Mark Scheme Patterns & Common Mistakes

Understanding how AQA awards marks — and how students lose them — is one of the most powerful exam strategies available to you. This lesson explains the marking system, identifies the most common mark-losing mistakes by topic, and teaches you how to present your answers in a way that maximises your marks.

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How AQA Awards Marks

Every mark in an AQA GCSE Mathematics exam is classified as one of three types:

Mark Type	Symbol	Meaning	How It Works
Method mark	M	Awarded for using a correct method or approach	You can earn M marks even if your final answer is wrong, provided the method is correct
Accuracy mark	A	Awarded for a correct answer following correct working	Usually depends on the preceding M mark being awarded — you cannot get an A mark without the corresponding M mark
Independent mark	B	Awarded independently for a correct answer or statement	Does not depend on other marks — you either get it or you don't

How M, A, and B marks work together

A typical 3-mark question might be marked as M1 A1 A1 or M1 M1 A1 or B1 M1 A1.

Example: 3-mark question

Question: Solve 3x + 7 = 22

Mark	Awarded For	Student Working
M1	Starting to solve the equation correctly (e.g., subtracting 7)	3x = 15
A1	Correct division	x = 15/3
A1	Correct final answer	x = 5

What this means for you

• Even if your final answer is wrong, you can still score method marks. This is why showing working is so important.
• If you skip the working and write only a wrong answer, you score 0. There is no working for the examiner to award method marks for.
• If you skip the working and write only a correct answer, you usually get full marks — but this is risky because any small error means you get 0 instead of potentially 2 out of 3.

Exam Tip: Always show your working. The only exception is 1-mark questions where the command word is "State" or "Write down". For everything else, show every step.

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Why Correct Answers Can Score Zero

This is a critical concept that catches many students off guard. In certain types of questions, a correct final answer with no working scores zero marks.

When this happens

1. "Show that" questions — The answer is already given. If you just write the answer, you have shown nothing. The marks are entirely for the working.

2. Multi-step questions worth 3+ marks — If the mark scheme says M1 A1 A1 and the final A1 depends on the M1, writing only the answer without showing the method means the M1 cannot be awarded, and without M1, the dependent A marks cannot be awarded either.

3. Questions that say "You must show your working" — This instruction means exactly what it says. A correct answer without working may score 0.

flowchart TD
    A["Question worth 3 marks<br>M1 A1 A1"] --> B{"Did you show working?"}
    B -- Yes --> C{"Is the method correct?"}
    C -- Yes --> D["M1 awarded"]
    D --> E{"Is the final answer correct?"}
    E -- Yes --> F["A1 A1 awarded<br>Total: 3/3"]
    E -- No --> G["Check if intermediate<br>steps are correct"]
    G --> H["Possibly A1 for<br>intermediate step<br>Total: 1/3 or 2/3"]
    B -- No --> I{"Is the answer correct?"}
    I -- Yes --> J["Usually full marks<br>BUT not on ’show that’<br>or ’show your working’<br>questions"]
    I -- No --> K["0/3 — no working<br>to award marks for"]

Exam Tip: If you see "You must show your working" or "Show that", treat every step of your calculation as a potential mark. Write it down, even if it feels obvious.

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Common Mark-Losing Mistakes by Topic

The AQA examiners' reports, published after each exam series, consistently highlight the same mistakes. Here are the most common ones, organised by topic.

Algebra Mistakes

Common Mistake	Correct Approach	Marks Typically Lost
Sign errors when expanding brackets — e.g., -2(x - 3) = -2x - 6	-2(x - 3) = -2x + 6 — the negative multiplied by the negative gives a positive	1 mark
Not expanding brackets correctly — e.g., (x + 3)² = x² + 9	(x + 3)² = x² + 6x + 9 — you must use FOIL or the grid method	1-2 marks
Incorrect factorisation — e.g., x² + 5x + 6 = (x + 1)(x + 6)	x² + 5x + 6 = (x + 2)(x + 3) — check: the two numbers must multiply to give 6 AND add to give 5	2 marks
Forgetting to find both solutions to a quadratic	A quadratic equation has two solutions (or one repeated root). Write both.	1 mark
Errors with negative numbers in substitution — e.g., if x = -3, writing x² = -9	(-3)² = 9 — squaring a negative number gives a positive result	1 mark
Not reversing the inequality sign when multiplying/dividing by a negative	If -2x > 6, then x < -3 (the inequality reverses)	1 mark
Writing = signs incorrectly — e.g., 3x + 2 = 14 = 3x = 12 = x = 4	Each line should be a separate, correct equation: 3x + 2 = 14, then 3x = 12, then x = 4	QWC mark

