ZIMSEC O Level Mathematics Paper 2 November 2023

Question 101

[1 marks]Fractions, Decimals & Percentages

The price of a packet of sweets was $1,20. The price increased to $1,50. Calculate the percentage increase.

Answer this when you sit the paper.

Question 102

[2 marks]Fractions, Decimals & Percentages

A new cereal packet contains 20% more cereal than the old packet. If the new packet has a mass of 264 g, calculate the mass, in grams, of the cereal in the old packet.

Answer this when you sit the paper.

Question 103

[2 marks]Consumer Arithmetic

A painter got a 7% discount after buying a large amount of paint. If the discount was $91, find the value, in dollars, of the paint he bought.

Answer this when you sit the paper.

Question 104

[3 marks]Circle Geometry

AB

is a diameter of a circle centre O, and

C

is a point on the circumference such that

AC = 7,5

cm and

BC = 5

cm. Calculate the length of

AB

, in centimetres.

Answer this when you sit the paper.

Question 201

[2 marks]Constructions & Loci

Triangle ABC has

AB = 6

cm,

AC = 5,8

cm and

B\hat{A}C = 135°

. Calculate the length, in centimetres, of the perpendicular from C to BA produced.

Answer this when you sit the paper.

Question 202

[1 marks]Constructions & Loci

Describe fully the locus of points 4,5 cm from a fixed point B.

Answer this when you sit the paper.

Question 203

[2 marks]Constructions & Loci

In triangle ABC,

AB = 6

cm,

AC = 5,8

cm and

B\hat{A}C = 135°

, and C is 4,1 cm from the line AB. Describe fully the locus represented by the line parallel to AB passing through C.

Answer this when you sit the paper.

Question 301

[1 marks]Sets

The universal set is

\xi = \{x : x

is an integer and

30 \le x \le 40\}

and

P = \{x : x

is a prime number

\}

. Find

n(P)

Answer this when you sit the paper.

Question 302

[2 marks]Sets

The universal set is

\xi = \{x : x

is an integer and

30 \le x \le 40\}

P

is the set of prime numbers in

\xi

and

Q

is the set of multiples of 4 in

\xi

. List the members of

Q \cap P'

Answer this when you sit the paper.

Question 303

[3 marks]Trigonometry, Bearing & Distances

In triangle XYZ,

XY = 17

cm,

XZ = 8

cm and

Y\hat{X}Z = 65°30'

. Calculate the area of triangle XYZ, in square centimetres.

Answer this when you sit the paper.

Question 304

[2 marks]Probability

There are 25 red sweets and

x

blue sweets in a box. One sweet is selected at random and the probability that it is blue is

\dfrac{3}{8}

. Find

x

Answer this when you sit the paper.

Question 305

[3 marks]Variation

P varies directly as q and inversely as the square of

r

. Given that

P = 15

when

q = 9

and

r = 6

, find

P

when

q = 7

and

r = 2

Answer this when you sit the paper.

Question 401

[2 marks]Algebraic Expressions

Remove the brackets and simplify

4(3 - 2p) - 3(1 - p)

Answer this when you sit the paper.

Question 402

[2 marks]Algebraic Expressions

Remove the brackets and simplify

(3q - r)(q + 2r)

Answer this when you sit the paper.

Question 403

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

Factorise completely

8ab + 6ab^2

Answer this when you sit the paper.

Question 404

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

Factorise completely

18t^2 - 2

Answer this when you sit the paper.

Question 405

[1 marks]Substitution

Given that

y = 18 + 3x^2

, find the value of

y

when

x = -2

Answer this when you sit the paper.

Question 406

[2 marks]Quadratic Equations

Given that

y = 18 + 3x^2

, find the values of

x

when

y = 93

Answer this when you sit the paper.

Question 407

[2 marks]Change of Subject of Formula

Given that

y = 18 + 3x^2

, express

x

in terms of

y

Answer this when you sit the paper.

Question 501

[3 marks]Algebraic Fractions

Express

\dfrac{4}{y-3} - \dfrac{3}{y+4}

as a single fraction in its simplest form.

Answer this when you sit the paper.

Question 502

[3 marks]Quadratic Equations

Solve the equation

\dfrac{y-1}{8} = \dfrac{2}{y-1}

Answer this when you sit the paper.

Question 503

[2 marks]Inequalities

Solve the inequality

21 < 4n - 3 \le 27

Answer this when you sit the paper.

Question 504

[1 marks]Co-ordinate Geometry

Points

P

and

Q

have coordinates

(9; 8)

and

(12; 4)

respectively. Find the gradient of

QP

Answer this when you sit the paper.

Question 505

[2 marks]Co-ordinate Geometry

The line PQ has gradient

-\dfrac43

and the point

R

(4; -2)

. Find the equation of the line passing through

R

and parallel to

PQ

Answer this when you sit the paper.

Question 601

[1 marks]Statistics & Probability

The ages of 40 learners are grouped as

8 \le x < 10

(frequency density 3,5),

10 \le x < 11

(8),

11 \le x < 12

(6),

12 \le x < 14

(5),

14 \le x < 16

(1,5) and

16 \le x < 19

(2). State the modal class.

