Is AQA A-Level Maths 2027 Predicted Practice Paper — Paper 3 an official exam paper?

No. It is an original StudyVector predicted-practice paper for revision. It is not official, leaked or guaranteed, and students should still revise the full specification.

How many marks and questions are in this predicted paper?

This paper has 100 marks across 13 questions and is designed for a 120-minute practice session.

What are the A-Level Mathematics Paper 3 predictions for 2027?

StudyVector's 2027 A-Level Mathematics Paper 3 predicted paper focuses on integration-by-parts-and-substitution, parametric-differentiation, vectors-in-3d, differential-equations, binomial-series-approximation, hypothesis-testing-normal-distribution. This is an independent, AQA-style predicted-practice paper modelled on the published specification — it is not a leaked paper and is not official.

What is the A-Level Mathematics Paper 3 format (7357/3)?

A-Level Mathematics Paper 3 (7357/3) is 100 marks over 120 minutes. 7357/3 model: 100 marks, 120 minutes.

Published 8 March 2026Updated 22 April 2026By Lizzie D., founderPrivacy Policy

Source note: use official specifications as the source of truth. StudyVector is an independent revision platform. AQA, Pearson Edexcel and OCR

Direct answer

This page hosts StudyVector’s independent 2027 A-Level Mathematics Paper 3 predicted-practice paper modelled on 7357/3,100 marks over 120 minutes. Predicted focus topics: integration-by-parts-and-substitution, parametric-differentiation, vectors-in-3d, differential-equations, binomial-series-approximation. It is not an official paper, not a leaked paper and not a guarantee — students should still revise the full specification and verify against official past papers from AQA.

Qualification: A-Level Mathematics
Exam board model: AQA
Paper code: 7357/3
Total marks: 100 marks
Time allowed: 120 minutes
Last reviewed: 16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

Predicted paper

AQA A-Level Maths 2027 Predicted Practice Paper — Paper 3

Q: Which topics are likely to come up in A-Level Mathematics Paper 3 2027?

Based on the AQA-style structure and recent paper patterns, StudyVector's prediction prioritises: integration-by-parts-and-substitution; parametric-differentiation; vectors-in-3d; differential-equations; binomial-series-approximation; hypothesis-testing-normal-distribution. Students should still revise the full specification because exam boards rotate topics.

A-Level Mathematics · AQA-style · 120 minutes · 100 marks

Modelled component: 7357/3 · Calculator permitted

7357/3 model: 100 marks, 120 minutes.

Prediction type: predicted_paper · Evidence mode: historical · Full-length original StudyVector predicted-practice paper modelled on public exam-board structure. It is not official, leaked or guaranteed.

Evidence basis: public exam-board specification structure, historical topic weighting patterns, StudyVector practice-quality review.

AI-generated practice paper. Not an official AQA-style paper, not leaked exam content, and not an exam-board endorsement.

Predicted difficulty score (practice signal)

0–100 model (higher = more demanding)

Candidate focus topics (not guarantees)

integration-by-parts-and-substitution
parametric-differentiation
vectors-in-3d
differential-equations
binomial-series-approximation
hypothesis-testing-normal-distribution

Preview mode

0/13 questions attempted · score 0/100 (0%)

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Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working.

Section A: Pure Mathematics

Pure mathematics questions. Answer ALL questions.

