of both sides, applying a log law (such as log(ab) = log a + log b, or log(a^n) = n·log a), rearranging to isolate the unknown, or converting between exponential and logarithmic form. A final accuracy mark rewards the correct numerical answer, usually to a specified degree of accuracy. For instance, solving 3^(2x+1) = 50 might earn M1 for taking logs of both sides: (2x+1)log3 = log50, M1 for expanding and rearranging to x = (log50/log3 − 1)/2, M1 for correct isolation, and A1 for x ≈ 1.32. Students who apply an incorrect log law but otherwise work correctly may lose an accuracy mark but retain some method marks. Showing each algebraic step clearly is essential to maximise method mark recovery.

Drawing linear graph questions use two structures: M1 A1 A1 A1 (4 marks, longer papers) and M1 A1 (2 marks, Paper 1). In the 4-mark structure, the single M1 is typically awarded for evidence of a correct method — such as constructing a table of values or correctly calculating two coordinate points — even if subsequent plotting is inaccurate. The three A1 marks then reward: correct calculation of at least two points, accurate plotting of those points, and a ruled straight line drawn through them. On Paper 1 (2-mark structure), M1 is for the correct method of finding points and A1 for a correctly drawn line. A common mark loss pattern is: students calculate points correctly (earning M1 and the first A1) but then plot them inaccurately or draw a freehand (non-ruled) line, losing the final A marks. For a line like y = 2x − 3, computing (0, −3) and (3, 3) correctly earns method credit, but both points must be plotted within the accepted tolerance (usually ±1 small square) and joined with a ruler.

Simultaneous equation questions consistently carry M3 structures (M3 A1 or M3 A1 A1), reflecting that examiners identify three distinct methodological steps. For elimination: M1 for correctly scaling one or both equations to match coefficients, M2 for correctly adding or subtracting to eliminate one variable, and M3 for substituting back to find the second variable. For substitution: M1 for correctly rearranging one equation to express one variable, M2 for substituting into the second equation and simplifying, M3 for solving the resulting single-variable equation. In the M3 A1 A1 structure (seen in 0606 data, likely for non-linear simultaneous equations), the two A marks reward the two solution values or solution pairs. For example, solving 2x + y = 7 and x − y = 2: adding gives 3x = 9 (M1 + M2), so x = 3 (M3), then y = 1 (A1). If a student makes an error at the elimination step but proceeds correctly, they can still earn M3 by correct follow-through substitution. A bare answer with no working loses all method marks.

Kinematics questions involving calculus (differentiation to find velocity/acceleration, or integration to find displacement) follow the standard multi-M-mark pattern, with either M1 A1 (2 marks) or M2 A1 (3 marks) depending on complexity. The method marks reward: correctly identifying which calculus operation is needed (differentiation for rate of change, integration for cumulative quantity), correctly performing that operation on the given expression, and — in two-step problems — applying a boundary condition or evaluating at a specific time. The accuracy mark requires the correct numerical or algebraic answer. For example, given s = t³ − 6t² + 9t, finding velocity at t = 2: M1 for differentiating to get v = 3t² − 12t + 9, M1 for substituting t = 2, A1 for v = 3(4) − 12(2) + 9 = −3 m/s. Students who integrate when they should differentiate (or vice versa) lose all method marks, so identifying the correct operation is the critical first step.

Differentiation questions consistently follow a pattern of M2 A1 (or M3 A1 for more complex cases), showing that examiners expect to see a clearly staged process rather than just a final derivative. The method marks reward distinct steps: for example, one mark for correctly applying the relevant rule (product rule, chain rule, or quotient rule) in set-up form, a second mark for correctly differentiating each component, and — in harder questions — a third mark for algebraic simplification or substitution to find a specific value. The final A1 rewards the fully correct answer. For instance, differentiating y = x²·sin(x) using the product rule: M1 for writing dy/dx = x²·cos(x) + sin(x)·2x (correct rule applied), M1 for correct individual derivatives, A1 for the simplified or evaluated answer. A student who states the product rule incorrectly but otherwise differentiates consistently may still earn a follow-through mark. Students who only write the final answer without showing rule application risk losing all marks if the answer is wrong.