Answer this when you sit the paper.

Question 602

[3 marks]Statistics & Probability

The ages of 40 learners are grouped as

8 \le x < 10

(7 learners),

10 \le x < 11

(8),

11 \le x < 12

(6),

12 \le x < 14

(10),

14 \le x < 16

(3) and

16 \le x < 19

(6). Calculate an estimate of the mean age, in years.

Answer this when you sit the paper.

Question 603

[1 marks]Probability

In a group of 40 learners the youngest age class recorded is

8 \le x < 10

. One learner is chosen at random. Calculate the probability that the learner is below the age of 8 years.

Answer this when you sit the paper.

Question 604

[1 marks]Probability

In a group of 40 learners, 6 are in the class

16 \le x < 19

and the rest are younger than 16. One learner is chosen at random. Calculate the probability that the learner is below the age of 16 years.

Answer this when you sit the paper.

Question 605

[2 marks]Probability

Of 40 learners, 3 are in the age group

14 \le x < 16

. If two learners are chosen at random, find the probability that they are both in that age group.

Answer this when you sit the paper.

Question 701

[2 marks]Functional Graphs

A table of values for

y = 6 - x - x^2

gives

y = p

when

x = -4

and

y = q

when

x = 0

. Find the value of

p

and the value of

q

Answer this when you sit the paper.

Question 702

[1 marks]Functional Graphs

The graph of

y = 6 - x - x^2

is drawn for

-4 \le x \le 3

. Use it to find the maximum value of

6 - x - x^2

Answer this when you sit the paper.

Question 703

[1 marks]Functional Graphs

The graph of

y = 6 - x - x^2

is drawn for

-4 \le x \le 3

. Write down the equation of its line of symmetry.

Answer this when you sit the paper.

Question 704

[2 marks]Functional Graphs

The graph of

y = 6 - x - x^2

is drawn for

-4 \le x \le 3

. Use a tangent to find the gradient of the graph when

x = -2

Answer this when you sit the paper.

Question 705

[2 marks]Functional Graphs

The graph of

y = 6 - x - x^2

passes through

(-2; 4)

(-1; 6)

and

(0; 6)

. Estimate the area, in square units, bounded by the graph, the

x

-axis, the

y

-axis and the line

x = -2

Answer this when you sit the paper.

Question 801

[1 marks]Measures & Mensuration

A solid right cone has a base radius of 8 cm and a height of 15 cm. Calculate its slant height, in centimetres.

Answer this when you sit the paper.

Question 802

[2 marks]Measures & Mensuration

A solid right cone has a base radius of 8 cm and a height of 15 cm. Taking

\pi

to be

\frac{22}{7}

, calculate the volume of the cone, in cubic centimetres.

Answer this when you sit the paper.

Question 803

[2 marks]Measures & Mensuration

A solid right cone has a base radius of 8 cm and a slant height of 17 cm. Taking

\pi

to be

\frac{22}{7}

, calculate the curved surface area of the cone, in square centimetres.

Answer this when you sit the paper.

Question 804

[1 marks]Measures & Mensuration

A solid right cone has a base radius of 8 cm and a curved surface area of

\frac{2992}{7}\ \text{cm}^2

. Taking

\pi

to be

\frac{22}{7}

, calculate the total surface area of the cone, in square centimetres.

Answer this when you sit the paper.

Question 805

[2 marks]Measures & Mensuration

A square based cuboid of height 2 cm is made from

50\ \text{cm}^3

of clay. Find the length, in centimetres, of the side of the square base.

Answer this when you sit the paper.

Question 806

[2 marks]Measures & Mensuration

A pyramid with a base area of

15\ \text{cm}^2

is made from

50\ \text{cm}^3

of clay. Find the height of the pyramid, in centimetres.

Answer this when you sit the paper.

Question 807

[2 marks]Measures & Mensuration

A sphere is made from

50\ \text{cm}^3

of clay. Taking

\pi

to be

\frac{22}{7}

, calculate the radius of the sphere, in centimetres. [Volume of a sphere

= \frac43\pi r^3

]

Answer this when you sit the paper.

Question 901

[3 marks]Geometrical Transformation

Triangle A has vertices

(2;2)

(4;2)

and

(4;5)

. It is mapped onto triangle C by an enlargement centre

(0;0)

, scale factor

-2

. Write down the vertices of triangle C.

Answer this when you sit the paper.

Question 902

[3 marks]Geometrical Transformation

Triangle A has vertices

(2;2)

(4;2)

and

(4;5)

. Triangle D is its image under a clockwise rotation of 90° about the point

(2;-2)

. Write down the vertices of triangle D.

Answer this when you sit the paper.

Question 903

[2 marks]Geometrical Transformation

Triangle A has vertices

(2;2)

(4;2)

(4;5)

and triangle B has vertices

(-4;3)

(-2;3)

(-2;6)

. Describe fully the single transformation that maps triangle A onto triangle B.

Answer this when you sit the paper.

Question 904

[2 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 1001

[2 marks]Matrices

Given that

A = \begin{pmatrix} -3 & 4 \\ -\frac12 & 2 \end{pmatrix}

and

B = \begin{pmatrix} -2 & 2 \\ 6 & 1 \end{pmatrix}

, find

A + B

Answer this when you sit the paper.

