ZIMSEC O Level Mathematics Paper 1 November 2025

Question 101

[1 marks]Fractions, Decimals & Percentages

Evaluate

-2 + 3 \times 4 - 4

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Question 102

[1 marks]Fractions, Decimals & Percentages

Simplify

5,7 \div 0,19

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Question 103

[1 marks]Fractions, Decimals & Percentages

Simplify

\frac{1}{2} - \frac{2}{3} + \frac{3}{4}

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Question 201

[1 marks]Approximations & Estimations

Estimate 4,9985 correct to 3 significant figures.

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Question 202

[2 marks]Approximations & Estimations

A line

l

measures 7 cm correct to the nearest centimetre. Express the limits of the length of the line in the form

a \le l < b

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Question 301

[3 marks]Number Bases

Simplify

43_5 + 101110_2

, giving the answer in base 2.

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Question 401

[1 marks]Change of Units

Convert

3,5\ \text{m}^2

\text{cm}^2

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Question 402

[2 marks]Change of Units

Convert

0,75\ \text{g/cm}^3

\text{kg/m}^3

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Question 501

[1 marks]Trigonometry, Bearing & Distances

A man sitting on top of a cliff sees a boy 200 m away from the bottom of the cliff. The angle of depression of the boy from the man is 30°. State the angle of elevation of the man from the boy.

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Question 502

[2 marks]Trigonometry, Bearing & Distances

A man sitting on top of a cliff sees a boy 200 m away from the bottom of the cliff. The angle of depression of the boy from the man is 30°. Calculate the height of the cliff, in metres. [Sin 30° = 0,500; Cos 30° = 0,866; Tan 30° = 0,577]

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Question 601

[1 marks]Trigonometry, Bearing & Distances

Convert N47°W to a three-figure bearing.

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Question 602

[2 marks]Trigonometry, Bearing & Distances

P and Q are points on level ground. The bearing of P from Q is N47°W. Find the three-figure bearing of Q from P.

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Question 701

[2 marks]Logarithms

Given that

\log x = 0,2

and

\log y = 0,3

, find

\log(xy)

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Question 702

[2 marks]Logarithms

Given that

\log x = 0,2

and

\log y = 0,3

, find

\log\left(\frac{1}{y}\right)

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Question 801

[2 marks]Consumer Arithmetic

Mrs Moyo took ZW$34 000 to a bank to exchange for US dollars and obtained US$400. Find the exchange rate used, in the form

US\$1 : ZW\$n

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Question 802

[2 marks]Consumer Arithmetic

Mrs Moyo imported a machine worth US$345 including 15% excise duty. Calculate how much she paid as excise duty, in US dollars.

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Question 901

[2 marks]Measures & Mensuration

Triangle XYZ is right angled at Y and

YZ = 12

cm. The area of triangle XYZ is

30\ \text{cm}^2

. Find the length of XY, in centimetres.

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Question 902

[2 marks]Measures & Mensuration

Triangle XYZ is right angled at Y,

YZ = 12

cm and

XY = 5

cm. Find the length of XZ, in centimetres.

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Question 1001

[1 marks]Polygons, Symmetry & Circles

The diagram shows an isosceles trapezium ABCD, with AB parallel to DC. Name a pair of equal sides.

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Question 1002

[2 marks]Polygons, Symmetry & Circles

The diagram shows an isosceles trapezium ABCD, with AB parallel to DC. Name two pairs of equal angles.

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Question 1003

[1 marks]Polygons, Symmetry & Circles

State the number of lines of symmetry of an isosceles trapezium.

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Question 1004

[1 marks]Polygons, Symmetry & Circles

State the order of rotational symmetry of an isosceles trapezium.

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Question 1101

[2 marks]Algebraic Expressions

Remove brackets and simplify

2x + y - (x - 2y)

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Question 1102

[3 marks]Algebraic Fractions

Simplify

\dfrac{w^2 + w - 6}{w^2 - 9}

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Question 1201

[2 marks]Inequalities & Linear Programming

In the diagram, lines

l

m

and

n

are the boundaries of the unshaded region R, which contains the solution set of three simultaneous inequalities. Line

l

is the solid line through

(0; 4)

and

(4; 0)

. Find the inequality whose boundary is line

l

Answer this when you sit the paper.

Question 1202

[2 marks]Inequalities & Linear Programming

In the diagram, lines

l

m

and

n

are the boundaries of the unshaded region R, which contains the solution set of three simultaneous inequalities. Line

m

is the broken line through

(1; 0)

and

(0; -1)

. Find the inequality whose boundary is line

m

Answer this when you sit the paper.

Question 1203

[1 marks]Inequalities & Linear Programming

In the diagram, lines

l

m

and

n

are the boundaries of the unshaded region R, which contains the solution set of three simultaneous inequalities. Line

n

is the solid vertical line through

x = 1

. Find the inequality whose boundary is line

n

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Question 1301

[2 marks]Ratios, Rates & Proportions

Express the ratio

1,7 : 8,5

in the form

1 : n

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Question 1302

[3 marks]Ratios, Rates & Proportions

P, Q and R share $36 so that for every

1 that P gets, Q gets

2, and for every

1 that Q gets, R gets

3. Find R's share, in dollars.

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Question 1401

[1 marks]Sets

A = \{x : 1 \le x \le 20,\ x \in \mathbb{Z},\ x \text{ is a prime number}\}

. List the elements of A.

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Question 1402

[1 marks]Sets

A = \{x : 1 \le x \le 20,\ x \in \mathbb{Z},\ x \text{ is a prime number}\}

and

B = \{y : 0 < y \le 20,\ y \in \mathbb{Z},\ y \text{ is a perfect square}\}

. List the elements of

A \cap B

Answer this when you sit the paper.

