ZIMSEC O Level Mathematics Paper 2 November 2025

Question 101

[2 marks]Sets

The universal set is

\xi = \{1; 2; 3; ...; 10\}

P = \{2; 3; 5; 7\}

and Q is the set of factors of 42. List all elements of

P \cap Q

Answer this when you sit the paper.

Question 102

[2 marks]Sets

The universal set is

\xi = \{1; 2; 3; ...; 10\}

P = \{2; 3; 5; 7\}

and

Q = \{1; 2; 3; 6; 7\}

. Find

n(P \cup Q)'

Answer this when you sit the paper.

Question 103

[2 marks]Sets

In the Venn diagram, set A is made up of the regions containing

x

, 2, 4 and 6. Given that

n(A) = 22

, find the value of

x

Answer this when you sit the paper.

Question 104

[2 marks]Sets

In the Venn diagram, the region

B \cap C

holds 4 elements and the region inside both A and C but outside B holds 6 elements. B lies entirely inside A. Find

n(A \cap C)

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Question 201

[2 marks]Algebraic Expressions

Expand

(3 - 2y)^2

Answer this when you sit the paper.

Question 202

[2 marks]Factorisation, H.C.F & L.C.M

Factorise

2x^2 - 3x + 1

Answer this when you sit the paper.

Question 203

[3 marks]Linear Equations

Solve the equation

3(2x - 1) - (2 - x) = 7

Answer this when you sit the paper.

Question 204

[3 marks]Simultaneous Equations

Solve the simultaneous equations

3m + n = -5

and

m = 1 - 3n

Answer this when you sit the paper.

Question 301

[3 marks]Consumer Arithmetic

A vendor bought 120 cabbages for $7 200 and sold all of them at $45 each. Calculate the percentage loss made by the vendor.

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Question 302

[2 marks]Consumer Arithmetic

The exchange rate on a certain day was ZWL$85 to USA$1. Express USA$170 in Zimbabwean dollars on that day.

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Question 303

[2 marks]Consumer Arithmetic

Calculate the Simple Interest, in dollars, if $6 000 is invested at 7,5 % per annum for a period of 5 years.

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Question 304

[3 marks]Consumer Arithmetic

A bank lends at a compound interest rate of 4,5% per annum. Calculate the total amount, in dollars, to be paid by a farmer who borrows $45 000 for a period of 2 years.

Answer this when you sit the paper.

Question 401

[1 marks]Matrices

Given that

\begin{pmatrix} 3 & a \\ 4 & 2 \end{pmatrix} + 2\begin{pmatrix} -2 & 4 \\ b & -5 \end{pmatrix} = \begin{pmatrix} -1 & 15 \\ 10 & c \end{pmatrix}

, find

a

Answer this when you sit the paper.

Question 402

[1 marks]Matrices

Given that

\begin{pmatrix} 3 & a \\ 4 & 2 \end{pmatrix} + 2\begin{pmatrix} -2 & 4 \\ b & -5 \end{pmatrix} = \begin{pmatrix} -1 & 15 \\ 10 & c \end{pmatrix}

, find

b

Answer this when you sit the paper.

Question 403

[1 marks]Matrices

Given that

\begin{pmatrix} 3 & a \\ 4 & 2 \end{pmatrix} + 2\begin{pmatrix} -2 & 4 \\ b & -5 \end{pmatrix} = \begin{pmatrix} -1 & 15 \\ 10 & c \end{pmatrix}

, find

c

Answer this when you sit the paper.

Question 404

[2 marks]Matrices

Matrix

M = \begin{pmatrix} 6 & 3 \\ 1 & 3 \end{pmatrix}

and matrix

N = \begin{pmatrix} 7 \\ -3 \end{pmatrix}

. Find

MN

Answer this when you sit the paper.

Question 405

[2 marks]Matrices

Matrix

M = \begin{pmatrix} 6 & 3 \\ 1 & 3 \end{pmatrix}

. Find the determinant of M.

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Question 406

[3 marks]Matrices

Matrix

M = \begin{pmatrix} 6 & 3 \\ 1 & 3 \end{pmatrix}

has determinant 15. Find matrix P for which

MP = \begin{pmatrix} 3 & -6 \\ -4 & -1 \end{pmatrix}

Answer this when you sit the paper.

Question 501

[1 marks]Scales & Simple Map Problems

Village Q is 1,4 km from village P. On a construction drawn to a scale of 1 cm to represent 200 m, find the length, in centimetres, of PQ.

Answer this when you sit the paper.

Question 502

[1 marks]Scales & Simple Map Problems

Village R is 2 km from village P. On a construction drawn to a scale of 1 cm to represent 200 m, find the length, in centimetres, of PR.

Answer this when you sit the paper.

Question 503

[1 marks]Trigonometry, Bearing & Distances

Village Q is on a bearing of N 45° W from village P and village R is on a bearing of N 60° E from village P. Find

Q\hat{P}R

, in degrees.