Question SECTION-A-PURE-MATHEMATICS1 (6 marks)
The equation x^3 - 2x - 5 = 0 has a single real root, alpha. (a) Show that alpha lies between x = 2 and x = 3. [2 marks] (b) Using the Newton-Raphson method with the iterative formula x_(n+1) = x_n - f(x_n)/f'(x_n), where f(x) = x^3 - 2x - 5, and taking x_0 = 2, find x_1 and x_2, giving each to 4 decimal places. [4 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS1 is 6 marks)
Question SECTION-A-PURE-MATHEMATICS2 (7 marks)
(a) Use integration by parts to find the exact value of the integral of x*e^(2x) with respect to x, evaluated between the limits x = 0 and x = 1. Give your answer in terms of e. [5 marks] (b) Hence state whether the value found in part (a) is greater than or less than 2, justifying your answer briefly. [2 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS2 is 7 marks)
Question SECTION-A-PURE-MATHEMATICS3 (8 marks)
A curve is defined parametrically by x = t^2 and y = t^3 - 3t, where t is a real parameter. (a) Find dy/dx in terms of t, simplifying your answer. [3 marks] (b) Find the exact value of dy/dx at the point where t = 2. [2 marks] (c) Find the values of t at which the curve has a stationary point (where dy/dx = 0). [3 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS3 is 8 marks)
Question SECTION-A-PURE-MATHEMATICS4 (6 marks)
(a) Express (3x + 4)/((x + 1)(x + 2)) in partial fractions. [3 marks] (b) Hence find the exact value of the integral of (3x + 4)/((x + 1)(x + 2)) with respect to x between the limits x = 0 and x = 2, giving your answer as a single logarithm. [3 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS4 is 6 marks)
Question SECTION-A-PURE-MATHEMATICS5 (7 marks)
A population P (in thousands) of a colony of insects at time t days satisfies the differential equation dP/dt = P*cos(t), where t is measured in radians. Initially, when t = 0, the population is 2 thousand. (a) Solve the differential equation to find P as a function of t. [5 marks] (b) Find the exact population when t = pi/2. [2 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS5 is 7 marks)
Question SECTION-A-PURE-MATHEMATICS6 (8 marks)
Two vectors are given by a = 2i - j + 3k and b = i + 4j - 2k. (a) Find a . b (the scalar product). [2 marks] (b) Find the exact magnitudes |a| and |b|. [2 marks] (c) Hence find the angle between a and b, giving your answer in degrees to 1 decimal place. [4 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS6 is 8 marks)
Question SECTION-A-PURE-MATHEMATICS7 (6 marks)
Solve the equation 3*sin(x) = 2*cos^2(x) for x in the interval 0 degrees <= x <= 360 degrees. Give your answers to 1 decimal place where appropriate. [6 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS7 is 6 marks)
Question SECTION-A-PURE-MATHEMATICS8 (7 marks)
(a) Find the binomial series expansion of (1 + 3x)^(1/2) in ascending powers of x, up to and including the term in x^3. State the range of values of x for which the expansion is valid. [5 marks] (b) By substituting a suitable value of x into your expansion, find an approximation to sqrt(1.3), giving your answer to 4 decimal places. [2 marks]
(Total for Question SECTION-A-PURE-MATHEMATICS8 is 7 marks)

Section B: Statistics

Statistics, probability and data interpretation questions. Answer ALL questions.

Question SECTION-B-STATISTICS1 (9 marks)
In a large batch of manufactured components, 15% are known to be faulty. A quality inspector selects a random sample of 20 components. Let X be the number of faulty components in the sample, modelled by X ~ B(20, 0.15). (a) State two assumptions required for the binomial model to be valid. [2 marks] (b) Find P(X = 2), giving your answer to 4 decimal places. [2 marks] (c) Find P(X <= 3), giving your answer to 4 decimal places. [2 marks] (d) Find the mean and variance of X. [3 marks]
(Total for Question SECTION-B-STATISTICS1 is 9 marks)
Question SECTION-B-STATISTICS2 (10 marks)
The weights, in grams, of apples from an orchard are modelled by a normal distribution X ~ N(50, 8^2), i.e. mean 50 g and standard deviation 8 g. (a) Find P(X > 60), giving your answer to 4 decimal places. [3 marks] (b) Find P(42 < X < 58), giving your answer to 4 decimal places. [3 marks] (c) Apples are classed as 'premium' if they are among the heaviest 10%. Find, to 1 decimal place, the minimum weight for an apple to be classed as premium. [4 marks]
(Total for Question SECTION-B-STATISTICS2 is 10 marks)
Question SECTION-B-STATISTICS3 (8 marks)
A researcher claims that the mean daily screen time of teenagers in a town has fallen below the national average of 50 minutes. Screen times are known to be normally distributed with a population standard deviation of 8 minutes. A random sample of 25 teenagers gives a sample mean of 47.5 minutes. Test, at the 5% significance level, whether there is evidence that the mean screen time in the town is less than 50 minutes. State your hypotheses clearly and give a conclusion in context. [8 marks]
(Total for Question SECTION-B-STATISTICS3 is 8 marks)
Question SECTION-B-STATISTICS4 (9 marks)
The table shows the number of hours of revision, r, and the mark scored (out of 100), m, for a sample of 8 students. The following summary statistics were calculated: sum of r = 40, sum of m = 520, sum of r^2 = 240, sum of r*m = 2820, sum of m^2 = 35200. (n = 8.) (a) Calculate the equation of the least squares regression line of m on r, in the form m = a + b*r, giving a and b to 2 decimal places. [5 marks] (b) Use your line to estimate the mark for a student who revises for 7 hours, and comment on the reliability of this estimate given that the sample values of r ranged from 1 to 9 hours. [2 marks] (c) Give one reason why the regression line of m on r would not be appropriate for predicting the number of revision hours from a given mark. [2 marks]
(Total for Question SECTION-B-STATISTICS4 is 9 marks)
Question SECTION-B-STATISTICS5 (9 marks)
A spinner has four sectors coloured red, blue, green and yellow. It is biased so that P(red) = 0.4, P(blue) = 0.3, P(green) = 0.2 and P(yellow) = 0.1. The spinner is spun twice, and the two spins are independent. (a) Find the probability that both spins land on the same colour. [3 marks] (b) Find the probability that at least one spin lands on red. [3 marks] (c) Given that at least one spin landed on red, find the probability that both spins landed on red. Give your answer to 4 decimal places. [3 marks]
(Total for Question SECTION-B-STATISTICS5 is 9 marks)

