ZIMSEC O Level Mathematics Paper 2 June 2025

Question 101

[2 marks]Approximations and Estimations

Estimate the value of

\frac{1,98 + 8,75 \times 6,05}{6,89}

by first rounding each of the given numbers off to the nearest whole number.

Question 102

[3 marks]Approximations and Estimations

The side of a cube is 8,7 cm given correct to the nearest millimetre. Find the least possible volume of the cube, correct to 2 decimal places.

Answer this when you sit the paper.

Question 103

[3 marks]Approximations and Estimations

Simplify

2\frac{1}{2} \div 3\frac{3}{4} + 1\frac{1}{5}

, giving the answer as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 201

[3 marks]Sets

In a group of 160 form one learners, every learner plays at least one of volleyball, netball or tennis. 40 play netball only, 25 play tennis only and 28 play volleyball only. 50 play netball and tennis, 35 play netball and volleyball, 30 play tennis and volleyball, and

x

play all three games. Find the value of

x

Answer this when you sit the paper.

Question 202

[2 marks]Sets

In the Venn diagram the region for netball and volleyball but not tennis is marked

35-x

, where

x

is the number who play all three games. Given that 30 learners play tennis and volleyball, which expression belongs in the region for tennis and volleyball but not netball?

A $x - 30$
B $30 - 2x$
C $30 + x$
D $30 - x$

Question 203

[2 marks]Sets

The universal set is

\xi = \{x : 1 \le x < 10, x \in \mathbb{Z}\}

and A is the set of odd numbers in

\xi

. List all the elements of set A.

Answer this when you sit the paper.

Question 204

[2 marks]Sets

The universal set is

\xi = \{x : 1 \le x < 10, x \in \mathbb{Z}\}

, A is the set of odd numbers and B is the set of factors of 10. Find

n(A' \cap B)

Answer this when you sit the paper.

Question 301

[2 marks]Measures and Mensuration

A circular reservoir has a radius of 1,4 m. Taking

\pi

to be

\frac{22}{7}

, calculate the area covered by the reservoir in square metres.

Answer this when you sit the paper.

Question 302

[3 marks]Measures and Mensuration

A rectangular vegetable garden is 50,7 m long and 30,5 m wide. A circular reservoir inside it covers 6,16 square metres and the rest of the garden grows vegetables. It costs \$38 507 to spray the space for growing vegetables. Find the cost per square metre, to the nearest dollar.

Answer this when you sit the paper.

Question 303

[3 marks]Measures and Mensuration

An arc AB of a circle centre O subtends an angle of

60°

at the centre and is 11 cm long. Taking

\pi

to be

\frac{22}{7}

, calculate the radius of the circle in centimetres.

Answer this when you sit the paper.

Question 304

[2 marks]Measures and Mensuration

The sector AOB has an angle of

60°

at the centre O, a radius of 10,5 cm and an arc AB of length 11 cm. Taking

\pi

to be

\frac{22}{7}

, calculate the area of the sector.

A346,5 cm $^2$
B57,75 cm $^2$
C28,875 cm $^2$
D115,5 cm $^2$

Question 401

[1 marks]Variation

The cost, C, of a party is partly constant and partly varies with the number, n, of people attending. Using constants

h

and

k

, which expression gives C in terms of

n

A $C = hkn$
B $C = hn + kn$
C $C = \frac{h}{n} + k$
D $C = h + kn$

Question 402

[3 marks]Variation

The cost of a party is

C = h + kn

dollars for

n

people. The cost is \$700 for 5 people and \$1 340 for 13 people. Find the value of

k

Answer this when you sit the paper.

Question 403

[3 marks]Variation

The cost of a party is

C = h + kn

dollars for

n

people. The cost is \$700 for 5 people and \$1 340 for 13 people. Calculate the cost if 25 people attend.

Answer this when you sit the paper.

Question 404

[2 marks]Variation

P

varies directly as

Q

, and

P = 12

when

Q = 5

. Find the formula connecting

P

and

Q

A $P = \frac{60}{Q}$
B $P = 2,4Q$
C $P = Q + 7$
D $P = \frac{5}{12}Q$

Question 405

[2 marks]Variation

P

varies directly as

Q

, and

P = 12

when

Q = 5

. Calculate the value of

Q

when

P = 42

Answer this when you sit the paper.

