ZIMSEC O Level Mathematics Paper 2 June 2023

Question 101

[2 marks]Standard Form, Percentages and Ratios

Simplify

0,92 - 0,33 + 0,24

and give the answer in standard form.

Answer this when you sit the paper.

Question 102

[2 marks]Standard Form, Percentages and Ratios

Amos sold a radio for

\$66,00

and made a profit of 10%. Find the cost price of the radio.

A $\$72,60$ , by adding a further 10% onto the selling price
B $\$60,00$ , since $\$66,00$ is 110% of the cost price
C $\$56,00$ , by subtracting a flat $\$10,00$ from the selling price
D $\$59,40$ , by taking 10% off the selling price of $\$66,00$

Question 103

[3 marks]Standard Form, Percentages and Ratios

\$286,00

in the ratio

1 : 1\frac{1}{2} : 4

. How much is the largest share?

Answer this when you sit the paper.

Question 104

[2 marks]Standard Form, Percentages and Ratios

Remove brackets and simplify

(d + 3)(6d - 1)

Answer this when you sit the paper.

Question 201

[2 marks]Change of Subject, Simple Interest and Algebraic Fractions

Given that

T = g + \sqrt{n^3 - m}

, find

T

when

g = -4

n = 3

and

m = -9

Answer this when you sit the paper.

Question 202

[3 marks]Change of Subject, Simple Interest and Algebraic Fractions

Make

m

the subject of the formula

T = g + \sqrt{n^3 - m}

A $m = n^3 - (T - g)^2$
B $m = n^3 - T^2 + g^2$
C $m = n^3 - (T + g)^2$
D $m = (T - g)^2 - n^3$

Question 203

[2 marks]Change of Subject, Simple Interest and Algebraic Fractions

Find the rate of interest per year when

\$144,00

earns

\$22,68

simple interest in

3\frac{1}{2}

years.

Answer this when you sit the paper.

Question 204

[3 marks]Change of Subject, Simple Interest and Algebraic Fractions

Express

\frac{2 - x}{x^2 - 4} - \frac{1 + x}{x + 2}

as a single fraction in its simplest form.

Answer this when you sit the paper.

Question 301

[2 marks]Linear Equations, Factorisation and Wages

Solve the equation

\frac{3}{5}(f - 1) = \frac{1}{5}f

Answer this when you sit the paper.

Question 302

[3 marks]Linear Equations, Factorisation and Wages

Solve the equation

\left(2\frac{2}{3} - p\right)^2 = 1\frac{7}{9}

A $p = 4$ only, because the other root makes the bracket negative
B $p = \frac{4}{9}$ or $p = \frac{44}{9}$ , squaring each term inside the bracket
C $p = 1\frac{1}{3}$ or $p = 4$ , one root from each square root of $\frac{16}{9}$
D $p = 1\frac{1}{3}$ only, taking just the positive square root of $\frac{16}{9}$

Question 303

[2 marks]Linear Equations, Factorisation and Wages

Factorise completely

10m^2 - tr - 2mt + 5mr

Answer this when you sit the paper.

Question 304

[2 marks]Linear Equations, Factorisation and Wages

Factorise completely

p^3 - 16p

Answer this when you sit the paper.

Question 305

[2 marks]Linear Equations, Factorisation and Wages

A carpenter is paid at a rate of

\$3,65

per hour. Calculate her wage for working a 38 hour week.

Answer this when you sit the paper.

Question 401

[2 marks]Constructions and Loci

In a quadrilateral

ABCD

, a point moves so that it stays the same distance from the line

AB

as from the line

BC

. Which construction gives its path?

AThe perpendicular bisector of the side $AB$ of the quadrilateral
BThe line drawn through $B$ parallel to the side $AD$
CThe bisector of the angle $A\hat{B}C$ , drawn from $B$
DA circle centred on $B$ and passing through $A$ and $C$

Question 402

[2 marks]Constructions and Loci

A point moves so that it stays 3 cm from a straight line

AB

. Describe the whole of its path.

AOne line parallel to $AB$ and 3 cm above it, with nothing below
BTwo arcs of radius 3 cm, one centred on $A$ and one on $B$
CA single circle of radius 3 cm centred on the midpoint of $AB$
DA pair of lines parallel to $AB$ , one 3 cm on each side of it

Question 403

[2 marks]Constructions and Loci

Inside a quadrilateral

ABCD

two loci are drawn: the bisector of

A\hat{B}C

, and the line parallel to

AB

and 3 cm from it on the same side as

DC

. What does their point of intersection represent?