Question 1403

[1 marks]Sets

A = \{2; 3; 5; 7; 11; 13; 17; 19\}

and

B = \{1; 4; 9; 16\}

, where

x \in A

and

y \in B

. Find the smallest value of

\dfrac{x}{y}

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Question 1404

[1 marks]Sets

A = \{2; 3; 5; 7; 11; 13; 17; 19\}

and

B = \{1; 4; 9; 16\}

, where

x \in A

and

y \in B

. Find the largest value of

x - y

Answer this when you sit the paper.

Question 1501

[1 marks]Statistics & Probability

Jane noted the number of letters in each of twenty-five words on a list. Number of letters 2, 3, 4, 5, 6, 7, 8 with frequencies 2, 6, 5, 5, 4, 0, 3 respectively. State the mode.

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Question 1502

[1 marks]Statistics & Probability

Jane noted the number of letters in each of twenty-five words on a list. Number of letters 2, 3, 4, 5, 6, 7, 8 with frequencies 2, 6, 5, 5, 4, 0, 3 respectively. Find the median.

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Question 1503

[3 marks]Statistics & Probability

Jane noted the number of letters in each of twenty-five words on a list. Number of letters 2, 3, 4, 5, 6, 7, 8 with frequencies 2, 6, 5, 5, 4, 0, 3 respectively. Calculate the mean.

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Question 1601

[3 marks]Scales & Simple Map Problems

On a map, a building of area

50\ \text{m}^2

is represented by an area of

32\ \text{cm}^2

. Find the scale used to draw the map, in the form

1 : n

Answer this when you sit the paper.

Question 1602

[2 marks]Scales & Simple Map Problems

A map is drawn to a scale of

1 : 125

. Find the actual length, in metres, of a room represented on the map by a line 6 cm long.

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Question 1701

[2 marks]Functional Notation

Given that

f(x) = x^2 + x - 20

, find

f(1)

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Question 1702

[3 marks]Quadratic Equations

Given that

f(x) = x^2 + x - 20

, find the values of

x

for which

f(x) = 0

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Question 1801

[1 marks]Similarity & Congruency

In the diagram, AB, CD and EF are parallel lines, and lines AF and BE intersect at O.

AB = CD = 2

cm,

AO = OD = 3

cm and

EF = 8

cm. Name the triangle which is congruent to triangle OAB.

Answer this when you sit the paper.

Question 1802

[1 marks]Similarity & Congruency

In the diagram, AB, CD and EF are parallel lines, and lines AF and BE intersect at O.

AB = CD = 2

cm,

AO = OD = 3

cm and

EF = 8

cm. Name the triangle which is similar to triangle OAB.

Answer this when you sit the paper.

Question 1803

[3 marks]Similarity & Congruency

In the diagram, AB, CD and EF are parallel lines, and lines AF and BE intersect at O.

AB = CD = 2

cm,

AO = OD = 3

cm and

EF = 8

cm. Calculate the length of DF, in centimetres.

Answer this when you sit the paper.

Question 1901

[3 marks]Change of Subject of Formula

Make

x

the subject of the formula

p = \dfrac{k}{\sqrt{x}}

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Question 1902

[3 marks]Simultaneous Equations

Solve the simultaneous equations

3x + 2y = 4

and

2y + x = 0

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Question 2001

[2 marks]Travel Graphs

The graph shows the movement of a particle which accelerates from 10 m/s to 20 m/s in 5 seconds. It then retards uniformly at

4\ \text{m/s}^2

until it comes to rest at time T seconds. Calculate the acceleration of the particle during the first 5 seconds, in

\text{m/s}^2

Answer this when you sit the paper.

Question 2002

[2 marks]Travel Graphs

A particle accelerates from 10 m/s to 20 m/s in 5 seconds, then retards uniformly at

4\ \text{m/s}^2

until it comes to rest at time T seconds. Calculate T, the total time taken for the journey, in seconds.

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Question 2003

[2 marks]Travel Graphs

A particle accelerates uniformly from 10 m/s to 20 m/s in 5 seconds. Calculate the distance travelled by the particle during the first 5 seconds, in metres.

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Question 2101

[1 marks]Variation

A quantity C is the sum of two parts. The first part varies directly as the cube of

x

and the second part varies inversely as the square of

x

. Write down the equation connecting C and

x

, using constants

a

and

b

Answer this when you sit the paper.

Question 2102

[3 marks]Variation

Given that

C = ax^3 + \dfrac{b}{x^2}

, with

C = 74

when

x = 1

and

C = 34

when

x = 2

, find the value of

a

and the value of

b

Answer this when you sit the paper.

Question 2103

[2 marks]Variation

Given that

C = 2x^3 + \dfrac{72}{x^2}

, find the value of C when

x = 3

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Question 2201

[2 marks]Matrices

Evaluate

\begin{pmatrix} 1 & -2 \\ -4 & 4 \end{pmatrix}\begin{pmatrix} 4 & 2 \\ 1 & 1 \end{pmatrix}

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Question 2202

[3 marks]Matrices

Find the inverse of

\begin{pmatrix} 4 & 2 \\ 1 & 1 \end{pmatrix}

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Question 2203

[2 marks]Matrices

Given that the matrix

A = \begin{pmatrix} 1 & 8 \\ 2 & y^2 \end{pmatrix}

is a singular matrix, find the possible values of

y

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Mathematics Paper 1 November 2025

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1004

Question 1101

Question 1102

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1401

Question 1402

Question 1403

Question 1404

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

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The answers, and why they are the answers

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