Question 501

[2 marks]Constructions and Loci

In triangle ABC,

AB = 10

cm,

A\hat{B}C = 45°

and

B\hat{A}C = 60°

. Find

A\hat{C}B

in degrees.

Answer this when you sit the paper.

Question 502

[1 marks]Constructions and Loci

A point B is marked on a sheet of paper. Which construction gives the locus of all points that are 4,5 cm from B?

AAn arc of centre A with radius 4,5 cm
BA circle of centre B and radius 4,5 cm
CA straight line parallel to AB and 4,5 cm from it
DThe perpendicular bisector of the side AB

Question 503

[2 marks]Constructions and Loci

In triangle ABC the side AB has been drawn. Which construction gives the locus of points that are 1,5 cm from AB on the same side of AB as C?

AA straight line parallel to AB, drawn 1,5 cm from AB on the same side as C
BAn arc of radius 1,5 cm drawn with centre B, on the same side of AB as C
CA pair of straight lines parallel to AB, one drawn 1,5 cm on each side of it
DA circle of radius 1,5 cm drawn with the midpoint of AB as its centre

Question 504

[2 marks]Constructions and Loci

In triangle ABC,

AB = 10

cm,

A\hat{B}C = 45°

and

B\hat{A}C = 60°

. Calculate the length of AC in centimetres, correct to 1 decimal place.

Answer this when you sit the paper.

Question 601

[3 marks]Algebraic Fractions

Solve the equation

\frac{2a + 3}{4} + \frac{a - 5}{3} = 1

Answer this when you sit the paper.

Question 602

[2 marks]Algebraic Fractions

It is given that

M = \frac{N}{N + P}

. Find the value of

M

when

N = 60

and

P = 45

, giving the answer as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 603

[3 marks]Algebraic Fractions

It is given that

M = \frac{N}{N + P}

. Make N the subject of the formula.

A $N = \frac{MP}{1 - M}$
B $N = \frac{MP}{M - 1}$
C $N = \frac{P}{1 - M}$
D $N = MP - M$

Question 604

[3 marks]Algebraic Fractions

Solve the equation

\log_3 (x - 2)^2 = 2

Answer this when you sit the paper.

Question 701

[3 marks]Statistics and Probability

The ages in years of 100 grandfathers are grouped as

50 \le x < 55

with frequency 6,

55 \le x < 60

with 10,

60 \le x < 65

with 22,

65 \le x < 70

with 32,

70 \le x < 75

with 20 and

75 \le x < 80

with 10. Calculate an estimate of the mean age.

Answer this when you sit the paper.

Question 702

[1 marks]Statistics and Probability

The ages of 100 grandfathers give the running totals

x<50

: 0,

x<55

: 6,

x<60

: 16,

x<65

: 38,

x<70

p

x<75

: 90 and

x<80

: 100. The class

65 \le x < 70

holds 32 grandfathers. Find the value of

p

Answer this when you sit the paper.

Question 703

[2 marks]Statistics and Probability

A cumulative frequency curve is drawn for grandfathers' ages grouped as

50 \le x < 55

55 \le x < 60

60 \le x < 65

and so on. The class

60 \le x < 65

has frequency 22 and the running total up to the end of that class is 38. Which point is plotted for that class?

A $(65; 38)$
B $(62,5; 22)$
C $(65; 22)$
D $(60; 22)$

Question 704

[3 marks]Statistics and Probability

A cumulative frequency curve for the ages of 100 grandfathers passes through

(60; 16)

(65; 38)

(70; 70)

and

(75; 90)

. Estimate the median age.

A67 years
B70 years
C63 years
D65 years

Question 705

[3 marks]Statistics and Probability

A cumulative frequency curve for the ages of 100 grandfathers passes through

(60; 16)

(65; 38)

(70; 70)

and

(75; 90)

. Estimate the interquartile range, in years, correct to the nearest whole number.

Answer this when you sit the paper.

Question 801

[3 marks]Inequalities and Linear Programming

Mr Ndou plants

x

hectares of beans and

y

hectares of peas in a 5-hectare field. Beans need 2 bags of fertilizer per hectare and peas need 4 bags, and he has 16 bags. He plants at least 1,5 hectares of beans and at least 1 hectare of peas. Which set of inequalities states these conditions?