Question 1002

[2 marks]Matrices

Given that

A = \begin{pmatrix} -3 & 4 \\ -\frac12 & 2 \end{pmatrix}

, find

A^{-1}

, the inverse of matrix A.

Answer this when you sit the paper.

Question 1003

[3 marks]Matrices

The determinant of the matrix

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

is 14. Find the possible values of

k

Answer this when you sit the paper.

Question 1004

[1 marks]Circle Geometry

In the diagram P, Q, R and S lie on a circle centre O, PS is a diameter and

S\hat{P}R = 43°

. Find

P\hat{S}R

, in degrees.

Answer this when you sit the paper.

Question 1005

[1 marks]Circle Geometry

In the diagram P, Q, R and S lie on a circle centre O and

P\hat{O}Q = 68°

. Find

P\hat{R}Q

, in degrees.

Answer this when you sit the paper.

Question 1006

[1 marks]Circle Geometry

In the diagram the tangent to the circle at Q meets SP produced at T, and

T\hat{O}Q = 68°

. Find

P\hat{T}Q

, in degrees.

Answer this when you sit the paper.

Question 1007

[1 marks]Circle Geometry

In the diagram P, Q, R and S lie on a circle centre O, PS is a diameter,

T\hat{O}Q = 68°

and

S\hat{P}R = 43°

. Find

R\hat{Q}O

, in degrees.

Answer this when you sit the paper.

Question 1101

[1 marks]Vector Geometry

In the diagram

\vec{OA} = a

and

\vec{OB} = b

. Express

\vec{AB}

in terms of

a

and

b

Answer this when you sit the paper.

Question 1102

[1 marks]Vector Geometry

In the diagram

\vec{OA} = a

\vec{OB} = b

and

AX : XB = 2 : 3

, with X on AB. Express

\vec{BX}

in terms of

a

and

b

Answer this when you sit the paper.

Question 1103

[2 marks]Vector Geometry

In the diagram

\vec{OA} = a

\vec{OB} = b

and

AX : XB = 2 : 3

, with X on AB. Express

\vec{OX}

in terms of

a

and

b

Answer this when you sit the paper.

Question 1104

[2 marks]Vector Geometry

In the diagram

\vec{OA} = a

\vec{OB} = b

and

\vec{BC} = k\vec{OA}

. Express

\vec{AC}

in terms of

k

a

and

b

Answer this when you sit the paper.

Question 1105

[1 marks]Vector Geometry

In the diagram

\vec{OA} = a

\vec{OB} = b

and

\vec{BC} = k\vec{OA}

. Express

\vec{OC}

in terms of

k

a

and

b

Answer this when you sit the paper.

Question 1106

[1 marks]Vector Geometry

Given that

\vec{OX} = \frac35 a + \frac25 b

and

\vec{OC} = h\vec{OX}

, express

\vec{OC}

in terms of

h

a

and

b

Answer this when you sit the paper.

Question 1107

[3 marks]Vector Geometry

Given that

\vec{OC} = ka + b

and also

\vec{OC} = \frac{3h}{5}a + \frac{2h}{5}b

, find the values of

k

and

h

Answer this when you sit the paper.

Question 1108

[1 marks]Vector Geometry

Given that

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

and

k = 1,5

, express

\vec{AC}

in terms of

a

and

b

Answer this when you sit the paper.

Question 1201

[3 marks]Trigonometry, Bearing & Distances

Points X, Y and Z lie on horizontal ground with

Y\hat{X}Z = 85°

XY = 6,5

m and

XZ = 7,2

m. Calculate YZ, in metres.

Answer this when you sit the paper.

Question 1202

[3 marks]Trigonometry, Bearing & Distances

In triangle XYZ,

Y\hat{X}Z = 85°

XZ = 7,2

m and

YZ = 9,27

m. Calculate

X\hat{Y}Z

, in degrees correct to one decimal place.

Answer this when you sit the paper.

Question 1203

[3 marks]Trigonometry, Bearing & Distances

The bearing of Z from X is 250°,

Y\hat{X}Z = 85°

with Y on the northern side of XZ, and

X\hat{Y}Z = 50,7°

. Calculate the bearing of Z from Y, correct to the nearest degree.

Answer this when you sit the paper.

Question 1204

[2 marks]Trigonometry, Bearing & Distances

In triangle XYZ,

XY = 6,5

XZ = 7,2

Y\hat{X}Z = 85°

and

YZ = 9,27

m. Calculate the shortest distance from X to YZ, in metres.

Answer this when you sit the paper.

Mathematics Paper 2 November 2023

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 104

Question 201

Question 202

Question 203

Question 301

Question 302

Question 303

Question 304

Question 305

Question 401

Question 402

Question 403

Question 404

Question 405

Question 406

Question 407

Question 501

Question 502

Question 503

Question 504

Question 505

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 806

Question 807

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 1105

Question 1106

Question 1107

Question 1108

Question 1201

Question 1202

Question 1203

Question 1204

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The answers, and why they are the answers

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