AThe midpoint of the side $AB$ lifted 3 cm above the line $AB$
BThe centre of the circle that passes through $A$ , $B$ and $C$
CThe point equidistant from $AB$ and $BC$ that is also 3 cm from $AB$
DThe point that is 3 cm from both $AB$ and $BC$ , measured perpendicularly

Question 404

[2 marks]Constructions and Loci

In a quadrilateral

ABCD

AB = 4,8

cm,

AD = 8,9

cm,

BC = 6,6

cm,

B\hat{A}D = 60^\circ

and

A\hat{B}C = 135^\circ

P

is the point that is equidistant from

AB

and

BC

and 3 cm from

AB

, on the same side of

AB

DC

. Find the length of

PC

in cm.

Answer this when you sit the paper.

Question 501

[2 marks]Number, Time and Functional Notation

Simplify

25,8 - 13 + 15,25

Answer this when you sit the paper.

Question 502

[2 marks]Number, Time and Functional Notation

Add 3 days 15 hours 40 minutes to 2 days 8 hours 40 minutes.

A6 days 1 hour 20 minutes
B6 days 0 hours 20 minutes
C5 days 23 hours 80 minutes
D5 days 24 hours 20 minutes

Question 503

[2 marks]Number, Time and Functional Notation

Tafadzwa borrows

\$600

from Tendai at the start of the year. He agrees that at the end of the year he will repay Tendai and also give him

\frac{2}{5}

of any profit he makes. The

\$600

grows to

\$1250

. How much does Tafadzwa hand over to Tendai at the end of the year?

Answer this when you sit the paper.

Question 504

[2 marks]Number, Time and Functional Notation

Express 676 as a product of its prime factors in index notation.

Answer this when you sit the paper.

Question 505

[1 marks]Number, Time and Functional Notation

Find the square root of 676.

Answer this when you sit the paper.

Question 506

[2 marks]Number, Time and Functional Notation

Given that

f(x) = 3x + 5

, find

f(3)

and the value of

x

for which

f(x) = 83

A $f(3) = 9$ and $x = 26$
B $f(3) = 14$ and $x = 26$
C $f(3) = 14$ and $x = 29\frac{1}{3}$
D $f(3) = 8$ and $x = 78$ , adding 5 to 3 and to 78

Question 601

[2 marks]Variation, Mensuration and Quadratic Equations

The cost

C

of printing a newspaper is partly constant and partly varies as

n

, the number of newspapers printed. Which relation expresses

C

in terms of

n

and the constants

k

and

h

A $C = k + hn$ , a fixed part plus a part proportional to $n$
B $C = khn$ , the two constants multiplied together with $n$
C $C = kn + hn^2$ , two parts that both change as $n$ changes
D $C = k + \frac{h}{n}$ , a fixed part plus a part inversely proportional to $n$

Question 602

[3 marks]Variation, Mensuration and Quadratic Equations

The cost

C

of printing

n

newspapers is

C = k + hn

. Printing 500 newspapers costs

\$320

and printing 1 000 newspapers costs

\$540

. Find the cost of printing 750 newspapers.

Answer this when you sit the paper.

Question 603

[2 marks]Variation, Mensuration and Quadratic Equations

KLMN

is a trapezium in which

KL

is parallel to

NM

and

K\hat{L}M = 90^\circ

, with

KL = (3x - 1)

cm,

NM = (x + 3)

cm and

LM = (x - 3)

cm. Write an expression in

x

for the area of the trapezium, in factorised form.

Answer this when you sit the paper.

Question 604

[2 marks]Variation, Mensuration and Quadratic Equations

Solve the equation

2x^2 - 5x - 18 = 0

Answer this when you sit the paper.

Question 605

[3 marks]Variation, Mensuration and Quadratic Equations

A trapezium has parallel sides of

(3x - 1)

cm and

(x + 3)

cm, and the perpendicular side joining them is

(x - 3)

cm. Its area is 15 cm

^2

. Find the length of that perpendicular side, in cm.

Answer this when you sit the paper.

Question 701

[1 marks]Household Bills and Variation

A household water meter read 762 Kl at the start of a month and 776 Kl at the end. Find the consumption for the month, in Kl.

Answer this when you sit the paper.

Question 702

[2 marks]Household Bills and Variation

A family is allowed 11 Kl of water a month at a permitted rate, and that permitted consumption is charged

\$17,05

in total. Find the rate charged per Kl for the permitted consumption.

