Edexcel GCSE Maths exam technique

How the exams work

Pearson Edexcel GCSE Mathematics (1MA1) Higher tier is examined by three written papers at the end of the course, each worth one third of the GCSE, and any topic can be tested on any paper. Across the qualification, algebra carries about 30% of the marks, ratio, proportion and rates of change and geometry and measures about 20% each, and number and probability and statistics about 15% each; about 40% of the marks test standard techniques (AO1), 30% reasoning and communicating (AO2) and 30% problem solving (AO3). Higher tier awards grades 4 to 9, with a grade 3 allowed if you only just miss a grade 4.

Paper	Time	Marks	Calculator	What’s on it
Paper 1 (1MA1/1H)	1 h 30 min	80	Not allowed	The whole specification: number; algebra; ratio, proportion and rates of change; geometry and measures; probability; statistics. Questions start easier and get harder. With no calculator, expect written methods and exact answers: fractions, surds, answers in terms of π and exact trigonometric values.
Paper 2 (1MA1/2H)	1 h 30 min	80	Allowed	The whole specification, as for Paper 1: number; algebra; ratio, proportion and rates of change; geometry and measures; probability; statistics. Questions start easier and get harder, and numbers can be awkward, so rounding and accuracy matter.
Paper 3 (1MA1/3H)	1 h 30 min	80	Allowed	The whole specification, as for Papers 1 and 2: number; algebra; ratio, proportion and rates of change; geometry and measures; probability; statistics. Topics already tested on Papers 1 and 2 can come up again, so keep revising everything between papers.

Exam technique

In the weeks before

Revise the whole specification for every paper. Edexcel can set any topic on any of the three papers, so never assume a topic is “due” on Paper 3 because it was missing from Paper 1.
Recent exam series have provided a formulae sheet: check with your teacher what you will have, and learn it by using it, not by reading it. It has included things like the quadratic formula, Pythagoras and the trigonometric ratios, the sine and cosine rules, ½ab sin C and compound interest, but it will not tell you which one a question needs.
Memorise what is not on the sheet: angle facts and circle theorems, exact trigonometric values, the equation of a circle, y = mx + c, speed = distance ÷ time and density = mass ÷ volume, and the formulae for the area of a triangle and a parallelogram and the volume of a cuboid. Formulae you are not expected to know, such as the volume of a cone or sphere, are printed in the question when needed.
From about six weeks out, practise mixed papers rather than one topic at a time. Real papers jump from topic to topic, and recognising what a question is about is a skill in itself.
In the last month, sit at least one full 90-minute paper a week, alternating the non-calculator paper and a calculator paper, and write your answers on paper as you will in the exam.
Keep a mistakes list: the question, what went wrong and the correct method. Redo each one a week later without looking at the answer.
Use the same calculator all year so you know exactly where every function is.

The night before and the morning of the exam

Pack the night before: black pens (and spares), an HB pencil, sharpener, eraser, a ruler marked in centimetres and millimetres, a protractor and a pair of compasses. For Papers 2 and 3, add your calculator and check the battery. Tracing paper may be used, so ask the invigilator if you want some for rotations or reflections.
The night before, only review: your cheatsheets, the facts you must memorise, the formulae sheet and your mistakes list. Do not start new topics, and get a proper night’s sleep.
On the morning, do 10 to 15 minutes of easy warm-up questions to get into maths mode, not a full paper. Before Paper 1, include some written arithmetic: a long multiplication, a fraction division and a surd to simplify.
Before Papers 2 and 3, check your calculator is in degrees (a D or DEG on the display) so trigonometry answers come out right.
Eat breakfast, arrive early, and bring a clear water bottle with the label removed if your centre allows it.

The first five minutes

Fill in your name, centre number and candidate number in the boxes on the front cover first.
Read the front cover: it confirms 80 marks, whether you may use a calculator, and that diagrams are not accurately drawn unless the question says so.
Flick through the whole paper. Questions start easier and get harder, but not perfectly: a later question can still have an easy first part, so note where the quick marks are.
Work out your checkpoints from the start time and jot them down, for example: start 9:00, about halfway through the marks by 9:40, last question by 10:20, then 10 minutes to check.
Start at question 1 and work forwards. Early questions build confidence and bank time for the hard ones at the end.

