ZIMSEC O Level Mathematics Paper 2 November 2024

Question 101

[3 marks]H.C.F and L.C.M

Find the Highest Common Factor (H.C.F) of 96 and 120.

Answer this when you sit the paper.

Question 102

[2 marks]H.C.F and L.C.M

On a certain day the temperature rose from

-5\,^\circ

C to

+27\,^\circ

C. Calculate the rise in temperature, in degrees Celsius.

Answer this when you sit the paper.

Question 103

[2 marks]H.C.F and L.C.M

Given that

r = 4,2 \times 10^5

and

q = 7 \times 10^{-3}

, evaluate

qr

, leaving the answer in standard form.

Answer this when you sit the paper.

Question 104

[2 marks]H.C.F and L.C.M

Simplify

3\sqrt{7} + \sqrt{14} \times \sqrt{2}

, leaving the answer in surd form.

Answer this when you sit the paper.

Question 201

[1 marks]Matrices

Write down the order of the matrix

\begin{pmatrix} 2 & 8 \end{pmatrix}

Answer this when you sit the paper.

Question 202

[2 marks]Matrices

Matrix

A = \begin{pmatrix} 5 & 0 \\ -8 & 9 \end{pmatrix}

and matrix

B = \begin{pmatrix} 6 & -4 \\ 0 & 2 \end{pmatrix}

. Evaluate

A - \frac{1}{2}B

, giving the four entries in order.

Answer this when you sit the paper.

Question 203

[2 marks]Matrices

Matrix

A = \begin{pmatrix} 5 & 0 \\ -8 & 9 \end{pmatrix}

and matrix

B = \begin{pmatrix} 6 & -4 \\ 0 & 2 \end{pmatrix}

. Evaluate

AB

, giving the four entries in order.

Answer this when you sit the paper.

Question 204

[2 marks]Matrices

The matrix

\begin{pmatrix} x - 1 & 6 \\ 2 & x + 3 \end{pmatrix}

is singular. Write down its determinant in terms of

x

, before expanding the brackets.

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Question 205

[3 marks]Matrices

Solve the equation

x^2 + 2x - 15 = 0

Answer this when you sit the paper.

Question 301

[2 marks]Consumer Arithmetic

The selling price of a mobile phone is

\$2\,760,00

including Value Added Tax of 15%. Calculate the price of the phone excluding Value Added Tax.

Answer this when you sit the paper.

Question 302

[2 marks]Consumer Arithmetic

A mobile phone sells for ZWL

\$2\,760,00

. On a certain day the exchange rate was ZWL

\$9,00

to 1 Botswana Pula. Find the cost of the phone in Pula, correct to 2 decimal places.

Answer this when you sit the paper.

Question 303

[3 marks]Consumer Arithmetic

A sales person is paid 3,5% commission on each mobile phone sold at

\$2\,760,00

. Calculate the total commission earned when 23 such phones are sold.

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Question 304

[3 marks]Consumer Arithmetic

Electricity is charged at

\$2,25

per unit for the first 50 units,

\$4,51

per unit for units 51 to 100,

\$11,26

per unit for units 101 to 300 and

\$12,94

per unit for 301 units and above. Calculate the cost of 375 units.

Answer this when you sit the paper.

Question 401

[2 marks]Measures and Mensuration

An athletics field is a rectangle ABDE with a semicircle of radius 31,8 m on each end, and

AB = 100

m. Taking

\pi

to be 3,142, calculate the length of arc BCD, in metres.

Answer this when you sit the paper.

Question 402

[2 marks]Measures and Mensuration

An athletics field is a rectangle ABDE with a semicircular end of radius 31,8 m at each end, and

AB = ED = 100

m. Taking

\pi

to be 3,142, calculate the perimeter of the field, in metres.

Answer this when you sit the paper.

Question 403

[3 marks]Measures and Mensuration

An athletics field is a rectangle ABDE with a semicircle of radius 31,8 m on each end, and

AB = 100

m. Taking

\pi

to be 3,142, calculate the total area of the field, correct to the nearest square metre.

Answer this when you sit the paper.

Question 404

[2 marks]Measures and Mensuration

An athletics field has a total area of

9\,537

^2

. Calculate the cost of covering the whole field with grass at

\$620

per square metre.

Answer this when you sit the paper.

Question 405

[2 marks]Measures and Mensuration

On a map, the length

AB = 100

m of an athletics field is drawn as a line 4 cm long. Find the scale used, in the form

1 : n

where

n

is an integer.

Answer this when you sit the paper.

Question 501

[1 marks]Constructions and Loci

Triangle ABC is constructed with

BC = 10,5

cm,

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

and

B\hat{C}A = 30^\circ

. Measure and write down the length of AB, in centimetres.

Answer this when you sit the paper.

Question 502

[2 marks]Constructions and Loci

In triangle ABC,

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

and

B\hat{C}A = 30^\circ

. Find

B\hat{A}C

, in degrees.

Answer this when you sit the paper.

Question 503

[2 marks]Constructions and Loci

In triangle ABC, which construction gives the locus of the points inside the triangle that are equidistant from the lines AB and AC?

