Sec 4 E-Math prelim papers

Looking for Sec 4 E-Math prelim papers? Practise full O-Level style Paper 1 (short questions) and Paper 2 (structured questions), 90 marks each in 2 hours 15 minutes, in the same style as school prelim papers and O-Level past year papers (4052).

Do as many as you need: every paper comes with answers and full worked solutions, and a follow-up paper on exactly what you got wrong. WA test papers on chosen chapters are there too.

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

O-Level stylePaper 190 marks · 2 h 15 minAbout 26 short questions on every topicFree sample paper (PDF) with answers →
O-Level stylePaper 290 marks · 2 h 15 min9 to 10 structured questions on every topicFree sample paper (PDF) with answers →
WAWA30 marks · 45 minShort questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 160 marks · 1 h 30 minMany short questions, 1–5 marks each. You choose the chapters.Free sample paper (PDF) with answers →
Final examPaper 280 marks · 2 hLonger structured questions. You choose the chapters.Free 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

In the diagram,

OAB

is a sector of a circle with centre

O

and radius

10

cm, and angle

AOB = 0.9

radians. The tangent to the circle at

A

meets

OB

produced at

T

. The region bounded by

AT

BT

and the arc

AB

is shaded.

(a)Find the length of

AT

, correct to 3 significant figures.[2]

(b)Find the length of

BT

.[2]

(c)Find the perimeter of the shaded region.[2]

(d)Find the area of the shaded region.[3]

Show the worked solution

(a)

\angle OAT = 90^\circ

(tangent ⊥ radius)

\tan 0.9 = \dfrac{AT}{10}

AT = 10 \tan 0.9

\phantom{AT} = 12.6015\ldots

AT = 12.6

(b)

\cos 0.9 = \dfrac{10}{OT}

OT = \dfrac{10}{\cos 0.9}

\phantom{OT} = 16.0872\ldots

BT = 16.0872\ldots - 10

\phantom{BT} = 6.0872\ldots

BT = 6.09

(c)

\text{Arc } AB = 10 \times 0.9

\phantom{\text{Arc } AB} = 9

\text{Perimeter} = 12.6015\ldots + 6.0872\ldots + 9

\phantom{\text{Perimeter}} = 27.6888\ldots

\text{Perimeter} = 27.7

(d)

\text{Area of } \triangle OAT = \dfrac{1}{2} \times 10 \times 12.6015\ldots

\phantom{\text{Area of } \triangle OAT} = 63.0079\ldots

\text{Area of sector } OAB = \dfrac{1}{2} \times 10^2 \times 0.9

\phantom{\text{Area of sector } OAB} = 45

\text{Shaded area} = 63.0079\ldots - 45

\phantom{\text{Shaded area}} = 18.0079\ldots

\text{Shaded area} = 18.0

cm²

Sample question 2 · 6 marks

In triangle

ABC

AB = 6

cm,

AC = 14

cm and angle

BAC = 115^\circ

(a)Find the length of

BC

, correct to 3 significant figures.[2]

(b)Find angle

ACB

, correct to 1 decimal place.[2]

(c)Find the area of triangle

ABC

, correct to 3 significant figures.[2]

Show the worked solution

(a)

BC^2 = 14^2 + 6^2 - 2(14)(6) \cos 115^\circ

BC^2 = 302.9998\ldots

BC = 17.4068\ldots

\phantom{BC} = 17.4

(b)

\dfrac{\sin C}{6} = \dfrac{\sin 115^\circ}{17.4068\ldots}

(use the unrounded

BC

)

\sin C = 0.3123\ldots

C = \sin^{-1}(0.3123\ldots)

C = 18.2036\ldots

\phantom{C} = 18.2^\circ

(acute: it is opposite the shorter side)

(c)

\text{Area} = \dfrac{1}{2} \times 14 \times 6 \times \sin 115^\circ

= 38.0649\ldots

\phantom{} = 38.1

cm²

Topics covered

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 · Area and volume of similar figures · Circle properties

Sec 4

Sets · Probability · Statistics · Matrices · Vectors · 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

Sec 4 E-Math prelim papers

Do as many as you need: every paper comes with answers and full worked solutions, and a follow-up paper on exactly what you got wrong. WA test papers on chosen chapters are there too.