Timing

Each paper is 80 marks in 90 minutes: about 1 minute per mark, leaving about 10 minutes to check. A 2-mark part is worth about 2 minutes; a 5-mark problem about 5 or 6.
The marks for each part are shown in brackets and each question ends with its total. Use them to judge how much working is expected and how long to spend.
Early questions usually take less than a minute per mark. Keep that spare time for the final questions, which often take longer per mark.
If a question has taken a couple of minutes more than its marks suggest and you are not getting anywhere, circle the question number, write down anything you have, and move on.
Save the last 10 minutes for circled questions first, then checking.
Never leave a question blank because of time: a first step written in 30 seconds can earn a method or process mark.

Reading the question

Underline what you are actually asked to find: “the area of the shaded region”, “how many more”, “the percentage profit”, “the total cost including delivery”.
Circle any instruction about the form of the answer: simplest form, in terms of π, in the form a + b√3, in standard form, as a fraction, correct to 3 significant figures. Ignoring it usually loses the final accuracy mark.
Look for mixed units (cm and m, minutes and hours, g and kg) and for the unit printed on the answer line.
“You must show all your working” (or “you must show your working”) means an answer on its own scores no marks, even if it is correct.
“Give reasons for your answer” or “give reasons for each stage of your working” means the reasons are part of the marks, not an optional extra.
“Hence” means use the result you have just found. “Hence, or otherwise” lets you use another method, but the previous part is usually the quickest route.
Every piece of information in a question is there for a reason. If you finish without using a length, a ratio or a fact such as “the cross-section is uniform”, check whether you have missed a step.
“Diagram NOT accurately drawn” means you must work from the information given, not measure the diagram.

Short questions and multi-step problems

1-mark “write down” questions need only the answer. Do not spend time on long working.
Standard 2 and 3 mark questions (expand and simplify, solve an equation, find the nth term, work out a percentage change) are usually a method mark then an accuracy mark. Write one clear step per line.
Unstructured problems worth 4 to 6 marks give a context (tiles, paint, fuel, a savings account) and no guidance on the steps. Edexcel awards a P mark for each correct process, so every correct step you write down counts.
Before writing, plan: what does the question want, what can you work out from the information, and what must you find first? Working backwards from the final answer often reveals the route.
Label each calculation so the examiner can follow it: “Area of wall = 4.5 × 2.4 = 10.8 m²” is clearer than a string of numbers.
Decision questions (“Does Maya have enough?”, “Which is the better value?”) end with a communication mark. State the decision and the figures that support it, for example: “No, she needs 11 litres but only has 10 litres.”
In multi-part questions, later parts often use earlier answers. If you cannot do part (a), use a sensible value or your own answer in part (b): you can still earn follow-through marks.

Reasoning, explaining and assumptions

When asked to give a reason or explain, write one precise mathematical sentence that uses values: “No, because the mean for Year 10 is 6.2 and for Year 11 is 5.8.” “Because it is bigger” earns nothing.
Error-spotting questions show someone’s working (“Sam’s method is shown. What mistake has he made?”). Name the exact step and say what should have happened: “He divided by 1.2 instead of multiplying by 1.2.”
Assumption questions ask you to state one assumption you made, often with a follow-up asking how it affects your answer. Tie the assumption to the context (“each worker fills boxes at the same rate”, “the price does not change”) and say whether your answer would be too big or too small, and why.
When comparing two distributions, make one comparison of an average (median or mean) and one of spread (range or interquartile range), each with values and in context: “Group A’s times were more consistent because their IQR was smaller (4 minutes compared with 9).”
Angle and circle theorem reasons must use the proper wording: “alternate angles are equal”, “angles on a straight line add up to 180°”, “the angle at the centre is twice the angle at the circumference”. Informal names such as Z angles or F angles are not accepted.
Give a reason for every angle you use in a chain, not just the last one.

