To score higher in Edexcel International A Level Maths, you need to choose a suitable method, carry it out accurately and show enough reasoning for an examiner to follow it. You also need to answer exactly what was asked: every solution in the stated interval, exact values when requested, justified conclusions and answers interpreted in context.
Most lost marks are not about missing knowledge. They come from habits — rounding too early, dividing away a solution, skipping a step the question required, or forgetting +C. This guide shows you how to fix those habits across the four Pure units, using what Pearson's own examiner reports say students got wrong.
The essentials
- Show the method the question needs, especially when it says not to rely on a calculator.
- Keep full precision until the final answer, and give exact values when asked.
- Solve in the transformed interval for questions like sin 2x = ½, then convert every solution back.
- Never divide by something that could be zero without checking that case first.
- Justify sign-sensitive steps in proofs, and make counterexamples meet every condition.
- Label sketches with intercepts, asymptotes and key points.
- Mark practice papers precisely, then fix the first wrong step, not just the final answer.
1. Know which papers you are preparing for
| Unit | Paper code | Main focus in this guide |
|---|---|---|
| Pure Mathematics 1 | WMA11/01 | Algebra, surds, quadratics, coordinate geometry, graph transformations, trigonometry and introductory calculus |
| Pure Mathematics 2 | WMA12/01 | Proof, sequences and series, the binomial expansion, logarithms, circles, further trigonometry and calculus |
| Pure Mathematics 3 | WMA13/01 | Functions, advanced trigonometry, logarithmic graphs, differentiation, integration and numerical methods |
| Pure Mathematics 4 | WMA14/01 | Partial fractions, advanced integration, differential equations, implicit and parametric differentiation, vectors and proof by contradiction |
Each paper lasts 90 minutes and is worth 75 raw marks — an average of 1.2 minutes per mark, including checking. This table is a revision overview, not a replacement for the full specification. The four Pure units are also not the whole qualification: you need two applied units in an approved combination too. Our guide to Edexcel IAL Maths explains the units and combinations.
What does an A* require?
For IAL Mathematics, Pearson requires both at least 480 UMS out of 600 overall and at least 180 UMS out of 200 across P3 and P4 combined. These are UMS marks, not raw percentages, and the 180 is a combined total: 94 in P3 and 86 in P4 meets it, as long as your overall total also reaches 480.
Watch out
raw grade boundaries change every series. When you judge a practice paper, use the boundaries and UMS conversion for that exact paper.
2. Understand how maths marks are awarded
Assessment objectives
Pearson's specification sets five assessment objectives, with these minimum weightings across the qualification:
| Objective | What it tests | Minimum weighting |
|---|---|---|
| AO1 | Recall, select and use mathematical knowledge and techniques | 30% |
| AO2 | Construct rigorous arguments and proofs, and manipulate expressions | 30% |
| AO3 | Use mathematical models and interpret their results and limitations | 10% |
| AO4 | Translate real contexts into mathematics and comment on the results | 5% |
| AO5 | Use calculators and permitted resources accurately and efficiently | 5% |
These are minimums for the whole qualification, not a fixed split for every question. AO4 is not essay-style evaluation: adding a "balanced judgement" to a calculation does not earn extra marks.
Method, accuracy and independent marks
These are the labels you will meet when you self-mark with an official mark scheme:
| Label | Meaning | What it means for you |
|---|---|---|
| M1 | Method mark, for knowing a method and attempting to apply it | Show a valid method being used |
| A1 | Accuracy mark, which needs the related M mark first | Correct processing and results matter |
| B1 | Unconditional accuracy mark, independent of M marks | State the required fact, result or feature |
| dM1 | Dependent method mark | An earlier specified mark must be earned first |
| ft | Follow through | A mark may be allowed using your earlier wrong value |
| cao | Correct answer only | An earlier error can lose this mark |
| awrt | Answers which round to | Your answer must round to the stated value |
Pearson's mark schemes state that A marks are "correct answer only" unless they are marked as follow-through. So follow-through is not automatic — and writing a formula down does not always earn M1, because some schemes need a substitution or a completed step.