Answer this when you sit the paper.

Question 504

[2 marks]Constructions & Loci

Villages P, Q and R are on level ground, with

PQ = 1,4

km,

PR = 2

km and

Q\hat{P}R = 105°

. A borehole B is equidistant from all three villages. Calculate the distance, in kilometres, of village R from the borehole, correct to 3 significant figures.

Answer this when you sit the paper.

Question 601

[3 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{3}{4} \times \left(2\dfrac{1}{2} - \dfrac{4}{5}\right)

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

Answer this when you sit the paper.

Question 602

[3 marks]Factorisation, H.C.F & L.C.M

Three pieces of wire of lengths 36 cm, 90 cm and 108 cm are cut into equal pieces. Find the greatest length, in centimetres, of each piece if no wire is left over.

Answer this when you sit the paper.

Question 603

[2 marks]Ratios, Rates & Proportions

Sarah and Nobuhle shared a packet of sweets in the ratio 3 : 5 respectively and Sarah received 60 sweets. Express Nobuhle's share as a percentage of the total number of sweets in the packet.

Answer this when you sit the paper.

Question 604

[2 marks]Ratios, Rates & Proportions

Nobuhle's share of a packet of sweets is 100 sweets. Calculate the number of sweets she would get if her share is reduced in the ratio 2 : 3.

Answer this when you sit the paper.

Question 605

[2 marks]Number Bases

Evaluate

503_6 - 231_5

, giving the answer in base 6.

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Question 701

[2 marks]Variation

P

varies directly with

r

and inversely with

(q^2 - 3)

, so that

P = \dfrac{kr}{q^2-3}

. Given that

P = 10

when

q = 5

and

r = 11

, find the value of

k

Answer this when you sit the paper.

Question 702

[3 marks]Variation

Given that

P = \dfrac{20r}{q^2-3}

, find the two possible values of

q

when

r = 9,2

and

P = 4

Answer this when you sit the paper.

Question 703

[1 marks]Variation

The price

B

of a jacket partly varies as the cost

C

of its material and partly as the time

T

taken to make it. Express

B

in terms of

C

T

and two constants

m

and

n

Answer this when you sit the paper.

Question 704

[3 marks]Variation

The price of a jacket is

B = mC + nT

, where

C

is the cost of the material and

T

the time in hours. A jacket taking 4 hours with material costing $225 has price $2 225, and one taking 7 hours with material costing $450 has price $8 900. Find the value of

m

and the value of

n

Answer this when you sit the paper.

Question 705

[2 marks]Variation

The price of a jacket is

B = 89C - 4450T

, where

C

is the cost of the material in dollars and

T

the time in hours. Find the price, in dollars, of a jacket that is made in 5 hours with material costing $350.

Answer this when you sit the paper.

Question 801

[2 marks]Measures & Mensuration

A hollow cylindrical metal pipe has an internal diameter of 3,2 cm. Taking

\pi

to be 3,142, calculate the circumference of the inner circle, in centimetres.

Answer this when you sit the paper.

Question 802

[2 marks]Measures & Mensuration

A hollow cylindrical metal pipe is 60 cm long with an internal diameter of 3,2 cm. Taking

\pi

to be 3,142, calculate the internal curved surface area, in square centimetres.

Answer this when you sit the paper.

Question 803

[3 marks]Measures & Mensuration

The cross section of a hollow pipe has internal diameter 3,2 cm and external diameter 3,5 cm. Taking

\pi

to be 3,142, calculate the area of the shaded region of the cross section, in square centimetres.

Answer this when you sit the paper.

Question 804

[2 marks]Measures & Mensuration

A hollow pipe is 60 cm long and the ring of metal in its cross section has area

1,578\,855\ \text{cm}^2

. Calculate the volume of the metal in the pipe, in cubic centimetres.

Answer this when you sit the paper.

Question 805

[2 marks]Measures & Mensuration

A cube of solid metal has a mass of 2,42 kg and a volume of

125,3\ \text{cm}^3

. Calculate the density of the metal, in

\text{g/cm}^3

Answer this when you sit the paper.

Question 901

[2 marks]Functional Graphs

A table of values for

y = \dfrac{12}{x}

gives

y = m

when

x = 1\frac{1}{2}

and

y = n

when

x = 5

. Find the value of

m

and the value of

n

Answer this when you sit the paper.

Question 902

[2 marks]Functional Graphs

The graph of

y = \dfrac{12}{x}

is drawn for

1 \le x \le 6

. Use a tangent to find the gradient of the curve at

x = 3

Answer this when you sit the paper.

Question 903

[2 marks]Functional Graphs

The graph of

y = \dfrac{12}{x}

is drawn for

1 \le x \le 6

. Estimate the area, in square units, of the region bounded by the curve, the

x

-axis and the lines

x = 2

and

x = 4

Answer this when you sit the paper.