A $x + y \le 5$ , $2x + 4y \le 16$ , $x \ge 1,5$ , $y \ge 1$
B $x + y \le 16$ , $2x + 4y \le 5$ , $x \ge 1,5$ , $y \ge 1$
C $x + y \le 5$ , $4x + 2y \le 16$ , $x \ge 1$ , $y \ge 1,5$
D $x + y \ge 5$ , $2x + 4y \ge 16$ , $x \le 1,5$ , $y \le 1$

Question 802

[2 marks]Inequalities and Linear Programming

Mr Ndou plants

x

hectares of beans and

y

hectares of peas, subject to

x + y \le 5

and

2x + 4y \le 16

. Find the value of

y

at the point where the two boundary lines

x + y = 5

and

2x + 4y = 16

cross.

Answer this when you sit the paper.

Question 803

[2 marks]Inequalities and Linear Programming

Beans earn a profit of \$30 000 per hectare and peas \$40 000 per hectare. Calculate the profit, in dollars, from planting 1,5 hectares of beans and 3,25 hectares of peas.

Answer this when you sit the paper.

Question 804

[3 marks]Inequalities and Linear Programming

Mr Ndou plants

x

hectares of beans and

y

hectares of peas subject to

x + y \le 5

2x + 4y \le 16

x \ge 1,5

and

y \ge 1

. Beans earn \$30 000 per hectare and peas \$40 000 per hectare. Calculate the maximum possible profit, in dollars.

Answer this when you sit the paper.

Question 901

[2 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(3;2), B(4;2), C(4;3) and D(3;4). It is mapped onto

A_1B_1C_1D_1

by the translation vector

\begin{pmatrix} 3 \\ -5 \end{pmatrix}

. Write down the coordinates of

A_1

Answer this when you sit the paper.

Question 902

[3 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(3;2), B(4;2), C(4;3) and D(3;4). Its image

A_2B_2C_2D_2

has vertices

A_2(1\frac{1}{2}; 1)

B_2(2; 1)

C_2(2; 1\frac{1}{2})

and

D_2(1\frac{1}{2}; 2)

. Describe fully the single transformation that maps ABCD onto

A_2B_2C_2D_2

AAn enlargement of scale factor 2 with centre the origin $(0; 0)$
BAn enlargement of scale factor $\frac{1}{2}$ with centre the origin $(0; 0)$
CAn enlargement of scale factor $\frac{1}{2}$ with centre the point $(1; 1)$
DA stretch of factor $\frac{1}{2}$ parallel to the $x$ -axis with the $y$ -axis invariant

Question 903

[3 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(3;2), B(4;2), C(4;3) and D(3;4). It is rotated through

90°

clockwise about the centre

(1; 1)

to give

A_3B_3C_3D_3

. Write down the coordinates of

C_3

Answer this when you sit the paper.

Question 904

[2 marks]Geometrical Transformation

Write down the matrix representing a stretch parallel to the

x

-axis with a stretch factor of 3.

A $\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}$
B $\begin{pmatrix} 0 & 3 \\ 1 & 0 \end{pmatrix}$
C $\begin{pmatrix} 3 & 0 \\ 0 & 1 \end{pmatrix}$
D $\begin{pmatrix} 1 & 0 \\ 0 & 3 \end{pmatrix}$

Question 1001

[3 marks]Matrices

Matrix

A = \begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix}

and matrix

B = \begin{pmatrix} 4 & -1 \\ 2 & 5 \end{pmatrix}

. Evaluate

3A - B

Answer this when you sit the paper.

Question 1002

[2 marks]Matrices

Matrix

B = \begin{pmatrix} 4 & -1 \\ 2 & 5 \end{pmatrix}

and matrix

C = \begin{pmatrix} -2 \\ 3 \end{pmatrix}

. Evaluate

BC

Answer this when you sit the paper.

Question 1003

[3 marks]Matrices

Find the inverse of the matrix

A = \begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix}

A $\frac{1}{5}\begin{pmatrix} 1 & 4 \\ -2 & -3 \end{pmatrix}$
B $\frac{1}{5}\begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix}$
C $-\frac{1}{11}\begin{pmatrix} 1 & -4 \\ 2 & -3 \end{pmatrix}$
D $\frac{1}{5}\begin{pmatrix} 1 & -4 \\ 2 & -3 \end{pmatrix}$

Question 1004

[3 marks]Matrices

Using the inverse of

\begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix}

, or otherwise, solve the simultaneous equations

-3x + 4y = 11

and

-2x + y = 4

. Give the values of

x

and

y

Answer this when you sit the paper.