AThe bisector of angle BAC, drawn from A
BThe perpendicular bisector of the side BC
CThe line through A parallel to the side BC
DThe perpendicular from A to the side BC

Question 504

[2 marks]Constructions and Loci

What is the locus of the points that are 3 cm from the line BC?

AThe perpendicular bisector of BC, marked 3 cm from B
BA pair of lines parallel to BC, one 3 cm on each side of it
CA single line parallel to BC and 3 cm above it
DA circle of radius 3 cm centred on the midpoint of BC

Question 601

[2 marks]Factorisation

Factorise completely

a^2 + ay - ax - xy

Answer this when you sit the paper.

Question 602

[2 marks]Factorisation

Factorise completely

x^2y^2 - 9

Answer this when you sit the paper.

Question 603

[3 marks]Factorisation

Each side of a regular hexagon is

\frac{3x - 5}{2}

cm long and its perimeter is 15 cm. Find the value of

x

Answer this when you sit the paper.

Question 604

[2 marks]Factorisation

Given that

V = kr^2h

, find

V

when

k = \frac{22}{7}

r = 3,5

and

h = 15

Answer this when you sit the paper.

Question 605

[2 marks]Factorisation

Given that

V = kr^2h

, express

r

in terms of

k

V

and

h

Answer this when you sit the paper.

Question 701

[1 marks]Functional Graphs

A particle moves so that its velocity,

v

m/s, after

t

seconds is

v = t^2 - 5t + 10

. Find the value of

v

when

t = 5

Answer this when you sit the paper.

Question 702

[1 marks]Functional Graphs

The velocity of a particle is

v = t^2 - 5t + 10

m/s after

t

seconds. Find the minimum velocity reached, in metres per second.

Answer this when you sit the paper.

Question 703

[2 marks]Functional Graphs

The velocity of a particle is

v = t^2 - 5t + 10

m/s after

t

seconds. Find its acceleration when

t = 1

, in m/s

^2

Answer this when you sit the paper.

Question 704

[2 marks]Functional Graphs

The velocity of a particle is

v = t^2 - 5t + 10

m/s after

t

seconds, for

0 \le t \le 6

. Find the range of values of

t

for which the velocity is less than 7 m/s.

Answer this when you sit the paper.

Question 705

[2 marks]Functional Graphs

The velocity of a particle is

v = t^2 - 5t + 10

m/s after

t

seconds. Estimate the distance travelled between

t = 2

and

t = 4

, in metres.

Answer this when you sit the paper.

Question 801

[1 marks]Statistics and Probability

In a Mathematics test the marks of 100 learners fall in the classes

0 \le x < 10

(7 learners),

10 \le x < 20

(13),

20 \le x < 30

(31),

30 \le x < 40

(37) and

40 \le x < 50

(12). State the modal class.

Answer this when you sit the paper.

Question 802

[3 marks]Statistics and Probability

The marks of 100 learners fall in the classes

0 \le x < 10

(7 learners),

10 \le x < 20

(13),

20 \le x < 30

(31),

30 \le x < 40

(37) and

40 \le x < 50

(12). Calculate an estimate of the mean mark.

Answer this when you sit the paper.

Question 803

[1 marks]Statistics and Probability

The marks of 100 learners fall in the classes

0 \le x < 10

(7 learners),

10 \le x < 20

(13),

20 \le x < 30

(31),

30 \le x < 40

(37) and

40 \le x < 50

(12). State the class interval in which the median mark lies.

Answer this when you sit the paper.

Question 804

[2 marks]Statistics and Probability

In a class of 100 learners, 7 scored

0 \le x < 10

, 13 scored

10 \le x < 20

, 31 scored

20 \le x < 30

, 37 scored

30 \le x < 40

and 12 scored

40 \le x < 50

. One learner is picked at random. Find the probability that the mark is at least 10 but less than 40.

Answer this when you sit the paper.

Question 901

[2 marks]Inequalities and Linear Programming

A dressmaker has 18 m of cloth. Each pair of trousers needs 0,75 m and each skirt needs 0,5 m. Taking

x

as the number of trousers and

y

as the number of skirts, write down the cloth inequality before it is simplified.

Answer this when you sit the paper.

Question 902

[2 marks]Inequalities and Linear Programming

A dressmaker should make at least 6 pairs of trousers and at least 10 skirts, where

x

is the number of trousers and

y

the number of skirts. Write down the two inequalities that state these conditions.

Answer this when you sit the paper.

Question 903

[1 marks]Inequalities and Linear Programming

A dressmaker makes

x

pairs of trousers and

y

skirts, and the number of skirts should be more than the number of trousers. Form an inequality for this condition.

Answer this when you sit the paper.

Question 904

[2 marks]Inequalities and Linear Programming

A dressmaker makes

x

pairs of trousers and

y

skirts subject to

3x + 2y \le 72

x \ge 6

y \ge 10

and

y > x

. Each pair of trousers profits

\$300

and each skirt

\$120

. Calculate the maximum possible profit.