When calculating bearings, examiners award method marks in stages reflecting the geometric reasoning required. The dominant pattern is M2 A1 (3 marks) or M2 A1 A1 (4 marks), meaning two method marks must be earned before the accuracy mark is accessible. The first M mark is typically awarded for identifying and using a correct geometric relationship — such as recognising co-interior angles, alternate angles, or North line geometry — to set up the calculation. The second M mark is awarded for correctly combining these relationships (e.g., adding or subtracting angles to find the bearing). The A1 is then awarded only for the correct final answer, usually a three-figure bearing. In 4-mark versions, a second A1 covers an intermediate angle value. For example, to find the bearing of B from A given a diagram with a North line: M1 for identifying the alternate angle as 48°, M1 for forming 180° + 48° = 228°, A1 for the answer 228°. Critically, if both method marks are earned, a follow-through accuracy mark may be awarded even if an arithmetic slip occurs. Students who jump to an answer without showing geometric reasoning risk losing both method marks and the accuracy mark simultaneously.

For angle calculations involving polygons, the examiner awards a method mark for demonstrating use of a correct angle sum formula or property, and an accuracy mark for the correct answer. In simpler 2-mark questions (M1 A1), the method mark is earned by writing down the correct angle sum — for example, writing (n−2)×180° for interior angles, or 360° for exterior angles — even if the arithmetic that follows is incorrect. In harder 3-mark questions (M2 A1), two method marks are needed: typically one for establishing the total angle sum and a second for correctly isolating the required angle (e.g., subtracting known angles). For example, finding an interior angle of a pentagon: M1 for (5−2)×180° = 540°, M1 for 540° − 4×110° = 100°, A1 for 100°. If a student writes 540° but makes an arithmetic error in the second step, they can still earn 2 out of 3 marks. Students frequently lose the method mark by simply writing an answer with no working, which forfeits all marks if the answer is wrong. Quoting the correct formula is enough for the first M mark even if the formula is then misapplied.

In extended Pythagoras problems (M3 A1, 4 marks), the examiner awards three method marks for three distinct stages of working. These typically correspond to: (1) correctly identifying the right-angled triangle(s) and writing a correct Pythagoras expression (a² + b² = c²); (2) correctly substituting known values; and (3) correctly finding the square root or completing a multi-stage calculation (e.g., combining two Pythagoras steps). The single A1 is awarded only for the correct final answer, usually requiring 3 significant figures or better. In simpler 2-mark versions (M1 A1), one method mark is awarded for correct substitution into Pythagoras and the A1 for the correct answer. A key examiner principle: if a student earns all three M marks but makes an arithmetic slip at the final step, they still earn 3 out of 4 marks. However, if a student writes only an answer with no working and it is wrong, all 4 marks are lost. For example, finding a diagonal of a cuboid requires finding a face diagonal first (M1 for a²+b², M1 for correct substitution, M1 for using the result in a second Pythagoras step, A1 for correct final value).

For vector problems requiring a student to 'Find' a resultant vector or prove a relationship, the M2 A1 pattern shows that two method marks are needed before the accuracy mark is accessible. The first method mark is awarded for attempting a valid vector path — writing the journey as a combination of known vectors (e.g., OA + AB = OB). The second method mark is awarded for correctly substituting the given vector expressions into that path and simplifying, including correctly handling scalar multiples. The accuracy mark A1 is then awarded for the fully simplified correct vector in component or column form. In 'Show that' questions (also appearing as M3 A1 in the data), the full chain of working must be shown with no gaps, and the final line must match the target expression exactly. Students lose method marks by stating an answer without showing the vector path, or by incorrectly reversing vector directions (forgetting that BA = −AB). A common error is writing vectors without clearly labelling the path, so the examiner cannot follow the reasoning — this risks losing the first method mark even if the algebra is correct.

Powers and roots questions on Paper 1 use M2 A1, indicating two distinct method marks before the final accuracy mark. This structure reflects that these questions typically require two separate applications of index laws or correct order-of-operations decisions. For example, evaluating (8/27)^(−2/3): M1 for correctly handling the negative index (reciprocal: (27/8)^(2/3)) or the fractional index (cube root first), M1 for correctly applying the remaining operation (squaring), A1 for 9/4 or 2.25. A student who applies one law correctly but fails on the second (e.g., correctly takes the cube root but then adds rather than squares) earns M1 but loses M1 and A1. A student who converts to decimals at an intermediate step often introduces rounding errors that cause loss of A1 even when both method marks are earned. For negative indices, a very common error is negating the base rather than taking the reciprocal (writing −8 instead of 1/8 for 8⁻¹), which loses all subsequent marks.