“Show that” and proof

In a “show that” question the answer is given, so every mark is for the working. Show every step, including the ones that feel obvious, and finish by writing the given result.
Start from the information in the question, not from the answer. For “show that the area is 36 cm²”, calculate the area from the lengths; do not start with 36.
When the given result is rounded, such as “show that x = 5.7 correct to 1 decimal place”, write a more accurate value first (5.73…) and then round it.
Algebraic proof: define your letters first. For an integer n, use 2n for an even number, 2n + 1 for an odd number and n, n + 1, n + 2 for consecutive integers. Expand, simplify, factorise out the number you need (for example 8(n + 1)) and finish with a sentence: “8(n + 1) is a multiple of 8 because n + 1 is an integer.”
Testing a few numbers never proves a statement is always true; one counter-example is enough to prove it is false.
To prove an identity, work on one side and simplify until it equals the other side. Do not treat it as an equation to solve.
Congruence proofs: give three pairs of equal sides or angles, each with a reason, then state the condition: SSS, SAS, ASA (or AAS) or RHS.
Recurring decimal proofs: let x equal the decimal, multiply by a power of 10 so the repeating parts line up, subtract to remove them, then write the fraction in its simplest form.
Vector proofs: to show three points lie on a straight line, show one vector is a multiple of another (for example PR = 3PQ) and state that they share a point.
To show an equation has a solution between two values, substitute both, show one result is positive and one negative, and write “there is a change of sign, so there is a solution between 2 and 3”.

Graphs, diagrams and constructions

Plot points with small, neat crosses in pencil. Join quadratic, cubic, reciprocal and exponential graphs with one smooth curve, not straight segments with a ruler, and never join a reciprocal graph across the axis it approaches.
When reading from a graph, draw the lines across to the curve and down to the axis so your method is visible. Examiners accept readings within a small tolerance, so an accurate graph and clear lines matter.
To solve an equation graphically, draw the extra line it needs (such as y = 2x + 1) on the same axes and read off the x-coordinates where the two graphs cross.
For a gradient at a point, draw a tangent with a ruler and use two points far apart on it. For the area under a curve, split it into strips (usually trapezia) and, if asked, say whether your estimate is too big or too small.
Cumulative frequency: plot each point at the upper end of its class. Histograms: the vertical axis is frequency density = frequency ÷ class width, and the frequency is the area of the bar.
Constructions use a ruler and compasses only. Leave all construction arcs visible: when the question says “you must show all your construction lines”, a correct line without arcs scores nothing. Shade loci regions clearly.
Describe transformations fully and as one single transformation: rotation (angle, direction and centre), reflection (equation of the mirror line), translation (column vector), enlargement (scale factor and centre). Giving a combination of two transformations scores no marks.
Tree diagrams: the probabilities on branches from each point add up to 1, and for “without replacement” the second-stage denominators go down by one. Venn diagrams: check every region and the total.
Write the lengths and angles you find onto the diagram as you go: it helps you see the next step, and the examiner can credit it.

Showing working: how the marks are given

Edexcel mark schemes use M marks for a correct method, P marks for a correct process in a problem-solving question, A marks for an accurate answer (usually only after the method is shown), B marks for a correct answer or fact that needs no method, and C marks for a correct statement or conclusion.
A correct answer with no working usually gets full marks, but a wrong answer with no working gets none. Working is your insurance against a slip.
Follow-through (ft) means that if you get part (a) wrong but use your answer correctly in part (b), you can still earn marks in part (b).
Write your final answer on the answer line. If the line is blank the examiner will look for an answer in your working, but a different value on the line from the one in your working can cost the accuracy mark.
Set out one step per line and only use = between things that really are equal. Writing 5 × 6 = 30 + 4 = 34 is wrong mathematics, even if 34 is the right answer.
The answer space is a guide only; there may be more space than you need. Scripts are scanned and marked on screen, so keep your writing inside the page and out of the side margins marked “DO NOT WRITE IN THIS AREA”.
Cross out with one neat line so the work can still be read. Crossed-out work is usually marked only if you have not replaced it. If you leave two different methods standing, you may only get the marks for the weaker one, so decide which to keep.
If you run out of space, ask the invigilator for extra paper and write next to the question where the rest of your answer is.