Worked example
Solve 2x² − 5x − 3 = 0.
2x² − 5x − 3 = (2x + 1)(x − 3) = 0
x = −½ or x = 3
The factorisation is visible evidence of the method, as well as the answers.
3. Follow calculator and working instructions precisely
You can use a calculator in all four Pure units, but individual questions can say that solutions relying on calculator technology are not acceptable. Read that instruction before choosing your method.
Pearson's Summer 2024 P1 examiner report describes exactly this: many students lost two marks by using their calculator to solve the quadratic 2x² − 4x − 96 = 0, and others lost marks by not showing the working for rationalising a denominator.
Worked example
Solve 2x² − 4x − 96 = 0, showing your working.
2x² − 4x − 96 = 2(x² − 2x − 48) = 2(x − 8)(x + 6) = 0
x = 8 or x = −6
The same report notes that students who wrote the factorisation as (x − 8)(x + 6), without the factor of 2 or showing the division by 2, also lost marks. Your factorisation must equal the expression you are solving.
When algebraic working is required:
- show factorisation, completing the square, or the quadratic formula with the values substituted;
- show how you rationalise a denominator;
- show the identities and rearrangements used in a proof;
- follow any specified method or answer format.
Worked example
Rationalise 3 ÷ (2 + √5).
Multiply top and bottom by the conjugate, 2 − √5:
3(2 − √5) ÷ ((2 + √5)(2 − √5)) = (6 − 3√5) ÷ (4 − 5) = (6 − 3√5) ÷ (−1)
= 3√5 − 6
Your turn
Rationalise 4 ÷ (3 − √5), showing every step.
AnswerShow answerHide answer
Multiply top and bottom by 3 + √5:
4(3 + √5) ÷ ((3 − √5)(3 + √5)) = (12 + 4√5) ÷ (9 − 5) = (12 + 4√5) ÷ 4
= 3 + √5
An answer without working does not always score zero — it depends on the question and mark scheme. But showing a method protects your chance of partial credit, and it is essential wherever a proof or full working is asked for.
4. Avoid the mistakes that cost capable students marks
Keep full precision until the final answer
The Summer 2024 P1 report says too many students lost the final accuracy mark through rounding and truncation errors in a multi-step triangle calculation.
Store intermediate values in your calculator's memory and use them unrounded. If a value is 1.732050807…, use the stored value, not 1.73. Round only the final answer. Keeping one extra significant figure is not always enough, especially when you subtract two close values.
For exact answers, keep fractions, surds, logarithms and multiples of π exact: π/6 is exact; 0.524 is an approximation.
Solve in the transformed interval
Worked example
Solve sin(2x) = ½ for 0° ≤ x < 360°.
Let u = 2x. The interval becomes 0° ≤ u < 720°.
sin u = ½ gives u = 30°, 150°, 390°, 510°.
Divide every solution by 2: x = 15°, 75°, 195°, 255°
For u = kx + α, transform both ends of the interval, then convert every solution back with x = (u − α) ÷ k. Reverse the order of the endpoints if you multiply by a negative number. And check your calculator's angle mode: the interval tells you whether to work in degrees or radians.
Your turn
Solve cos(2x − 30°) = ½ for 0° ≤ x < 180°.
AnswerShow answerHide answer
Let u = 2x − 30°. The interval becomes −30° ≤ u < 330°.
cos u = ½ gives u = 60° or 300° (−60° is below −30°, so it is outside the interval).
x = (u + 30°) ÷ 2, so x = 45° or 165°.
Do not divide away solutions
Worked example
Solve 2 sin x cos x = sin x.
Factorise: sin x (2 cos x − 1) = 0
So sin x = 0 or cos x = ½
Dividing straight away by sin x would lose the first set of solutions. The same applies whenever you divide by an expression that could be zero: deal with the zero case separately first.