Answer this when you sit the paper.

Question 1001

[2 marks]Geometrical Transformation

Triangle ABC has vertices A(4;2), B(4;4) and C(7;4). It is translated by the vector

\begin{pmatrix} 2 \\ -5 \end{pmatrix}

. Write down the coordinates of the image vertices

A_1

B_1

and

C_1

Answer this when you sit the paper.

Question 1002

[2 marks]Geometrical Transformation

Triangle ABC has vertices A(4;2), B(4;4) and C(7;4). It is reflected in the line

y = x + 2

. Write down the coordinates of the image vertices

A_2

B_2

and

C_2

Answer this when you sit the paper.

Question 1003

[3 marks]Geometrical Transformation

Triangle ABC has vertices A(4;2), B(4;4) and C(7;4). The matrix

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

maps it onto triangle

A_3B_3C_3

. Write down the coordinates of

A_3

B_3

and

C_3

Answer this when you sit the paper.

Question 1004

[3 marks]Geometrical Transformation

Describe fully the single transformation represented by the matrix

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

AA one way stretch parallel to the $x$ -axis with factor $-2\frac{1}{2}$
BA reflection in the $x$ -axis followed by a translation
CA shear with the $x$ -axis invariant and shear factor $-2\frac{1}{2}$
DA shear with the $y$ -axis invariant and shear factor $-2\frac{1}{2}$

Question 1101

[1 marks]Vector Geometry

PQRS is a parallelogram with

\vec{PQ} = \mathbf{a}

and

\vec{PS} = \mathbf{b}

. Express

\vec{RQ}

in terms of

\mathbf{a}

and/or

\mathbf{b}

Answer this when you sit the paper.

Question 1102

[1 marks]Vector Geometry

PQRS is a parallelogram with

\vec{PQ} = \mathbf{a}

and

\vec{PS} = \mathbf{b}

. Express

\vec{QS}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1103

[1 marks]Vector Geometry

PQRS is a parallelogram with

\vec{PQ} = \mathbf{a}

and

\vec{PS} = \mathbf{b}

, and M is the midpoint of SR. Express

\vec{PM}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1104

[1 marks]Vector Geometry

PQRS is a parallelogram with

\vec{PQ} = \mathbf{a}

and

\vec{PS} = \mathbf{b}

. Express

\vec{PR}

in terms of

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1105

[1 marks]Vector Geometry

In parallelogram PQRS, M is the midpoint of SR and

\vec{PM} = \frac{1}{2}\mathbf{a} + \mathbf{b}

. Given that

\vec{PN} = h\vec{PM}

, express

\vec{PN}

in terms of

h

\mathbf{a}

and

\mathbf{b}

Answer this when you sit the paper.

Question 1106

[3 marks]Vector Geometry

In parallelogram PQRS,

\vec{PN} = (1-k)\mathbf{a} + k\mathbf{b}

and also

\vec{PN} = \frac{1}{2}h\mathbf{a} + h\mathbf{b}

, where

\mathbf{a}

and

\mathbf{b}

are not parallel. Find the values of

h

and

k

Answer this when you sit the paper.

Question 1107

[1 marks]Vector Geometry

In parallelogram PQRS, PM and QS meet at N, and

\vec{PN} = \frac{2}{3}\vec{PM}

. Write down the numerical value of

\frac{MN}{NP}

Answer this when you sit the paper.

Question 1201

[2 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, PST is a straight line,

Q\hat{P}S = 65^\circ

R\hat{S}T = 100^\circ

and

P\hat{Q}O = 40^\circ

. Find

Q\hat{R}S

, in degrees.

Answer this when you sit the paper.

Question 1202

[2 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, with

Q\hat{P}S = 65^\circ

. Find the reflex angle

Q\hat{O}S

, in degrees.

Answer this when you sit the paper.

Question 1203

[2 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, PST is a straight line,

R\hat{S}T = 100^\circ

and

P\hat{Q}O = 40^\circ

. Find

O\hat{Q}R

, in degrees.

Answer this when you sit the paper.

Question 1204

[2 marks]Circle Geometry

P, Q, R and S lie on a circle centre O, with

Q\hat{P}S = 65^\circ

and

P\hat{Q}O = 40^\circ

. Find

P\hat{S}O

, in degrees.

Answer this when you sit the paper.

Question 1205

[1 marks]Circle Geometry

State the name given to the region of a circle enclosed by a chord PQ and the minor arc PQ.

Answer this when you sit the paper.

Question 1206

[1 marks]Circle Geometry

The interior angles of a polygon are in the ratio

2 : 3 : 4 : 5 : 6

. State the name of the polygon.

Answer this when you sit the paper.

Question 1207

[2 marks]Circle Geometry

The interior angles of a pentagon are in the ratio

2 : 3 : 4 : 5 : 6

. Calculate the size of the largest interior angle, in degrees.

Answer this when you sit the paper.

Mathematics Paper 2 November 2024

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 104

Question 201

Question 202

Question 203

Question 204

Question 205

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 605

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 1107

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

Question 1207

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