Ratio and proportion questions almost always follow an M2 A1 or M1 A1 structure. For M1 A1 questions (simpler, often on Paper 1), the single method mark is earned by demonstrating the correct ratio relationship — for example, multiplying one quantity by the ratio fraction. For M2 A1 questions (Paper 3), the two method marks typically correspond to: M1 for finding the value of one part or unit (e.g., dividing the total by the sum of ratio parts), and M1 for scaling correctly to find the required quantity. For example, sharing $240 in the ratio 3:5: M1 for 240 ÷ 8 = 30 (value of one part), M1 for 30 × 3 = 90 and 30 × 5 = 150, A1 for both correct values. A student who correctly finds the unit value but then multiplies by the wrong ratio part earns M1 but loses M1 and A1. Proportion problems (direct or inverse) follow the same logic: M1 for identifying the correct relationship (y = kx or y = k/x), M1 for finding k, A1 for the final answer.

When calculating quantities involving rates such as speed, density, or pressure, examiners award two method marks (M2) before the final accuracy mark (A1), reflecting that the solution requires two distinct procedural steps. Typically, the first method mark is earned by correctly identifying and applying the appropriate formula (e.g., speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area), and the second method mark is earned by correctly substituting the given values into that formula or by performing an intermediate conversion (e.g., converting units such as km/h to m/s). The accuracy mark is only awarded for the correct final answer with appropriate units. For example, if asked to find the speed of a train that travels 240 km in 1.5 hours: M1 is earned for writing speed = distance ÷ time, M1 again for substituting 240 ÷ 1.5, and A1 for the answer 160 km/h. Students who jump straight to a numerical answer without showing formula application risk losing both method marks if the answer is wrong. Crucially, if correct working leads to a wrong answer due to an arithmetic slip, the two M marks can still be awarded — protecting students from total mark loss.

Across nearly all percentage and fraction calculation questions, the mark scheme uses M1 A1 (2 marks) for straightforward questions and M2 A1 (3 marks) for multi-step problems such as reverse percentage, percentage change, or compound interest. The M1 is awarded for setting up the correct mathematical process — for example, writing 'original × 1.15' for a 15% increase, or writing '(change ÷ original) × 100' for percentage change — even if the arithmetic goes wrong. The A1 requires the correct final value. For M2 A1 questions, two process steps must be correct: for instance, in a reverse percentage problem, M1 for dividing by the correct multiplier and M1 for completing the reverse operation, then A1 for the correct original value. A very common error is performing a forward percentage when a reverse is required (e.g., subtracting 15% from the given value rather than dividing by 1.15), which loses all marks. Another common error is rounding prematurely at an intermediate step, which can cause the final A1 to be lost even when method marks are earned.

Both 'Write' and 'Calculate' estimation questions consistently use M1 A1 across all papers. The M1 is earned by rounding every value in the problem to 1 significant figure (or to a clearly sensible approximation that simplifies the calculation). The A1 requires the correct result of the simplified calculation — note this is not the exact answer to the original problem, but the answer obtained from the rounded values. For example, estimating 38.7 × 4.93 ÷ 0.196: M1 for writing 40 × 5 ÷ 0.2, A1 for 1000. A student who rounds to 2 significant figures typically does not earn M1 unless the mark scheme explicitly allows it. A student who rounds correctly (earning M1) but makes an arithmetic error in the simplified calculation loses A1 but retains M1. The 'Write' command word version requires students to show the rounded expression — simply writing the final estimate without showing rounded values risks losing M1 even if the answer is correct, because the examiner cannot verify the method.

Surd questions at both IGCSE (0580) and Additional Mathematics (0606) level follow M1 A1 or M2 A1 structures. For simplification (M1 A1), the method mark is awarded for identifying the largest perfect square factor and expressing the surd as a product — for example, √72 = √(36 × 2), earning M1, then 6√2 for A1. For rationalising or more complex expressions (M2 A1), M1 is typically awarded for multiplying numerator and denominator by the conjugate surd, and M1 for correctly expanding (recognising the difference of two squares in the denominator), with A1 for the fully simplified rational form. A common error losing the first M1 is choosing a non-largest square factor (e.g., writing √72 = √(4 × 18) = 2√18 and stopping), which earns M1 but then requires a further simplification step that is often missed, losing A1. For rationalisation, sign errors when expanding (a + √b)(a − √b) are the most frequent cause of losing A1 while retaining method marks.