Paper 1: without a calculator

Make written methods quick and reliable: long multiplication, division by a decimal, and all four operations with fractions and mixed numbers.
Leave answers exact unless told otherwise: fractions, simplified surds (√48 = 4√3) and multiples of π. Converting to a rounded decimal can lose the mark.
Know the exact values of sin and cos of 0°, 30°, 45°, 60° and 90°, and tan of 0°, 30°, 45° and 60°. They come up in non-calculator trigonometry.
Know squares up to 15², the cubes of 1 to 5 and 10, powers of 2, and common fraction, decimal and percentage equivalents.
For “work out an estimate”, round each number to 1 significant figure (unless a nearby number is clearly easier), write the rounded values down, then calculate. You may be asked whether your estimate is too big or too small.
Standard form: use index laws on the powers of 10, then adjust so the first number is at least 1 and less than 10.
Negative and fractional indices: take the root first, then the power, then the reciprocal if the index is negative, for example 27^−2/3 = 1/9.
Questions are designed to work out cleanly without a calculator. If your numbers become very awkward, recheck your earlier steps.

Papers 2 and 3: using your calculator

Check the calculator is in degrees before any trigonometry.
Use brackets generously: around a whole numerator and denominator, and around a negative number you are squaring, so (−4)² gives 16, not −16.
Do not round partway through. Keep full values in the calculator (the ANS key or memory) and round only the final answer. Early rounding is one of the most common reasons for losing the accuracy mark.
Write down the full calculator display before rounding, for example 23.41672… = 23.4. If the rounding goes wrong, you still get the method marks.
Iteration: type your starting value and press =, then type the formula using ANS in place of x and press = repeatedly. Write each value down to the accuracy asked.
Know your calculator’s keys for fractions, switching between fraction and decimal, standard form (×10^x), powers and roots, and reciprocals. If your calculator has a table function, use it to generate tables of values.
Use the π button. If your calculator does not have one, use 3.142 unless the question says otherwise.
Calculator papers still test algebra, proof and reasoning. The calculator can check them, though: substitute a value such as x = 3 into both sides of an expansion to test it.

Units, rounding and accuracy

Significant figures start at the first non-zero digit: 0.004387 to 2 significant figures is 0.0044. Decimal places count digits after the decimal point.
If no accuracy is given, 3 significant figures is a sensible choice for an answer that is not exact. Money is written to 2 decimal places: £4.50, not £4.5.
Convert units before calculating. 1 m² = 10 000 cm², 1 m³ = 1 000 000 cm³, 1 litre = 1000 cm³, and 2.25 hours is 2 hours 15 minutes, not 2 hours 25 minutes.
Error intervals use ≤ at the lower end and < at the upper end: a length of 6.4 cm to 1 decimal place is 6.35 ≤ L < 6.45. For truncation, the lower end is the truncated value itself: 6.4 ≤ L < 6.5.
Bounds in calculations: for the maximum of a sum or product, use both upper bounds; for the maximum of a difference or quotient, use the upper bound of the first value and the lower bound of the second. Swap them round for a minimum.
“To a suitable degree of accuracy” means round the upper and lower bounds to the most accurate value they both agree on, and say that this is why.
Probabilities must be fractions, decimals or percentages, never a ratio such as 1 : 4 or words such as 1 in 4.
If the answer line shows a unit, give your answer in that unit. If it does not, write the unit yourself.

Checking

In the final 10 minutes, deal with circled questions first, then check the high-mark questions you went through quickly.
Substitute solutions back into the original equation, and check simultaneous equation answers in both equations.
Sense-check sizes: a probability above 1, a negative length, an angle in a triangle over 180° or a person 12 m tall means something has gone wrong.
Check the form of each answer against the question: simplest form, exact value, units, the accuracy asked.
Look for parts you have missed, especially a part on the next page after “Turn over”, or a table or graph you were asked to complete.
Redo key calculator work by entering it a different way, rather than just reading your working again.