Include the constant of integration
Worked example
∫ 6x dx = 3x² + C
If the curve passes through (2, 5): 5 = 3(2)² + C, so C = −7
y = 3x² − 7
The constant matters just as much in the general solution of a differential equation. Pearson's Summer 2024 P4 report lists forgetting the constant of integration as a reason marks were lost. How much it costs depends on the scheme, but it can damage every later step.
Check domains and restrictions
Before you accept an answer, ask:
- Are logarithm arguments positive?
- Are square roots defined?
- Is any denominator zero?
- Did squaring introduce an extra solution?
- Is the value inside the stated interval?
- Must the number of terms be a positive integer?
- Is a length or time physically possible?
For example, ln(x − 2) = 0 gives x − 2 = 1, so x = 3 — and the condition x > 2 is satisfied.
Tell an expression from an equation
You may divide both sides of an equation by a non-zero constant. You cannot divide an expression by that constant and keep it the same. If f′(x) = 6x² − 4x, then f′(x) is not 3x² − 2x — but solving 6x² − 4x = 0 is equivalent to solving 3x² − 2x = 0.
5. Write convincing proofs and "show that" answers
A "show that" answer needs a derivation
Start from what you are given and build a valid chain to the printed result. Never assume the result is true and use it to justify itself.
Worked example
Show that (1 − cos 2x) ÷ sin 2x = tan x, wherever the expression is defined.
(1 − cos 2x) ÷ sin 2x
= (1 − (1 − 2sin²x)) ÷ (2 sin x cos x)
= 2sin²x ÷ (2 sin x cos x)
= sin x ÷ cos x
= tan x
Each identity and cancellation is visible. Checking a few angles numerically would not prove the identity.
Justify steps that depend on a sign
Pearson's Summer 2024 P2 report says that in an inequality proof, all but the very best students omitted the reasoning when dividing by an expression in positive variables, and lost the final mark.
If xyA < xyB, you can conclude A < B because x > 0 and y > 0, so xy > 0. State that reason. If the divisor were negative the inequality would reverse; if it were zero, dividing would be invalid.
Counterexamples must meet every condition
To disprove "every prime number is odd", the counterexample 2 works: it is prime and even.
For a claim of the form "if A, then B", your example must make A true and B false. An example where A is false proves nothing. The same P2 report notes that only a minority of students found a correct counterexample, and stresses the difference between variables being positive and being any real number.
Proof by contradiction (P4): finish the contradiction
Worked example
Prove that √7 is irrational.
- Assume √7 = a/b, where a and b are integers, b ≠ 0, and the fraction is in its lowest terms.
- Squaring gives a² = 7b², so 7 divides a². Since 7 is prime, 7 divides a.
- Write a = 7k. Then 49k² = 7b², so b² = 7k², and 7 also divides b.
- This contradicts a and b having no common factor. Therefore √7 is irrational.
Your ending must say what the contradiction is, not just that there is one.
6. Make graph sketches mathematically informative
The Summer 2024 P1 report records students losing marks for not marking where the graph meets the axes, even when the graph itself looked correct.
A sketch should show what the question needs: the shape, intercepts with coordinates, asymptotes, important points and a sensible domain. You do not need every turning point unless it is asked for.
Transform points correctly
For a point (a, b) on y = f(x):
| New graph | Where the point moves |
|---|---|
| y = f(x) + k | (a, b + k) |
| y = f(x − h) | (a + h, b) |
| y = cf(x) | (a, cb) |
| y = f(cx), c ≠ 0 | (a/c, b) |
| y = −f(x) | (a, −b) |
| y = f(−x) | (−a, b) |
Watch out
the old y-intercept does not always become the new one. For g(x) = f(x − 3), the old point (0, f(0)) moves to (3, f(0)) — but the new y-intercept is (0, f(−3)). Find new x-intercepts by solving g(x) = 0 and the y-intercept by substituting x = 0.
Label logarithmic graphs correctly (P3)
For T = ax^n, with positive quantities, taking logs gives:
Rule
log T = log a + n log x
On a graph of Y = log T against X = log x, the gradient is n and the vertical intercept is log a. If the intercept is c (using base b logs), then a = b^c.
