ZIMSEC O Level Mathematics Paper 2 June 2024

Question 101

[2 marks]Consumer Arithmetic

The sum of the interior angles of a polygon is double the sum of its exterior angles. Find the number of sides of the polygon.

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Question 201

[2 marks]Factorisation

Solve the equation

6x - 2 = 2x + 8

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Question 202

[3 marks]Factorisation

Factorise completely

5h^2 - 20k^2

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Question 203

[2 marks]Factorisation

Factorise completely

2mp - m - 6np + 3n

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Question 204

[3 marks]Factorisation

Express

\frac{3}{x-y} - \frac{2}{x+y}

as a single fraction in its simplest form.

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Question 301

[2 marks]Ordinary and Standard Form

Mr Dube had an appointment with a doctor at 1400. He arrived 14 minutes early and the doctor was 15 minutes late. Find how long Mr Dube waited, in minutes.

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Question 302

[1 marks]Ordinary and Standard Form

Find the difference between 4 weeks 3 days and 2 weeks 5 days, giving the answer in weeks and days.

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Question 303

[3 marks]Ordinary and Standard Form

Mary cycles to and from a school 5 times. The school is 5 km away, to the nearest km. Calculate the smallest possible distance she cycles, in kilometres.

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Question 304

[2 marks]Ordinary and Standard Form

The population of town A is

4,52 \times 10^7

and that of town B is

8,7 \times 10^6

. Calculate the difference between the two populations, giving the answer in standard form.

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Question 305

[2 marks]Ordinary and Standard Form

The population of town B is

8,7 \times 10^6

and 40% of them are adults. Calculate the number of adults in town B, giving the answer in ordinary form.

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Question 401

[2 marks]Number Bases

Simplify

\frac{0,35 + 0,25}{0,3 \times 0,04}

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Question 402

[3 marks]Number Bases

Evaluate

43_5 + 1001_2

, giving the answer in base two.

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Question 403

[3 marks]Number Bases

A rectangular garden measures 15 m by 12 m, each to the nearest metre. Calculate the least possible area of the garden, in square metres.

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Question 404

[2 marks]Number Bases

Given that

a = 3,12 \times 10^{-3}

and

b = 4,5 \times 10^{-4}

, find

a + b

, giving the answer in standard form.

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Question 405

[2 marks]Number Bases

Given that

a = 3,12 \times 10^{-3}

and

b = 4,5 \times 10^{-4}

, find

ab

, giving the answer in standard form.

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Question 501

[1 marks]Constructions and Loci

A quadrilateral ABCD is constructed with

AB = 8

cm,

BC = 10

cm and

A\hat{B}C = 90^\circ

, and a circle is drawn through A, B and C. Measure and write down the radius of that circle, in centimetres.

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Question 502

[2 marks]Constructions and Loci

In quadrilateral ABCD,

AB = 8

cm,

BC = 10

cm and

A\hat{B}C = 90^\circ

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

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Question 503

[2 marks]Constructions and Loci

Which construction gives the locus of the points that are equidistant from two points A and B?

AThe perpendicular bisector of the line AB
BThe bisector of the angle between AB and BC
CA circle centred on the midpoint of AB
DThe line through A and B extended both ways

Question 601

[2 marks]Sets

The universal set is

\xi = \{x : 1 < x \le 20,\ x \text{ is an integer}\}

and

X

is the set of prime numbers in it. List all the elements of

X

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Question 602

[1 marks]Sets

The universal set is

\xi = \{x : 1 < x \le 20,\ x \text{ is an integer}\}

and

Z

is the set of multiples of 5 in it. Find

n(Z)

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Question 603

[1 marks]Sets

\xi = \{x : 1 < x \le 20,\ x \text{ is an integer}\}

Y

is the set of even numbers and

Z

the set of multiples of 5. Find

n(Y \cup Z)

