A-Math prelim papers and O-Level practice papers

Looking for A-Math prelim papers or O-Level A-Math practice papers? Practise WA test papers on the chapters you choose, end-of-year and prelim-style Paper 1 and Paper 2, and full O-Level style papers on every topic (90 marks, 2 hours 15 minutes), in the same style as school prelim papers and past year papers.

Questions cover the whole syllabus, from quadratics and surds to calculus. Every paper comes with answers and worked solutions, and a follow-up paper on what you got wrong.

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Make a free account, pick the chapters your exam tests, and start a timed paper in under a minute.

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Paper types

WAWA40 marks · 1 hShorter questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 190 marks · 2 h 15 min12 to 14 questions, up to 10 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 290 marks · 2 h 15 min9 to 11 questions, up to 12 marks each. You choose the chapters.Free sample paper (PDF) with answers →
SEC stylePaper 190 marks · 2 h 15 minEvery topic: 12 to 14 questions, up to 10 marks eachFree sample paper (PDF) with answers →
SEC stylePaper 290 marks · 2 h 15 minEvery topic: 9 to 11 questions, up to 12 marks eachFree sample paper (PDF) with answers →

Sample questions with worked solutions

Questions like these make up the papers. Every paper has new numbers.

Sample question 1 · 6 marks

A point

P

moves along the curve

y = \ln(2x + 3)

, for

x > -\dfrac{3}{2}

, in such a way that its

x

-coordinate is increasing at a constant rate of

2

units per second.

(a)Find

\dfrac{dy}{dx}

.[1]

(b)Find the rate of change of the

y

-coordinate of

P

at the instant when

x = 0

.[2]

(c)Find the

x

-coordinate of

P

at the instant when its

y

-coordinate is increasing one third as fast as its

x

-coordinate.[3]

Show the worked solution

(a)

\dfrac{dy}{dx} = \dfrac{1}{2x + 3} \times 2

= \dfrac{2}{2x + 3}

(b)

\dfrac{dy}{dt} = \dfrac{dy}{dx} \times \dfrac{dx}{dt}

= \dfrac{2}{2(0) + 3} \times 2

= \dfrac{4}{3}

units per second

(c)

\dfrac{dy}{dt} = \dfrac{1}{3} \times \dfrac{dx}{dt}

, so

\dfrac{dy}{dx} = \dfrac{1}{3}

\dfrac{2}{2x + 3} = \dfrac{1}{3}

2x + 3 = 6

x = \dfrac{3}{2}

Sample question 2 · 8 marks

It is given that

f(x) = \dfrac{2x^{2} + 3x + 5}{x + 1}

, for

x > -1

(a)Express

f(x)

in the form

Ax + B + \dfrac{C}{x + 1}

, where

A

B

and

C

are integers.[3]

(b)Hence find

\displaystyle\int f(x) \, dx

.[2]

(c)Find the exact value of

\displaystyle\int_{0}^{1} f(x) \, dx

, giving your answer in the form

a + b\ln c

, where

a

b

and

c

are rational.[3]

Show the worked solution

(a)

2x^{2} + 3x + 5 = (x + 1)(2x + 1) + 4

f(x) = 2x + 1 + \dfrac{4}{x + 1}

(b)

\displaystyle\int \left(2x + 1 + \dfrac{4}{x + 1}\right) dx

= x^{2} + x + 4\ln(x + 1) + c

(c)

= \left[x^{2} + x + 4\ln(x + 1)\right]_{0}^{1}

= 2 + 4(\ln 2 - \ln 1)

= 2 + 4\ln 2

Topics covered

Sec 3

Quadratic functions · Equations and inequalities · Surds · Polynomials, cubic equations and partial fractions · Binomial theorem · Exponential and logarithmic functions · Coordinate geometry · Trigonometric functions and graphs · Trigonometric equations

Sec 4

Linear law · Trigonometric identities and formulae · Differentiation · Applications of differentiation · Differentiation of trigonometric, exponential and logarithmic functions · Integration · Definite integrals and areas · Kinematics · Proofs

Revise first: free notes

Questions parents ask

Are these past year papers (TYS) or school exam papers?

They're practice papers in the same style as past year papers and school exam papers: the same kinds of questions, marks and timing. They aren't copies of any school's papers or of SEAB's past year papers, which belong to them. Each paper is newly made, with numbers that change every time, so you can keep practising after you've finished your school's papers and the TYS.

Do the papers come with answers?

Yes. Every paper comes with the answers and full worked solutions, step by step, the way markers expect the working to be written.