Label the axes as log T and log x, not T and x. The Summer 2024 P3 report says sketching a log graph was challenging for many students, with missing intercept values among the errors.
7. Choose calculus methods deliberately
Differentiation: identify the structure first
| Structure | Likely method |
|---|---|
| A power of a function | Chain rule |
| Two functions multiplied | Product rule |
| A quotient | Quotient rule, or rewrite it |
| An equation mixing x and y | Implicit differentiation |
| x and y both given in terms of t | Parametric differentiation |
In implicit differentiation, y depends on x, so:
Rule
d/dx(y²) = 2y dy/dx and d/dx(xy) = y + x dy/dx
The Summer 2024 P4 report highlights students failing to differentiate the 2xy term fully.
For parametric curves, dy/dx = (dy/dt) ÷ (dx/dt), where dx/dt ≠ 0. Differentiate both before substituting a value of t.
For a tangent at (x₀, y₀), use y − y₀ = m(x − x₀). For the normal, use gradient −1/m when m ≠ 0. A horizontal tangent has a vertical normal, x = x₀.
Integration: use the form to choose a method
| Structure | Likely approach |
|---|---|
| Polynomials or powers | Rewrite, then integrate term by term |
| A function multiplied by its derivative | Substitution or reverse chain rule |
| A suitable product | Integration by parts |
| A rational function with a factorisable denominator | Partial fractions |
| Powers or products of trig functions | Identities, substitution or another suitable technique |
These are starting clues, not rigid rules — and if the question specifies a method, use it.
Watch out for the coefficient of the inner function:
Worked example
∫ 5 ÷ (2x − 1) dx = (5/2) ln|2x − 1| + C
The ½ compensates for the derivative of 2x − 1, which is 2. Differentiate your answer to check it.
For substitution, change every part, including the limits:
Worked example
Find ∫ from 0 to 1 of 2x√(x² + 1) dx, using u = x² + 1.
du = 2x dx. When x = 0, u = 1; when x = 1, u = 2.
= ∫ from 1 to 2 of u^(1/2) du = [(2/3)u^(3/2)] from 1 to 2
= (2/3)(2√2 − 1)
Alternatively, substitute back to x before using the original limits. Never apply x-limits to an answer still written in u.
For integration by parts, make clear what you differentiate and what you integrate: ∫ xe^x dx = xe^x − ∫ e^x dx = xe^x − e^x + C.
For areas, separate a signed integral from a geometric area: split at crossing points and integrate upper minus lower. For volumes of revolution about the x-axis, use V = π∫ y² dx, with cubic units where appropriate.
8. Treat vectors as geometry (P4)
Pearson's Summer 2024 P4 report notes students losing marks by subtracting vectors that should have been added, misunderstanding which vectors were perpendicular, and using a line's direction vector where they needed a point on the line. It suggests a diagram would often have helped.
If OA = a and OB = b, then AB = b − a. For a line r = a + λd, a locates a point on the line and d gives its direction.
- Perpendicular: for non-zero vectors, u · v = 0.
- Angle between vectors: cos θ = (u · v) ÷ (|u||v|). For the acute angle between two lines, use the absolute value of the scalar product of their direction vectors.
- Intersections in 3D: use a different parameter for each line, solve two component equations, then check the third. Two matching components are not enough.
- Foot of the perpendicular from P to a line: write the point Q on the line in terms of its parameter, solve QP · d = 0, then find |QP|.
A vector diagram does not need x- and y-axes. Labelled points, lines and angles are usually more useful.
9. Numerical methods (P3): justify roots and control iteration
A sign change needs continuity
Worked example
f(x) = x³ − x − 1.
f(1) = −1 and f(2) = 5. f is a polynomial, so it is continuous on [1, 2]. Because there is a sign change, there is a root between 1 and 2.
