G2 (N(A)) Maths exam papers and test papers

Looking for G2 or N(A) Maths exam papers? Practise WA test papers, end-of-year exam papers for every year, and N-Level / SEC style Paper 1 and Paper 2 on every topic (70 marks in 2 hours each), in the same style as school exam papers and past year papers.

Questions stay within the G2 syllabus. Every paper comes with answers and worked solutions, and a follow-up paper on what you got wrong.

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Paper types

WAWA30 marks · 50 minShort questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 150 marks · 1 h 15 minAbout 18 short questions, 2–5 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 250 marks · 1 h 15 minAbout 7 structured questions, 5–8 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 170 marks · 2 hAbout 25 short questions. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 270 marks · 2 hSection A: 9 to 10 structured questions; Section B: answer one of two. You choose the chapters.Free sample paper (PDF) with answers →
SEC stylePaper 170 marks · 2 hAbout 23 short questions on every topicFree sample paper (PDF) with answers →
SEC stylePaper 270 marks · 2 hSection A on every topic; Section B: answer one of twoFree 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 · 9 marks

The diagram shows a circle with centre

O

and radius

6

cm.

AB

is a chord of length

9

cm. The minor segment cut off by

AB

is shaded.

(a)Show that angle

AOB = 1.696

radians, correct to 4 significant figures.[2]

(b)Find the length of the major arc

AB

.[2]

(c)Find the area of the shaded segment.[3]

(d)Find the perimeter of the shaded segment.[2]

Show the worked solution

(a)

Let

M

be the midpoint of

AB

OM \perp AB

(⊥ from centre bisects chord)

\sin \angle AOM = \dfrac{AM}{OA}

\phantom{\sin \angle AOM} = \dfrac{4.5}{6}

\angle AOM = 0.8480\ldots

rad

\angle AOB = 2 \times 0.8480\ldots

\phantom{\angle AOB} = 1.6961\ldots

\angle AOB = 1.696

rad (to 4 s.f.) (shown)

(b)

\text{Reflex } \angle AOB = 2\pi - 1.6961\ldots

\phantom{\text{Reflex } \angle AOB} = 4.5870\ldots

rad

\text{Major arc } AB = 6 \times 4.5870\ldots

\phantom{\text{Major arc } AB} = 27.5223\ldots

\text{Major arc } AB = 27.5

(c)

\text{Area of sector } OAB = \dfrac{1}{2} \times 6^2 \times 1.6961\ldots

\phantom{\text{Area of sector } OAB} = 30.5302\ldots

\text{Area of } \triangle OAB = \dfrac{1}{2} \times 6^2 \times \sin 1.6961\ldots

\phantom{\text{Area of } \triangle OAB} = 17.8588\ldots

\text{Area of segment} = 30.5302\ldots - 17.8588\ldots

\phantom{\text{Area of segment}} = 12.6714\ldots

\text{Area of segment} = 12.7

cm²

(d)

\text{Minor arc } AB = 6 \times 1.6961\ldots

\phantom{\text{Minor arc } AB} = 10.1767\ldots

\text{Perimeter} = 10.1767\ldots + 9

\phantom{\text{Perimeter}} = 19.1767\ldots

\text{Perimeter} = 19.2

Sample question 2 · 5 marks

A ball is thrown upwards. Its height,

h

metres, above the ground

t

seconds after it is thrown is given by

h = 20t - 5t^2

(a)Find the height of the ball after

2

seconds.[1]

(b)Find the values of

t

when the ball is

15

m above the ground.[3]

(c)Explain why there are two answers to part (b).[1]

Show the worked solution

(a)

h = 20(2) - 5(2)^2

\phantom{h} = 40 - 20

\phantom{h} = 20

(b)

20t - 5t^2 = 15

5t^2 - 20t + 15 = 0

t^2 - 4t + 3 = 0

(t - 1)(t - 3) = 0

t = 1

t = 3

(c)

The ball is at

15

m on the way up, after

1

s, and again on the way down, after

3

Topics covered

Sec 1

Primes, HCF and LCM · Integers, rational and real numbers · Approximation and estimation · Basic algebra · Linear equations · Number sequences and patterns · Percentage · Ratio, rate and speed · Basic geometry and triangles · Perimeter and area · Volume and surface area · Statistics