For mensuration questions worth 3–5 marks, examiners award method marks for each correct stage of the calculation, with a final accuracy mark for the correct answer. The M2 or M3 structure means you must demonstrate at least two or three distinct correct steps — for example, correctly identifying and applying the right formula, correctly substituting values, and correctly combining parts (e.g., adding areas of faces for surface area). A student who writes only a final answer with no working scores zero, even if correct, because method marks cannot be inferred. Conversely, a student who makes an arithmetic slip on the final step but has shown correct method for all prior steps will typically earn M2 (or M3) but lose A1. For example, to find the volume of a compound solid: M1 for splitting into recognisable shapes, M1 for correctly applying the volume formula to each part, M1 (if M3 scheme) for combining correctly, A1 for the correct final answer. On 5-mark questions (M3 A1 A1), there are two separate accuracy marks, often for two distinct final values (e.g., volume and surface area in the same question). Always show every formula used, every substitution, and every intermediate result.

When calculating the mean from a frequency table or grouped data, examiners consistently award two method marks (M2) before the final accuracy mark (A1), following a 3-mark M2 A1 structure seen in 30 instances across multiple paper series. The first method mark (M1) is earned by showing the correct process of multiplying each value (or midpoint) by its frequency — i.e., forming the sum of (fx) products. The second method mark (M1dep) is earned by dividing the total sum of fx by the total frequency. Both steps must be clearly shown. The accuracy mark (A1) is only awarded if both method marks are earned and the final answer is correct. For example, if data shows values 2, 4, 6 with frequencies 3, 5, 2: M1 for 2×3 + 4×5 + 6×2 = 6+20+12 = 38; M1 for 38÷(3+5+2) = 38÷10; A1 for 3.8. If a student writes only '3.8' with no working, they risk losing both method marks. On Paper 1 (non-calculator), an M1 A1 pattern is used for simpler mean questions without frequency tables, meaning only one method step is needed. Always show the sum of products and the division step explicitly.

For single event probability calculations, the examiner applies either an M1 A1 (2-mark) or M2 A1 (3-mark) structure depending on paper tier, with 16 instances of each seen across the dataset. The M1 mark is earned by writing a correct probability fraction in the form (favourable outcomes)/(total outcomes), even if not fully simplified. For M2 questions, the second method mark typically requires combining or identifying the correct numerator from a multi-step count (e.g., counting items satisfying two conditions). The A1 mark requires the fully correct and simplified fraction, decimal, or percentage as appropriate. For example, finding the probability of picking a red ball from 4 red and 6 blue balls: M1 for writing 4/10; A1 for 2/5. If a student writes only '0.4' without showing the fraction, they may lose M1 if the answer is wrong, as the examiner cannot award the method mark retrospectively. Probabilities written as ratios (e.g., 2:5) or percentages without a prompt to give a percentage are penalised at the A1 stage. Always express probability as a fraction, decimal, or percentage and show the setup.

For combined probability questions involving tree diagrams, the dominant marking pattern is M2 A1 A1 (4 marks), seen 15 times across multiple papers. The two method marks reflect: M1 for correctly multiplying probabilities along a branch (e.g., P(A and B) = P(A) × P(B)), and M1 for correctly identifying and adding the probabilities of all relevant branches when the event can occur in more than one way. Each A1 mark then rewards the correct final probability for each part of the question. For example, finding P(exactly one red): M1 for P(red)×P(not red) = (3/5)×(2/5) = 6/25; M1 for adding both valid branches: 6/25 + 6/25; A1 for 12/25. A common error is forgetting to add all valid branches (only computing one branch), which loses the second M mark and the A mark. On harder papers (0580/4), M3 A1 A1 patterns appear for conditional or three-stage problems. The structure confirms that showing multiplication along branches and then summation of relevant branch products are both required for full method credit.

For histogram questions with unequal class widths, the M2 A1 (3-mark) pattern applies, confirming that examiners require two method steps before awarding the accuracy mark. M1 is earned for demonstrating understanding that frequency density = frequency ÷ class width (or equivalently, frequency = frequency density × class width), even if applied to only one bar. The second M1 is earned for correctly computing frequency densities for all bars or correctly using a given frequency density to find a missing frequency. The A1 is awarded for all bars drawn at exactly the correct heights with correct widths. For example, if a class 10–20 has frequency 30: M1 for recognising frequency density = 30÷10 = 3; if another class 20–35 has frequency density 2 and frequency is unknown: M1 for frequency = 2×15 = 30; A1 for all bars correct. A common error is treating all bars as if they have equal width and plotting frequency rather than frequency density — this forfeits all marks. The vertical axis must be labelled 'Frequency density' not 'Frequency'.