The specification itself requires f(x) to be continuous on the interval. A sign change alone is not enough: 1/x changes sign across 0 but has no root. And a sign change shows a root exists — it does not show there is only one.
Iteration checklist
- Write down the iteration formula and starting value.
- Use the latest value in each new calculation.
- Keep unrounded values in your calculator.
- Give the requested iterations, to the requested accuracy.
- If you must justify a rounded root, evaluate the original continuous function at the rounding boundaries. Two matching iterates alone may not be enough.
10. Revise each unit with its own priorities
These are suggested practice priorities, not predictions of the next paper.
P1: make foundation algebra reliable
Practise surds, indices, quadratics, the discriminant and inequalities, alongside coordinate geometry, graph transformations, radians, arcs and sectors, and basic calculus. Convert fractional and negative powers accurately. Remember that a line tangent to a curve gives a repeated root, so the discriminant is zero.
Check
can you solve a multi-step line-and-curve question without calculator-only algebra, then use the result in a later part?
P2: connect techniques and justify conclusions
Practise proof and counterexamples, arithmetic and geometric sequences and series, the binomial expansion, logarithmic equations, circles, trigonometric equations and integration.
For (a + b)^n, the general term is nCr × a^(n − r) × b^r. When finding a coefficient, work out which term gives the power of x you need before simplifying. Separate a single term from a sum of terms, and check that n is a whole number where it must be.
Check
can you explain why an inequality step is valid, and give a counterexample that meets every condition?
P3: control functions, trigonometry and numerical methods
Practise domains and ranges, inverse and composite functions, modulus equations, compound and double angles, differentiation, integration and numerical methods.
Worked example
For a sin x + b cos x = R sin(x + α), expand the right-hand side:
R sin x cos α + R cos x sin α
So R cos α = a, R sin α = b, and R = √(a² + b²).
Choose the quadrant of α from the signs of both coefficients — your calculator's tan⁻¹ alone can mislead you.
The Summer 2024 P3 report notes that many students did not write out the expression in full after finding R and α, which was needed for the final mark. It also found that many did not see how to use their answer from part (a) in part (b), and some left extra answers in the range or found only one of the two solutions.
Check
can you recover every solution after transforming an angle, and use an earlier result in a later part?
P4: organise longer solutions
Practise partial fractions, substitution, integration by parts, differential equations, implicit and parametric differentiation, vectors, binomial expansions and proof by contradiction.
For a separable differential equation, show the separation, the integration, the constant, the use of the initial condition and the final answer in context. For dy/dt = ky, the solution y = Ae^(kt) follows when y ≠ 0; if dividing by y excludes a possible zero solution, consider it separately where it matters.
For a binomial expansion of (1 + u)^n where n is not a positive integer, check the validity condition |u| < 1, and factor out constants correctly first.
Check
can you complete a long solution while keeping your variables, limits, constants and geometry consistent?
11. Understand command words
| Command | What to do |
|---|---|
| Find / calculate | Obtain the quantity, with suitable working |
| Solve | Give every solution, respecting the domain or interval |
| Show that | Derive the printed result convincingly |
| Prove | Give a general logical argument that covers the stated conditions |
| Disprove | Give a valid counterexample or another rigorous disproof |
| Hence | Use the previous result, as directed |
| Hence, or otherwise | The previous result is a suggested route; another valid method is allowed |
| Deduce | Draw a justified conclusion from what you already have |
| Sketch | Show the shape and the required features |
| State | Give the fact or result concisely |
| Explain / justify | Give a mathematical reason for your conclusion |
| Give an exact value | Use an exact expression, not a rounded decimal |
Command words do not have fixed mark ranges, so read the whole instruction, including any required method or answer form.
Tip
if an earlier part gives a printed result you could not derive, use it in the later parts. Do not abandon the rest of the question.
12. Use past papers to change your performance
Another past paper only helps if it shows you something you then improve. You can find every Pure unit on Starley's Edexcel International A Level Mathematics past papers page.