Geometry Mistakes

Common Mistake	Correct Approach	Marks Typically Lost
Not stating reasons in angle problems	You must name the angle fact used — e.g., "alternate angles are equal", "angles in a triangle sum to 180°", "co-interior angles sum to 180°"	1-2 marks
Missing units in area and volume	Area must be in square units (cm², m²). Volume must be in cubic units (cm³, m³).	1 mark
Confusing area and perimeter	Perimeter = total distance around the outside. Area = space inside. Read the question carefully.	All marks
Using the wrong formula for area of a triangle	Area = 1/2 x base x perpendicular height (NOT slant height)	1-2 marks
Rounding too early in multi-step geometry problems	Keep full calculator precision through intermediate steps and only round the final answer	1 mark
Not converting units before calculating area/volume	If lengths are in different units, convert first. Remember: 1 m² = 10000 cm² (not 100 cm²)	1-2 marks
Giving bearings incorrectly	Bearings must be three figures (e.g., 045° not 45°), measured clockwise from North	1 mark

Statistics Mistakes

Common Mistake	Correct Approach	Marks Typically Lost
Reading scales incorrectly	Count the number of small divisions between labelled values to find the value of each small division	1-2 marks
Using wrong averages from grouped data	For grouped data, the mean uses midpoints of each class interval. You cannot find the exact mean, median, or mode from grouped data — only estimates.	2-3 marks
Confusing mean, median, and mode	Mean = total / count. Median = middle value (when ordered). Mode = most common value.	1-2 marks
Not ordering data before finding the median	The median requires data to be in ascending order first	1 mark
Drawing bar charts with gaps for continuous data	Histograms (for continuous data) have no gaps between bars. Bar charts (for categorical data) have gaps.	1 mark

Ratio Mistakes

Common Mistake	Correct Approach	Marks Typically Lost
Not simplifying ratios	Always simplify ratios to their lowest terms: 12:8 = 3:2	1 mark
Incorrect sharing in a given ratio	To share 120 in the ratio 3:2, total parts = 5, one part = 24, so the shares are 72 and 48 (NOT 60 and 60, NOT 36 and 24)	2 marks
Confusing ratio with fraction	The ratio 3:2 means 3 parts to 2 parts. The fraction of the first part is 3/5 (NOT 3/2).	1-2 marks
Errors with ratio problems involving amounts already given	Read carefully — sometimes the question gives you one share and asks for the other, rather than giving the total	1-2 marks

Exam Tip: Before the exam, review the AQA examiners' reports for recent past papers. These reports highlight exactly where students lost marks and often include examples of common incorrect answers. They are freely available on the AQA website.

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Graph Sketching: What AQA Expects

When asked to "sketch" a graph, AQA expects you to show the key features — not plot every point.

Key features the examiner looks for

Graph Type	Required Features
Linear (y = mx + c)	Correct gradient direction (positive/negative), correct y-intercept, correct x-intercept if asked
Quadratic (y = ax² + bx + c)	Correct shape (U or ∩), vertex position, y-intercept, x-intercepts (roots) if they exist
Cubic (y = ax³ + ...)	Correct shape (S-curve), correct direction, key intercepts
Reciprocal (y = a/x)	Two branches, asymptotes at x = 0 and y = 0, correct quadrants
Exponential (y = a^x)	Correct shape, passes through (0, 1), asymptote at y = 0, correct growth/decay direction
Trigonometric	Correct period, correct amplitude, key values marked

Common graph-sketching errors

1. Not labelling axes — always label x and y axes.
2. Not marking key values — intercepts, turning points, and asymptotes should be labelled with coordinates.
3. Drawing straight lines for curves — use a smooth, continuous curve. Do not connect plotted points with straight line segments.
4. Wrong shape — a y = x² graph should be a smooth parabola, not a V-shape.
5. Ignoring asymptotes — for reciprocal and exponential graphs, draw the asymptote as a dashed line and ensure your curve approaches but never touches it.

Exam Tip: A sketch does not need to be perfectly accurate, but it must show the correct shape, the correct position relative to the axes, and all key features labelled. Use a pencil so you can adjust if needed.

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"Explain" and "Give a Reason" Questions

These questions test AO2 (reasoning and communication). Many students lose marks because they give a description of what they did rather than a mathematical explanation of why.

What counts as a mathematical explanation

Acceptable	Not Acceptable
"Alternate angles are equal"	"The angles look the same"
"The gradient is negative so the line slopes downward"	"It goes down"
"x² is always positive or zero, so x² + 3 is always at least 3"	"It cannot be less than 3"
"The sample is too small to be representative"	"It is not a good sample"
"Correlation does not imply causation"	"You can't say that"

Structure of a good mathematical explanation

1. State the mathematical fact or property you are using.
2. Apply it to the specific situation in the question.
3. Draw a clear conclusion that answers the question.

Worked Example