Paper types

O-Level stylePaper 190 marks · 2 h 15 minAbout 26 short questions on every topicFree sample paper (PDF) with answers →

O-Level stylePaper 290 marks · 2 h 15 min9 to 10 structured questions on every topicFree sample paper (PDF) with answers →

WAWA30 marks · 45 minShort questions, then structured ones. You choose the chapters.Free sample paper (PDF) with answers →

Final examPaper 160 marks · 1 h 30 minMany short questions, 1–5 marks each. You choose the chapters.Free sample paper (PDF) with answers →

Final examPaper 280 marks · 2 hLonger structured questions. You choose the chapters.Free 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

In the diagram,

OAB

is a sector of a circle with centre

O

and radius

10

cm, and angle

AOB = 0.9

radians. The tangent to the circle at

A

meets

OB

produced at

T

. The region bounded by

AT

BT

and the arc

AB

is shaded.

(a)Find the length of

AT

, correct to 3 significant figures.[2]

(b)Find the length of

BT

.[2]

(c)Find the perimeter of the shaded region.[2]

(d)Find the area of the shaded region.[3]

Show the worked solution

(a)

\angle OAT = 90^\circ

(tangent ⊥ radius)

\tan 0.9 = \dfrac{AT}{10}

AT = 10 \tan 0.9

\phantom{AT} = 12.6015\ldots

AT = 12.6

(b)

\cos 0.9 = \dfrac{10}{OT}

OT = \dfrac{10}{\cos 0.9}

\phantom{OT} = 16.0872\ldots

BT = 16.0872\ldots - 10

\phantom{BT} = 6.0872\ldots

BT = 6.09

(c)

\text{Arc } AB = 10 \times 0.9

\phantom{\text{Arc } AB} = 9

\text{Perimeter} = 12.6015\ldots + 6.0872\ldots + 9

\phantom{\text{Perimeter}} = 27.6888\ldots

\text{Perimeter} = 27.7

(d)

\text{Area of } \triangle OAT = \dfrac{1}{2} \times 10 \times 12.6015\ldots

\phantom{\text{Area of } \triangle OAT} = 63.0079\ldots

\text{Area of sector } OAB = \dfrac{1}{2} \times 10^2 \times 0.9

\phantom{\text{Area of sector } OAB} = 45

\text{Shaded area} = 63.0079\ldots - 45

\phantom{\text{Shaded area}} = 18.0079\ldots

\text{Shaded area} = 18.0

cm²

Sample question 2 · 6 marks

In triangle

ABC

AB = 6

cm,

AC = 14

cm and angle

BAC = 115^\circ

(a)Find the length of

BC

, correct to 3 significant figures.[2]

(b)Find angle

ACB

, correct to 1 decimal place.[2]

(c)Find the area of triangle

ABC

, correct to 3 significant figures.[2]

Show the worked solution

(a)

BC^2 = 14^2 + 6^2 - 2(14)(6) \cos 115^\circ

BC^2 = 302.9998\ldots

BC = 17.4068\ldots

\phantom{BC} = 17.4

(b)

\dfrac{\sin C}{6} = \dfrac{\sin 115^\circ}{17.4068\ldots}

(use the unrounded

BC

)

\sin C = 0.3123\ldots

C = \sin^{-1}(0.3123\ldots)

C = 18.2036\ldots

\phantom{C} = 18.2^\circ

(acute: it is opposite the shorter side)

(c)

\text{Area} = \dfrac{1}{2} \times 14 \times 6 \times \sin 115^\circ

= 38.0649\ldots

\phantom{} = 38.1

cm²

Topics covered

Sec 3

Sec 4

Sets · Probability · Statistics · Matrices · Vectors · Problems in real-world contexts

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.