Question 1101

[1 marks]Vector Geometry

PQRS is a parallelogram in which

\vec{PQ} = 3p

and

\vec{PS} = 3q

. Express

\vec{RS}

in terms of

p

and

q

A $3q$
B $-3q$
C $3p$
D $-3p$

Question 1102

[2 marks]Vector Geometry

PQRS is a parallelogram in which

\vec{PQ} = 3p

and

\vec{PS} = 3q

. Express

\vec{SQ}

in terms of

p

and

q

Answer this when you sit the paper.

Question 1103

[2 marks]Vector Geometry

PQRS is a parallelogram in which

\vec{PQ} = 3p

and

\vec{PS} = 3q

. The point X lies on QS so that

QS = 3XS

. Express

\vec{XQ}

in terms of

p

and

q

Answer this when you sit the paper.

Question 1104

[2 marks]Vector Geometry

PQRS is a parallelogram in which

\vec{PQ} = 3p

and

\vec{PS} = 3q

. The point X lies on QS so that

QS = 3XS

. Express

\vec{XP}

in terms of

p

and

q

Answer this when you sit the paper.

Question 1105

[3 marks]Vector Geometry

In parallelogram PQRS,

\vec{XP} = -p - 2q

. PX produced meets SR at N, where

\vec{NP} = h\vec{XP}

and also

\vec{NP} = -3kp - 3q

with

NS = kRS

. Find the value of

h

Answer this when you sit the paper.

Question 1106

[1 marks]Vector Geometry

In parallelogram PQRS, PX produced meets SR at N and it is found that

\vec{NP} = \frac{3}{2}\vec{XP}

, where

NS = kRS

and

k = \frac{1}{2}

. Write down the ratio

\frac{NS}{RS}

Answer this when you sit the paper.

Question 1201

[1 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, and TPV is a tangent at P.

Q\hat{P}V = 40°

Q\hat{S}R = 34°

and

R\hat{P}S = 54°

. Find

Q\hat{P}R

A $54°$
B $20°$
C $34°$
D $40°$

Question 1202

[1 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, and TPV is a tangent at P with

Q\hat{P}V = 40°

. Find

P\hat{R}Q

A $17°$
B $34°$
C $40°$
D $54°$

Question 1203

[2 marks]Circle Geometry

P, Q, R and S lie on a circle centre O and TPV is a tangent at P. Given

Q\hat{P}V = 40°

Q\hat{P}R = 34°

and

R\hat{P}S = 54°

, find

P\hat{Q}S

in degrees.

Answer this when you sit the paper.

Question 1204

[2 marks]Circle Geometry

In the circle PQRS the chords PR and QS meet at X. Given

R\hat{P}S = 54°

and

P\hat{S}Q = 40°

, find

P\hat{X}Q

in degrees.

Answer this when you sit the paper.

Question 1205

[1 marks]Circle Geometry

In the circle PQRS the chords PR and QS meet at X, with

X\hat{P}S = X\hat{Q}R = 54°

and

X\hat{S}P = X\hat{R}Q = 40°

. Name correctly the triangle which is similar to triangle PXS.

ATriangle XRQ
BTriangle QRX
CTriangle QXR
DTriangle RXQ

Question 1206

[2 marks]Circle Geometry

In the circle PQRS the chords PR and QS meet at X, and triangle PXS is similar to triangle QXR with P matching Q and S matching R. Given

PS = 12

cm,

QR = 8

cm and

SX = 9

cm, calculate the length of RX in centimetres.

Answer this when you sit the paper.

Question 1207

[2 marks]Circle Geometry

Triangle QRX is similar to triangle PSX, with

QR = 8

cm corresponding to

PS = 12

cm. Find the ratio of the area of triangle QRX to the area of triangle PSX.

Answer this when you sit the paper.

Mathematics Paper 2 June 2025

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 204

Question 301

Question 302

Question 303

Question 304

Question 401

Question 402

Question 403

Question 404

Question 405

Question 501

Question 502

Question 503

Question 504

Question 601

Question 602

Question 603

Question 604

Question 701

Question 702

Question 703

Question 704

Question 705

Question 801

Question 802

Question 803

Question 804

Question 901

Question 902

Question 903

Question 904

Question 1001

Question 1002

Question 1003

Question 1004

Question 1101

Question 1102

Question 1103

Question 1104

Question 1105

Question 1106

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

Question 1207

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