When you are stuck

Give it a couple of minutes, then circle the question and move on. Coming back later with fresh eyes often shows you the way in.
Write down what you know: mark lengths and angles on the diagram, write a relevant formula, work out anything you can. First steps earn P and M marks even if you never finish.
Ask yourself which topic this is and what the question is testing. Look for clues: an earlier part, the word “hence”, or information you have not used yet.
Call the unknown x and form an equation from the facts you are given; many hard problems turn into a linear or quadratic equation.
Try the idea with simpler numbers, or draw a sketch if there is no diagram.
If you cannot do an early part, still attempt later parts using a sensible value.
There is no penalty for a wrong answer, so always leave a sensible attempt rather than a blank.

Learning from mocks

Mark your mock honestly with the mark scheme and note which marks you dropped: method, process, accuracy or communication.
Sort every lost mark into one of four groups: did not know the topic, made a slip, misread the question, or ran out of time. Each group needs a different fix.
Topic gaps: relearn from the notes, do the worksheet, then a short custom paper on that subtopic. Slips: redo the question until you get it right, and add it to your mistakes list. Misreads: practise underlining the question and the answer form. Time: more timed papers, and move on sooner.
Redo every question you dropped marks on within a week, without looking at the answer.
Track your score for each paper and each topic from one mock to the next, so you can see whether your fixes are working.
Sit the next mock in real conditions: 90 minutes, no notes, no calculator on Paper 1, and a quiet room.

Command words

Word

What it means

How to answer

Example

Write down

The answer can be given straight away, with little or no working. Usually 1 mark.

Give the answer directly. A short step is fine but not required. Do not spend time on long methods.

Write down the value of 9⁰. (Answer: 1)

Work out / Calculate / Find

Use a method to reach an answer. They mean the same thing; “calculate” is common on calculator papers.

Show each step so method marks can be given, then write the final answer on the answer line with units and the accuracy asked.

Work out the area of a triangle with base 9 cm and height 6.4 cm. (½ × 9 × 6.4 = 28.8 cm²)

Estimate

Find an approximate answer: by rounding the numbers first, by reading from a graph, or from grouped data or a sample.

Write the rounded values down (usually 1 significant figure) and then calculate with them. For grouped data, use the midpoint of each class.

Work out an estimate for (48.7 × 3.12) ÷ 0.51. (50 × 3 ÷ 0.5 = 300)

Simplify

Write an expression, fraction, ratio or surd in its simplest form.

Collect like terms, cancel common factors or apply the index laws, and keep going until nothing more can be done.

Simplify (3x²y)³. (27x⁶y³)

Expand

Multiply out the brackets. “Expand and simplify” also means collect like terms.

Multiply every term in one bracket by every term in the other, watching the signs. For three brackets, expand two first, then multiply by the third.

Expand and simplify (x + 4)(2x − 3). (2x² + 5x − 12)

Factorise

Write an expression as a product using brackets. “Factorise fully” means take out the highest common factor completely.

Take out the HCF of the numbers and letters, or find the two brackets for a quadratic. Expand your answer in your head to check it.

Factorise fully 12x²y − 18xy. (6xy(2x − 3))

Solve

Find the value or values of the unknown that make an equation or inequality true.

Do the same to both sides at each step. Give every solution of a quadratic, keep the inequality sign in an inequality, and list integer values if the question asks for them.

Solve 5(x − 2) = 3x + 7. (5x − 10 = 3x + 7, so 2x = 17 and x = 8.5)

Make … the subject

Rearrange a formula so the named letter is on its own on one side.

Undo the operations in reverse order. If the letter appears twice, collect those terms on one side and factorise.

Make t the subject of v = u + at. (t = (v − u) ÷ a)

Write … in the form

Give your answer in exactly the form shown, such as (x + a)² + b, a + b√c or A × 10ⁿ.

Rearrange until your answer matches the form, then check the values of a, b and c meet any conditions given (for example integers).