Question 904

[2 marks]Functional Graphs

The graphs of

y = \dfrac{12}{x}

and

y = 3x + 1

are drawn on the same axes for

1 \le x \le 6

. Use them to solve the equation

\dfrac{12}{x} = 3x + 1

Answer this when you sit the paper.

Question 1001

[1 marks]Statistics & Probability

In a grouped frequency table, the class

170 < h \le 190

contains 13 learners. Find its frequency density

w

Answer this when you sit the paper.

Question 1002

[1 marks]Statistics & Probability

The heights of 30 learners are grouped as

150 < h \le 160

(frequency density 0,6),

160 < h \le 170

(0,9),

170 < h \le 190

(0,65) and

190 < h \le 200

(0,2). State the modal class.

Answer this when you sit the paper.

Question 1003

[3 marks]Statistics & Probability

The heights of 30 learners are grouped as

150 < h \le 160

(6 learners),

160 < h \le 170

(9),

170 < h \le 190

(13) and

190 < h \le 200

(2). Calculate an estimate for the mean height, in centimetres.

Answer this when you sit the paper.

Question 1004

[2 marks]Statistics & Probability

Of 30 learners, 9 have heights in the class

160 < h \le 170

. If the data is represented on a pie chart, calculate the angle of the sector for that class, in degrees.

Answer this when you sit the paper.

Question 1005

[1 marks]Statistics & Probability

Of 30 learners, 13 have heights in the range

170 < h \le 190

. Find the probability that a learner chosen at random has a height in that range.

Answer this when you sit the paper.

Question 1101

[2 marks]Geometrical Transformation

Triangle PQR has vertices P(2;2), Q(4;6) and R(2;6). It is mapped onto triangle

P_2Q_2R_2

by an enlargement, centre (2;0), scale factor

-1\frac{1}{2}

. Write down the coordinates of

P_2

Q_2

and

R_2

Answer this when you sit the paper.

Question 1102

[2 marks]Geometrical Transformation

Triangle PQR has vertices P(2;2), Q(4;6) and R(2;6). The matrix

\begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}

maps it onto triangle

P_3Q_3R_3

. Write down the coordinates of

P_3

Q_3

and

R_3

Answer this when you sit the paper.

Question 1103

[3 marks]Geometrical Transformation

Describe fully the single transformation represented by the matrix

\begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}

Answer this when you sit the paper.

Question 1201

[1 marks]Inequalities & Linear Programming

In the diagram, one boundary of region R is the broken vertical line through

x = -2

, with the region lying to its right. Write down the inequality whose boundary is that line.

Answer this when you sit the paper.

Question 1202

[1 marks]Inequalities & Linear Programming

In the diagram, one boundary of region R is the solid line through

(-2; -2)

and

(3; 3)

, with the unwanted side below it shaded. Write down the inequality whose boundary is that line.

Answer this when you sit the paper.

Question 1203

[2 marks]Inequalities & Linear Programming

In the diagram, one boundary of region R is the solid line through

(-2; 2)

and

(3; 3)

, with the unwanted side above it shaded. Write down the inequality whose boundary is that line.

Answer this when you sit the paper.

Question 1204

[2 marks]Inequalities & Linear Programming

A region R is bounded by

x > -2

y \ge x

and

5y \le x + 12

. Write down the coordinates of the point of R that gives the maximum value of

2x + y

Answer this when you sit the paper.

Question 1205

[2 marks]Inequalities & Linear Programming

A region R is bounded by

x > -2

y \ge x

and

5y \le x + 12

. Find the maximum value of

2x + y

in R.

Answer this when you sit the paper.

Question 1206

[1 marks]Inequalities & Linear Programming

At a conference,

x

is the number of male teachers from a school and the number of male teachers should not exceed 9. Write down the inequality for this restriction.

Answer this when you sit the paper.

Question 1207

[1 marks]Inequalities & Linear Programming

At a conference,

y

is the number of female teachers from a school and at least 5 female teachers from each school should attend. Write down the inequality for this restriction.

Answer this when you sit the paper.

Question 1208

[2 marks]Inequalities & Linear Programming

At a conference,

x

is the number of male teachers and

y

the number of female teachers from a school, and not more than 15 teachers from each school can attend. Write down the inequality for this restriction.

Answer this when you sit the paper.

Mathematics Paper 2 November 2025

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 104

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 406

Question 501

Question 502

Question 503

Question 504

Question 601

Question 602

Question 603

Question 604

Question 605

Question 701

Question 702

Question 703

Question 704

Question 705

Question 801

Question 802

Question 803

Question 804

Question 805

Question 901

Question 902

Question 903

Question 904

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1101

Question 1102

Question 1103

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

Question 1207

Question 1208

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The answers, and why they are the answers

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