Permutation and combination questions are marked with M2 A1 (3 marks), indicating that examiners expect students to demonstrate a two-stage reasoning process before arriving at the numerical answer. The first method mark is typically awarded for correctly identifying whether the situation requires a permutation or combination, and for writing the appropriate expression (e.g., nCr or nPr notation, or a factorial expression). The second method mark is awarded for correctly evaluating or setting up any multiplication of independent choices (applying the multiplication principle across stages of the selection). The accuracy mark requires the correct final integer answer. For example, finding the number of ways to choose a committee of 3 from 8 people where one specific person must be included: M1 for recognising 1 × 7C2 (fixing one person, choosing 2 from remaining 7), M1 for evaluating 7C2 = 21 correctly, A1 for the answer 21. Students who confuse combinations with permutations, or who fail to account for restrictions, typically lose both method marks.

For 'Draw' questions involving statistical diagrams (bar charts, pie charts, frequency diagrams), examiners award M2 before multiple accuracy marks, in patterns such as M2 A1 A1 A1 (5 marks) and M2 A1 A1 (4 marks), each seen 15 times across multiple paper series. The two method marks reflect: M1 for setting up a correct scale or structure (axes labelled with correct units, scale chosen appropriately), and M1 for using the correct method to plot at least some values accurately. The subsequent A1 marks are awarded for each correctly drawn bar, sector, or data point. For example, in a bar chart question: M1 for drawing axes with a uniform scale going up to the required maximum; M1 for at least one bar drawn at the correct height; A1 for each remaining bar drawn correctly. On Paper 1, the simpler M1 A1 pattern applies for straightforward plotting tasks. Losing marks most commonly happens when the scale is inconsistent or axes are unlabelled, which can forfeit the first M1 and make subsequent A marks unawardable. Always label axes with units and use a ruler for straight lines.

In 0606 'Solve' trigonometry questions with a 5-mark structure (M3 A1 A1), the three method marks reward systematic algebraic and trigonometric technique rather than just a correct answer. Typically: M1 is awarded for correctly applying a trigonometric identity to simplify or rewrite the equation (e.g., using sin²θ + cos²θ = 1 or tan θ = sin θ/cos θ), M1 for solving the resulting equation to find a principal value (e.g., θ = arcsin(0.5) = 30°), and M1 for correctly applying the general solution rules to find all solutions in the required interval (e.g., recognising that sin θ = 0.5 also gives θ = 150° in [0°, 360°]). The two A marks are for the correct individual solution values. A common error is finding only one solution and missing the second, losing the second A1. Another error is applying the general solution rule for the wrong function (e.g., applying the cosine symmetry rule to a sine equation). The examiner does not award marks for guessing solutions without working, even if correct.

In 5-mark sine or cosine rule questions (M3 A1 A1), examiners award three method marks and two accuracy marks. The three method marks follow a consistent structure: M1 for correctly stating or implying the appropriate rule (e.g., writing the cosine rule a² = b² + c² − 2bc cos A), M1 for correctly substituting the given values into the formula, and M1 for correctly rearranging to isolate the unknown (e.g., taking a square root or applying the inverse sine). The two A marks are typically awarded separately — one for an intermediate correct value (such as a² or sin A) and one for the final answer. This means even if your final answer is wrong due to an arithmetic slip, you can still earn 4 out of 5 marks if your method and intermediate value are correct. A common error is applying the cosine rule when the sine rule is appropriate (or vice versa), which loses the first M mark. For the sine rule, the formula must be written in the correct orientation for the unknown (i.e., if finding a side, write a/sin A = b/sin B, not its reciprocal form, though both are technically equivalent — ensure substitution is consistent).

When calculating a side or angle using SOH-CAH-TOA, examiners award method marks in stages. In a 4-mark question (M3 A1), three method marks are typically awarded: one for correctly identifying and labelling the right triangle or relevant sides, one for setting up the correct trigonometric ratio (e.g., sin θ = opposite/hypotenuse), and one for correctly rearranging to isolate the unknown (e.g., multiplying both sides by the hypotenuse or applying the inverse trig function). The final A1 is for the correct numerical answer. In a 3-mark question (M2 A1), the setup and rearrangement are combined into two method marks. For example, to find a missing side x in a right triangle where the hypotenuse is 12 cm and the angle is 35°: M1 for writing cos 35° = x/12, M1 for reaching x = 12 × cos 35°, A1 for x = 9.83 cm. You can still earn method marks even if you make an arithmetic error, provided your trig ratio and rearrangement are correct. The accuracy mark is typically 'cao' (correct answer only) and requires appropriate rounding. Errors that lose all marks include using the wrong trig ratio (e.g., using sin instead of cos) or inverting the ratio incorrectly.