Write x² − 8x + 5 in the form (x − a)² − b. ((x − 4)² − 11, so a = 4 and b = 11)

Show that

The answer is given; you must write the working that gets there.

Start from the information in the question, show every step and end with the given result. With a rounded answer, show a more accurate value first.

Show that the interior angles of a hexagon add up to 720°. ((6 − 2) × 180° = 720°)

Prove

Show that a statement is always true, using algebra or a chain of geometric reasons.

Define your letters, set out each step with reasons, and finish with a sentence stating what you have proved. Numerical examples are not a proof.

Prove that the sum of any three consecutive integers is a multiple of 3. (n + (n + 1) + (n + 2) = 3n + 3 = 3(n + 1), which is a multiple of 3)

Hence

Use the result you have just found. “Hence, or otherwise” allows another method, but the previous part is usually the fastest route.

Start from your answer to the earlier part. A method that ignores it may not get the marks when only “hence” is written.

(a) Factorise x² + 2x − 15. (b) Hence solve x² + 2x − 15 = 0. ((x + 5)(x − 3), so x = −5 or x = 3)

Explain / Give a reason

Write a short statement in words, backed up by mathematics.

Refer to specific values or facts. For angles, use the correct name of the fact. Answer any yes/no part clearly as well.

Ali says 0.3 × 0.2 = 0.6. Explain why he is wrong. (0.3 × 0.2 = 0.06: 3 × 2 = 6 and there are two decimal places in the question, so two in the answer)

Interpret

Say what a value, gradient or intercept means in the real-life context of the question.

Use the quantities and units from the question, for example “per hour” or “per year”.

A graph of a car’s value (£) against its age (years) has gradient −850. Interpret the gradient. (The car loses £850 of value each year)

Describe

Give the details in words. “Describe fully” means give every detail needed.

For a transformation, name one single transformation and give all its details. For correlation, give the type and what it means in context.

Triangle A has vertices (1, 1), (3, 1) and (1, 2). Triangle B has vertices (1, −1), (1, −3) and (2, −1). Describe fully the single transformation that maps triangle A onto triangle B. (Rotation 90° clockwise about (0, 0))

Compare

Say how two sets of data are similar or different.

Make one comparison of an average and one of spread, quoting values and relating each to the context.

Compare journey times for Bus A (median 24 min, IQR 6 min) and Bus B (median 19 min, IQR 11 min). (Bus B was quicker on average; Bus A’s times were more consistent)

Draw / Plot

Plot: mark points accurately on a grid. Draw: produce an accurate graph, line or diagram.

Use a sharp pencil and small crosses. Use a ruler for straight lines and a smooth freehand curve for quadratics, cubics and reciprocals.

Complete the table of values for y = x² − 3x, then draw the graph.

x	−1	0	1	2	3	4
y	4		−2		0

(Missing values: 0, −2 and 4. Plot all six points and join them with one smooth U-shaped curve, with its lowest point between x = 1 and x = 2)

Complete

Fill in the missing parts of a table, diagram or statement.

Fill in every gap and check totals: tree diagram branches from each point add to 1, and Venn diagram regions add to the total.

ξ = {1, 2, …, 12}, A = multiples of 3, B = even numbers. Draw and complete a Venn diagram for A and B. (A ∩ B = {6, 12}; A only {3, 9}; B only {2, 4, 8, 10}; outside both circles {1, 5, 7, 11})

Sketch

Show the general shape and key features of a graph or diagram. An accurate scale is not needed.

Get the shape right and label the important points with coordinates: intercepts, turning points, and any asymptotes.

Sketch y = (x − 2)² + 1, labelling the turning point and the y-intercept. (U-shaped curve, turning point (2, 1), y-intercept (0, 5))

Construct

Draw accurately using a ruler and a pair of compasses.

Keep the compass width fixed where needed and leave every construction arc visible. Without the arcs you will not get the marks.

Draw any angle ABC. Use ruler and compasses to construct the bisector of angle ABC. You must show all your construction lines. (Arc from B cutting both arms; equal arcs from those two points that cross; a ruled line from B through the crossing point)

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