A five-stage routine
- Attempt it on your own. Use topic questions to learn techniques and mixed, timed papers to practise choosing them. Keep some papers unseen for later.
- Mark it precisely. Read the M, A and B marks and the notes beside them. Do not give yourself marks for steps you meant to write but did not.
- Find the first error — the earliest line where your reasoning went wrong or was not enough.
- Write a specific correction. Replace "be careful" with something like "transform the interval before solving sin 2x" or "recalculate the y-intercept after a horizontal translation".
- Redo it without help. Come back after a few days, then try a different question on the same skill.
| Error type | Example | Next action |
|---|---|---|
| Knowledge | Missing identity or formula | Recall it, then apply it in short questions |
| Method choice | Wrong integration technique | Compare structures and explain your choice |
| Algebra | Sign or bracket error | Practise that specific manipulation |
| Instruction | Gave a decimal instead of an exact answer | Underline the answer requirements before solving |
| Completeness | Missing trig solution or proof ending | Use a targeted final check |
| Time | Too long on one hard part | Practise moving on and coming back |
Record marks lost by cause, not just paper totals. If several papers show the same weakness, fix that skill before doing another full paper.
How much practice?
There is no guaranteed number of papers for an A or A*. Better signs are choosing methods on your own, succeeding on delayed reattempts, finishing in time and making fewer repeated errors on unseen questions.
- Rebuilding basics? Prioritise short topic sets.
- Know the content but can't spot the method? Use mixed questions.
- Already scoring well? Focus on unfamiliar multi-step problems and small, recurring losses.
13. Manage the 90 minutes
One approach is to aim to finish your main attempt in about 75–80 minutes, leaving 10–15 minutes to revisit gaps and check. That is a suggestion to test in practice, not a Pearson rule.
Before each question, note the task, any restrictions, the answer format and any earlier results you can use. If you cannot see a route after a reasonable attempt, write down any valid setup, leave space and move on — later questions often have accessible parts.
When you check, look for specific errors rather than just rereading:
- Substitute solutions back into the original equation.
- Differentiate your integral.
- Check trig solutions and the ends of the interval.
- Check all three components of a vector intersection.
- Check graph intercepts using the transformed equation.
- Check units, signs, size and the requested accuracy.
Our guide to making an A Level revision timetable can help you fit regular timed practice into your week.
Frequently asked questions
Can I get marks if my final answer is wrong?
Yes. Valid method steps can earn credit, and some schemes allow follow-through. The exact marks depend on the question, so show your working clearly.
Do I need to show every tiny arithmetic step?
Show enough to establish the method and the important algebraic steps. Give fuller detail when you are proving a result or when the question says all working must be shown.
Must I write the differentiation rule before using it?
Not always. A clearly correct application can show the method. Quoting the formula can still help make your intention clear if you later slip in the substitution.
What if I cannot reach a "show that" answer?
Leave your genuine attempt visible. If the printed result is used in a later part, carry on from it rather than leaving that part blank.
Does a missing +C lose the whole question?
No, but it can lose a mark or derail later work, especially in differential equations. The question's mark scheme decides the consequences.
Is an exact answer always required?
Follow the instruction. Give exact values when asked, and keep your working exact where you can. If a decimal is asked for, round at the end to the stated accuracy.
Should I only learn the topics that come up most often?
No. Past papers show you question styles and your own weaknesses, but they do not remove anything from the specification. Use them alongside a complete topic checklist.
What should I do in the final week?
Review your recurring errors, redo selected hard questions, complete a manageable amount of timed practice, and make sure you know your formula booklet and calculator well.
Final exam checklist
Before you leave each solution, check:
- I have answered the actual question and used any required method.
- Enough working is visible to justify the result.
- I have included every valid solution and rejected invalid ones.
- My angle mode and transformed interval are correct.
- I kept full precision and used the requested answer form.
- I included a constant of integration where needed.
- My proof justifies sign-sensitive steps and reaches a stated conclusion.
- Graph features and vector relationships are clearly labelled.
- Answers in context are interpreted, with units where appropriate.