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Direct answer

Qualification

A-Level Mathematics

Exam board model

AQA

Paper code

7357/3

Total marks

100 marks

Time allowed

120 minutes

Last reviewed

16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

AQA A-Level Maths 2027 Predicted Practice Paper — Paper 3

A-Level Mathematics · AQA-style · 120 minutes · 100 marks

Modelled component: 7357/3 · Calculator permitted

7357/3 model: 100 marks, 120 minutes.

Evidence basis: public exam-board specification structure, historical topic weighting patterns, StudyVector practice-quality review.

Section A: Pure Mathematics

Pure mathematics questions. Answer ALL questions.

Question SECTION-A-PURE-MATHEMATICS1 (6 marks)

The equation x^3 - 2x - 5 = 0 has a single real root, alpha. (a) Show that alpha lies between x = 2 and x = 3. [2 marks] (b) Using the Newton-Raphson method with the iterative formula x_(n+1) = x_n - f(x_n)/f'(x_n), where f(x) = x^3 - 2x - 5, and taking x_0 = 2, find x_1 and x_2, giving each to 4 decimal places. [4 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS1 is 6 marks)

Question SECTION-A-PURE-MATHEMATICS2 (7 marks)

(a) Use integration by parts to find the exact value of the integral of x*e^(2x) with respect to x, evaluated between the limits x = 0 and x = 1. Give your answer in terms of e. [5 marks] (b) Hence state whether the value found in part (a) is greater than or less than 2, justifying your answer briefly. [2 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS2 is 7 marks)

Question SECTION-A-PURE-MATHEMATICS3 (8 marks)

A curve is defined parametrically by x = t^2 and y = t^3 - 3t, where t is a real parameter. (a) Find dy/dx in terms of t, simplifying your answer. [3 marks] (b) Find the exact value of dy/dx at the point where t = 2. [2 marks] (c) Find the values of t at which the curve has a stationary point (where dy/dx = 0). [3 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS3 is 8 marks)

Question SECTION-A-PURE-MATHEMATICS4 (6 marks)

(a) Express (3x + 4)/((x + 1)(x + 2)) in partial fractions. [3 marks] (b) Hence find the exact value of the integral of (3x + 4)/((x + 1)(x + 2)) with respect to x between the limits x = 0 and x = 2, giving your answer as a single logarithm. [3 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS4 is 6 marks)

Question SECTION-A-PURE-MATHEMATICS5 (7 marks)

A population P (in thousands) of a colony of insects at time t days satisfies the differential equation dP/dt = P*cos(t), where t is measured in radians. Initially, when t = 0, the population is 2 thousand. (a) Solve the differential equation to find P as a function of t. [5 marks] (b) Find the exact population when t = pi/2. [2 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS5 is 7 marks)

Question SECTION-A-PURE-MATHEMATICS6 (8 marks)