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Question 604

[2 marks]Sets

\xi = \{x : 1 < x \le 20,\ x \text{ is an integer}\}

Y

is the set of even numbers and

Z

the set of multiples of 5. Express

P = \{10; 20\}

in set notation using

Y

and

Z

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Question 605

[3 marks]Sets

Solve the inequality

-3 < 2x + 1 \le 7

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Question 606

[2 marks]Sets

Give the integral values that satisfy

-2 < x \le 3

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Question 701

[2 marks]Matrices

Given that

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

and the determinant of

A

is 5, find the value of

x

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Question 702

[2 marks]Matrices

Find the inverse of

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

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Question 703

[3 marks]Matrices

Solve the simultaneous equations

4x + 3y = 6

and

x + 2y = -1

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Question 704

[1 marks]Matrices

P, Q, R, S and T lie on the circumference of a circle and QS is a diameter. State briefly why

Q\hat{R}S = 90^\circ

AAngles in the same segment of a circle are equal
BThe angle in a semicircle is a right angle
COpposite angles of a cyclic quadrilateral are supplementary
DThe angle at the centre is twice the angle at the circumference

Question 705

[2 marks]Matrices

P, Q, R, S and T lie on a circle with QS as diameter, and

S\hat{Q}R = 34^\circ

. Find

Q\hat{S}R

, in degrees.

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Question 706

[2 marks]Matrices

P, Q, R, S and T lie on a circle, PT is parallel to QS and

Q\hat{S}T = 68^\circ

. Find

S\hat{T}P

, in degrees.

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Question 801

[1 marks]Functional Graphs

The function is

y = x^2 + x - 3

. Find the value of

y

when

x = -3

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Question 802

[1 marks]Functional Graphs

The function is

y = x^2 + x - 3

. Find the value of

y

when

x = 0

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Question 803

[1 marks]Functional Graphs

The graph of

y = x^2 + x - 3

is drawn for

-4 \le x \le 3

. Write down the equation of its line of symmetry.

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Question 804

[2 marks]Functional Graphs

The graph of

y = x^2 + x - 3

is drawn for

-4 \le x \le 3

. Write down the coordinates of the minimum point of the curve.

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Question 805

[2 marks]Functional Graphs

Use the graph of

y = x^2 + x - 3

to solve the equation

x^2 + x - 3 = -2

, giving both roots to 1 decimal place.

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Question 901

[2 marks]Statistics and Probability

A cumulative frequency curve for the journey times of 80 motorists gives cumulative totals of 20 at

t = 2

, 45 at 3, 64 at 4, 72 at 5, 76 at 6 and 80 at 8 hours. Find the three missing frequencies, for

4 < t \le 5

5 < t \le 6

and

6 < t \le 8

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Question 902

[3 marks]Statistics and Probability

The journey times of 80 motorists are

0 < t \le 2

(20 motorists),

2 < t \le 3

(25),

3 < t \le 4

(19),

4 < t \le 5

(8),

5 < t \le 6

(4) and

6 < t \le 8

(4). Calculate an estimate of the mean time, correct to the nearest hour.

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Question 903

[2 marks]Statistics and Probability

A cumulative frequency curve for the journey times of 80 motorists rises to 20 at

t = 2

hours and 45 at

t = 3

hours. Find the median journey time, in hours.

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Question 904

[3 marks]Statistics and Probability

A histogram is drawn for the classes

17 < m \le 21

(frequency 2),

21 < m \le 24

(3) and

24 < m \le 27

(9). Calculate the heights of these first three bars.

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Question 1001

[1 marks]Vector Geometry

OABC is a parallelogram with

\vec{OA} = 2\mathbf{a}

and

\vec{OC} = 2\mathbf{b}

, and S is the midpoint of AB. Express

\vec{AS}

in terms of

\mathbf{a}

and/or

\mathbf{b}

Answer this when you sit the paper.

Question 1002

[1 marks]Vector Geometry

OABC is a parallelogram with

\vec{OA} = 2\mathbf{a}

and

\vec{OC} = 2\mathbf{b}

, and S is the midpoint of AB. Express

\vec{OS}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1003

[1 marks]Vector Geometry

OABC is a parallelogram with

\vec{OA} = 2\mathbf{a}

and

\vec{OC} = 2\mathbf{b}

, and R is the midpoint of BC. Express

\vec{OR}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1004

[1 marks]Vector Geometry

OABC is a parallelogram with

\vec{OA} = 2\mathbf{a}

and

\vec{OC} = 2\mathbf{b}

, and R is the midpoint of BC. Express

\vec{AR}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1005

[1 marks]Vector Geometry

In parallelogram OABC,

\vec{OS} = 2\mathbf{a} + \mathbf{b}

and

\vec{OT} = k\vec{OS}

. Express

\vec{OT}

in terms of

\mathbf{a}

\mathbf{b}

and

k

Answer this when you sit the paper.