How are the papers marked?

Your answers are marked as soon as you hand the paper in. You see the full working for every question, which marks you lost, and why. If your final answer is wrong but your working is right, you can tick the method marks your working earns, like a real marker would.

What happens after a paper?

MugCorner shows which question types cost you marks, and makes a follow-up paper on exactly those. Each chapter also has guided notes and topical practice with step-by-step help.

Is it free?

Everything is free during early access. After that, a free account still gets 2 papers a month, with topical practice and notes. MugCorner Plus gives unlimited papers and follow-up papers.

Try a full paper, free

Make a free account, pick the chapters your exam tests, and start a timed paper in under a minute.

Start a free paper

A-Math prelim papers and O-Level practice papers

Questions cover the whole syllabus, from quadratics and surds to calculus. Every paper comes with answers and worked solutions, and a follow-up paper on what you got wrong.

Paper types

WAWA40 marks · 1 hShorter questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →

Final examPaper 190 marks · 2 h 15 min12 to 14 questions, up to 10 marks each. You choose the chapters.Free sample paper (PDF) with answers →

Final examPaper 290 marks · 2 h 15 min9 to 11 questions, up to 12 marks each. You choose the chapters.Free sample paper (PDF) with answers →

SEC stylePaper 190 marks · 2 h 15 minEvery topic: 12 to 14 questions, up to 10 marks eachFree sample paper (PDF) with answers →

SEC stylePaper 290 marks · 2 h 15 minEvery topic: 9 to 11 questions, up to 12 marks eachFree sample paper (PDF) with answers →

Sample questions with worked solutions

Questions like these make up the papers. Every paper has new numbers.

Sample question 1 · 6 marks

A point

P

moves along the curve

y = \ln(2x + 3)

, for

x > -\dfrac{3}{2}

, in such a way that its

x

-coordinate is increasing at a constant rate of

2

units per second.

(a)Find

\dfrac{dy}{dx}

.[1]

(b)Find the rate of change of the

y

-coordinate of

P

at the instant when

x = 0

.[2]

(c)Find the

x

-coordinate of

P

at the instant when its

y

-coordinate is increasing one third as fast as its

x

-coordinate.[3]

Show the worked solution

(a)

\dfrac{dy}{dx} = \dfrac{1}{2x + 3} \times 2

= \dfrac{2}{2x + 3}

(b)

\dfrac{dy}{dt} = \dfrac{dy}{dx} \times \dfrac{dx}{dt}

= \dfrac{2}{2(0) + 3} \times 2

= \dfrac{4}{3}

units per second

(c)

\dfrac{dy}{dt} = \dfrac{1}{3} \times \dfrac{dx}{dt}

, so

\dfrac{dy}{dx} = \dfrac{1}{3}

\dfrac{2}{2x + 3} = \dfrac{1}{3}

2x + 3 = 6

x = \dfrac{3}{2}

Sample question 2 · 8 marks

It is given that

f(x) = \dfrac{2x^{2} + 3x + 5}{x + 1}

, for

x > -1

(a)Express

f(x)

in the form

Ax + B + \dfrac{C}{x + 1}

, where

A

B

and

C

are integers.[3]

(b)Hence find

\displaystyle\int f(x) \, dx

.[2]

(c)Find the exact value of

\displaystyle\int_{0}^{1} f(x) \, dx

, giving your answer in the form

a + b\ln c

, where

a

b

and

c

are rational.[3]

Show the worked solution

(a)

2x^{2} + 3x + 5 = (x + 1)(2x + 1) + 4

f(x) = 2x + 1 + \dfrac{4}{x + 1}

(b)

\displaystyle\int \left(2x + 1 + \dfrac{4}{x + 1}\right) dx

= x^{2} + x + 4\ln(x + 1) + c

(c)

= \left[x^{2} + x + 4\ln(x + 1)\right]_{0}^{1}

= 2 + 4(\ln 2 - \ln 1)

= 2 + 4\ln 2

Topics covered

Sec 3

Sec 4

Questions parents ask

Are these past year papers (TYS) or school exam papers?

Do the papers come with answers?

Yes. Every paper comes with the answers and full worked solutions, step by step, the way markers expect the working to be written.

How are the papers marked?

What happens after a paper?

MugCorner shows which question types cost you marks, and makes a follow-up paper on exactly those. Each chapter also has guided notes and topical practice with step-by-step help.

Is it free?

Everything is free during early access. After that, a free account still gets 2 papers a month, with topical practice and notes. MugCorner Plus gives unlimited papers and follow-up papers.