Two vectors are given by a = 2i - j + 3k and b = i + 4j - 2k. (a) Find a . b (the scalar product). [2 marks] (b) Find the exact magnitudes |a| and |b|. [2 marks] (c) Hence find the angle between a and b, giving your answer in degrees to 1 decimal place. [4 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS6 is 8 marks)

Question SECTION-A-PURE-MATHEMATICS7 (6 marks)

Solve the equation 3*sin(x) = 2*cos^2(x) for x in the interval 0 degrees <= x <= 360 degrees. Give your answers to 1 decimal place where appropriate. [6 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS7 is 6 marks)

Question SECTION-A-PURE-MATHEMATICS8 (7 marks)

(a) Find the binomial series expansion of (1 + 3x)^(1/2) in ascending powers of x, up to and including the term in x^3. State the range of values of x for which the expansion is valid. [5 marks] (b) By substituting a suitable value of x into your expansion, find an approximation to sqrt(1.3), giving your answer to 4 decimal places. [2 marks]

(Total for Question SECTION-A-PURE-MATHEMATICS8 is 7 marks)

Section B: Statistics

Statistics, probability and data interpretation questions. Answer ALL questions.

Question SECTION-B-STATISTICS1 (9 marks)

In a large batch of manufactured components, 15% are known to be faulty. A quality inspector selects a random sample of 20 components. Let X be the number of faulty components in the sample, modelled by X ~ B(20, 0.15). (a) State two assumptions required for the binomial model to be valid. [2 marks] (b) Find P(X = 2), giving your answer to 4 decimal places. [2 marks] (c) Find P(X <= 3), giving your answer to 4 decimal places. [2 marks] (d) Find the mean and variance of X. [3 marks]

(Total for Question SECTION-B-STATISTICS1 is 9 marks)

Question SECTION-B-STATISTICS2 (10 marks)

The weights, in grams, of apples from an orchard are modelled by a normal distribution X ~ N(50, 8^2), i.e. mean 50 g and standard deviation 8 g. (a) Find P(X > 60), giving your answer to 4 decimal places. [3 marks] (b) Find P(42 < X < 58), giving your answer to 4 decimal places. [3 marks] (c) Apples are classed as 'premium' if they are among the heaviest 10%. Find, to 1 decimal place, the minimum weight for an apple to be classed as premium. [4 marks]

(Total for Question SECTION-B-STATISTICS2 is 10 marks)

Question SECTION-B-STATISTICS3 (8 marks)

A researcher claims that the mean daily screen time of teenagers in a town has fallen below the national average of 50 minutes. Screen times are known to be normally distributed with a population standard deviation of 8 minutes. A random sample of 25 teenagers gives a sample mean of 47.5 minutes. Test, at the 5% significance level, whether there is evidence that the mean screen time in the town is less than 50 minutes. State your hypotheses clearly and give a conclusion in context. [8 marks]

(Total for Question SECTION-B-STATISTICS3 is 8 marks)

Question SECTION-B-STATISTICS4 (9 marks)

The table shows the number of hours of revision, r, and the mark scored (out of 100), m, for a sample of 8 students. The following summary statistics were calculated: sum of r = 40, sum of m = 520, sum of r^2 = 240, sum of r*m = 2820, sum of m^2 = 35200. (n = 8.) (a) Calculate the equation of the least squares regression line of m on r, in the form m = a + b*r, giving a and b to 2 decimal places. [5 marks] (b) Use your line to estimate the mark for a student who revises for 7 hours, and comment on the reliability of this estimate given that the sample values of r ranged from 1 to 9 hours. [2 marks] (c) Give one reason why the regression line of m on r would not be appropriate for predicting the number of revision hours from a given mark. [2 marks]

(Total for Question SECTION-B-STATISTICS4 is 9 marks)

Question SECTION-B-STATISTICS5 (9 marks)

A spinner has four sectors coloured red, blue, green and yellow. It is biased so that P(red) = 0.4, P(blue) = 0.3, P(green) = 0.2 and P(yellow) = 0.1. The spinner is spun twice, and the two spins are independent. (a) Find the probability that both spins land on the same colour. [3 marks] (b) Find the probability that at least one spin lands on red. [3 marks] (c) Given that at least one spin landed on red, find the probability that both spins landed on red. Give your answer to 4 decimal places. [3 marks]

(Total for Question SECTION-B-STATISTICS5 is 9 marks)