Question 1006

[3 marks]Vector Geometry

In parallelogram OABC,

\vec{OT} = (2-h)\mathbf{a} + 2h\mathbf{b}

and also

\vec{OT} = 2k\mathbf{a} + k\mathbf{b}

, where

\mathbf{a}

and

\mathbf{b}

are not parallel. Find the values of

h

and

k

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Question 1007

[1 marks]Vector Geometry

In parallelogram OABC, OS and AR meet at T with

\vec{AT} = \frac{2}{5}\vec{AR}

. Find the ratio

\frac{TR}{AR}

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Question 1101

[3 marks]Geometrical Transformation

Triangle XYZ has vertices X(1;1), Y(4;1) and Z(2;3). The matrix

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

maps it onto triangle

X_1Y_1Z_1

. Write down the coordinates of

X_1

Y_1

and

Z_1

Answer this when you sit the paper.

Question 1102

[3 marks]Geometrical Transformation

Triangle

X_1Y_1Z_1

has vertices

(0;3)

(3;6)

and

(-1;8)

. It is rotated

90^\circ

anticlockwise about

(-2;0)

. Write down the coordinates of the image vertices.

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Question 1103

[3 marks]Geometrical Transformation

Triangle XYZ has vertices X(1;1), Y(4;1) and Z(2;3), and triangle

X_3Y_3Z_3

has vertices

(-3;-3)

(-12;-3)

and

(-6;-9)

. Describe fully the single transformation that maps XYZ onto

X_3Y_3Z_3

AAn enlargement, centre $(0;0)$ , scale factor $-3$
BAn enlargement, centre $(0;0)$ , scale factor $3$
CA rotation of $180^\circ$ about $(0;0)$ followed by no change of size
DAn enlargement, centre $(-3;-3)$ , scale factor $-3$

Question 1104

[1 marks]Geometrical Transformation

Write down the matrix that represents an enlargement, centre the origin, with scale factor

-3

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Question 1201

[1 marks]Fractions, Decimals and Percentages

Find the L.C.M of

2^3 \times 3^2 \times 7^2

2^4 \times 3^3 \times 5 \times 7^3

and

2^5 \times 3 \times 5^2 \times 7

, giving the answer in index form.

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Question 1202

[2 marks]Fractions, Decimals and Percentages

Simplify

6u \times 5 - 3 \times 4u - 12u

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Question 1203

[2 marks]Fractions, Decimals and Percentages

Simplify

4\frac{1}{8} \times \frac{4}{11} \div 6\frac{2}{3}

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Question 1204

[2 marks]Fractions, Decimals and Percentages

During a one hour radio programme there were 12 minutes of talking and the rest was music. Calculate the percentage of the programme that was music.

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Question 1205

[2 marks]Fractions, Decimals and Percentages

Given that

y = 2,9 \times 10^2

, evaluate

\sqrt{y - 1}

, giving the answer in standard form.

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Question 1206

[3 marks]Fractions, Decimals and Percentages

Evaluate

38_9 + 1001_4

, giving the answer in base five.

Answer this when you sit the paper.

Mathematics Paper 2 June 2024

Sit this paper online

The questions

Question 101

Question 201

Question 202

Question 203

Question 204

Question 301

Question 302

Question 303

Question 304

Question 305

Question 401

Question 402

Question 403

Question 404

Question 405

Question 501

Question 502

Question 503

Question 601

Question 602

Question 603

Question 604

Question 605

Question 606

Question 701

Question 702

Question 703

Question 704

Question 705

Question 706

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 1006

Question 1007

Question 1101

Question 1102

Question 1103

Question 1104

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

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The answers, and why they are the answers

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