Sec 2

Ratio and proportion · Algebraic expressions and formulae · Coordinates and linear graphs · Equations and inequalities · Quadrilaterals and polygons · Congruence and similarity · Pythagoras' theorem · Trigonometric ratios · Mensuration · Data handling and analysis · Probability

Sec 3

Algebraic manipulation · Quadratic equations · Inequalities · Indices, compound interest and standard form · Coordinate geometry · Graphs of functions · Further trigonometry · Applications of trigonometry · Arc length and sector area · Congruence and similarity · Circle properties

Sec 4

Probability · Statistics · Problems in real-world contexts

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

G2 (N(A)) Maths exam papers and test papers

Questions stay within the G2 syllabus. Every paper comes with answers and worked solutions, and a follow-up paper on what you got wrong.

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

Paper types

WAWA30 marks · 50 minShort questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 150 marks · 1 h 15 minAbout 18 short questions, 2–5 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 250 marks · 1 h 15 minAbout 7 structured questions, 5–8 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 170 marks · 2 hAbout 25 short questions. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 270 marks · 2 hSection A: 9 to 10 structured questions; Section B: answer one of two. You choose the chapters.Free sample paper (PDF) with answers →
SEC stylePaper 170 marks · 2 hAbout 23 short questions on every topicFree sample paper (PDF) with answers →
SEC stylePaper 270 marks · 2 hSection A on every topic; Section B: answer one of twoFree 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 · 9 marks

The diagram shows a circle with centre

O

and radius

6

cm.

AB

is a chord of length

9

cm. The minor segment cut off by

AB

is shaded.

(a)Show that angle

AOB = 1.696

radians, correct to 4 significant figures.[2]

(b)Find the length of the major arc

AB

.[2]

(c)Find the area of the shaded segment.[3]

(d)Find the perimeter of the shaded segment.[2]

Show the worked solution

(a)

Let

M

be the midpoint of

AB

OM \perp AB

(⊥ from centre bisects chord)

\sin \angle AOM = \dfrac{AM}{OA}

\phantom{\sin \angle AOM} = \dfrac{4.5}{6}

\angle AOM = 0.8480\ldots

rad

\angle AOB = 2 \times 0.8480\ldots

\phantom{\angle AOB} = 1.6961\ldots

\angle AOB = 1.696

rad (to 4 s.f.) (shown)

(b)

\text{Reflex } \angle AOB = 2\pi - 1.6961\ldots

\phantom{\text{Reflex } \angle AOB} = 4.5870\ldots

rad

\text{Major arc } AB = 6 \times 4.5870\ldots

\phantom{\text{Major arc } AB} = 27.5223\ldots

\text{Major arc } AB = 27.5

(c)

\text{Area of sector } OAB = \dfrac{1}{2} \times 6^2 \times 1.6961\ldots

\phantom{\text{Area of sector } OAB} = 30.5302\ldots

\text{Area of } \triangle OAB = \dfrac{1}{2} \times 6^2 \times \sin 1.6961\ldots

\phantom{\text{Area of } \triangle OAB} = 17.8588\ldots

\text{Area of segment} = 30.5302\ldots - 17.8588\ldots

\phantom{\text{Area of segment}} = 12.6714\ldots

\text{Area of segment} = 12.7

cm²

(d)

\text{Minor arc } AB = 6 \times 1.6961\ldots

\phantom{\text{Minor arc } AB} = 10.1767\ldots

\text{Perimeter} = 10.1767\ldots + 9

\phantom{\text{Perimeter}} = 19.1767\ldots

\text{Perimeter} = 19.2

Sample question 2 · 5 marks

A ball is thrown upwards. Its height,

h

metres, above the ground

t

seconds after it is thrown is given by

h = 20t - 5t^2

(a)Find the height of the ball after

2

seconds.[1]

(b)Find the values of

t

when the ball is

15

m above the ground.[3]

(c)Explain why there are two answers to part (b).[1]

Show the worked solution

(a)

h = 20(2) - 5(2)^2

\phantom{h} = 40 - 20

\phantom{h} = 20

(b)

20t - 5t^2 = 15

5t^2 - 20t + 15 = 0

t^2 - 4t + 3 = 0

(t - 1)(t - 3) = 0

t = 1

t = 3

(c)

The ball is at

15

m on the way up, after

1

s, and again on the way down, after

3

Topics covered

Sec 1

Sec 2

Sec 3

Sec 4

Probability · Statistics · Problems in real-world contexts

Revise first: free notes

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.

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