Answer this when you sit the paper.

Question 703

[2 marks]Household Bills and Variation

A family used 14 Kl of water in a month. The first 11 Kl are the permitted consumption; anything above that is charged at

\$2,50

per Kl. Find the amount paid for the excess water.

Answer this when you sit the paper.

Question 704

[3 marks]Household Bills and Variation

In one month a family used 14 Kl of water. The first 11 Kl are charged at

\$1,55

per Kl, water above 11 Kl is charged at

\$2,50

per Kl, and a fixed charge of

\$7,30

is added. Find the total amount due.

Answer this when you sit the paper.

Question 705

[1 marks]Household Bills and Variation

N

varies inversely as the square root of

M

. Which formula connects

N

M

and a constant

k

A $N = \frac{\sqrt{M}}{k}$
B $N = k\sqrt{M}$
C $N = \frac{k}{M^2}$
D $N = \frac{k}{\sqrt{M}}$

Question 706

[3 marks]Household Bills and Variation

N

varies inversely as the square root of

M

. Given that

N = 17

when

M = 20,25

, find the value of

M

when

N = 34

Answer this when you sit the paper.

Question 801

[3 marks]Geometrical Transformation

Triangle A has vertices

(-6; 2)

(-2; 2)

and

(-5; 6)

. Triangle B is the image of triangle A under a clockwise rotation of

90^\circ

about the point

(2; 2)

. Write down the coordinates of the image of the vertex

(-5; 6)

Answer this when you sit the paper.

Question 802

[3 marks]Geometrical Transformation

Triangle A has vertices

(-6; 2)

(-2; 2)

and

(-5; 6)

. Its image has vertices

(-6; 14)

(-2; 6)

and

(-5; 16)

. Describe fully the single transformation that maps A onto that image.

AA shear with the $y$ axis invariant and shear factor $-2$
BA shear with the $x$ axis invariant and shear factor $-2$
CA translation of 12 units upwards followed by an enlargement of factor 2
DA one way stretch parallel to the $y$ axis of factor 2, with the $x$ axis invariant

Question 803

[3 marks]Geometrical Transformation

Triangle A has vertices

(-6; 2)

(-2; 2)

and

(-5; 6)

. Its image has vertices

(-2; 2)

(-2; -2)

and

(2; -1)

. Describe fully the single transformation that maps A onto that image.

AA rotation of $180^\circ$ about the point midway between the two triangles
BA reflection in the line $y = x + 4$
CA rotation of $90^\circ$ clockwise about the point $(-2; 2)$
DA reflection in the line $y = -x - 4$ , which passes through $(-4; 0)$

Question 804

[3 marks]Geometrical Transformation

Triangle A has vertices

(-6; 2)

(-2; 2)

and

(-5; 6)

. A shear with the

y

axis invariant and shear factor

-2

is applied to it. Write down the image of the vertex

(-2; 2)

Answer this when you sit the paper.

Question 901

[2 marks]Measures and Mensuration

A solid prism has an isosceles triangular cross section

PQU

in which

QP = QU

PU = 24

cm, and the perpendicular from

Q

PU

is 5 cm. Find the length of

QU

, in cm.

Answer this when you sit the paper.

Question 902

[2 marks]Measures and Mensuration

A triangle

PQU

has

PU = 24

cm, and the perpendicular from

Q

PU

is 5 cm. Find its area.

A120 cm $^2$ , taking 24 times 5 without halving it
B65 cm $^2$ , adding the base to the height after doubling
C156 cm $^2$ , using the slant side of 13 cm as the height
D60 cm $^2$ , half of 24 multiplied by 5

Question 903

[2 marks]Measures and Mensuration

A prism has a triangular cross section of area 60 cm

^2

and a volume of 1 728 cm

^3

. Find the length of the prism, in cm.

Answer this when you sit the paper.

Question 904

[3 marks]Measures and Mensuration

A prism has a volume of 1 728 cm

^3

. The material it is made of has a density of 4 g/cm

^3

and costs

\$1,93

per kg. Find the cost of the material used to make the prism.

Answer this when you sit the paper.

Question 905

[3 marks]Measures and Mensuration

A prism of volume 1 728 cm

^3

is 28,8 cm long. A similar prism has a volume of 512 cm

^3

. Find its length, in cm.

Answer this when you sit the paper.

Question 1001

[3 marks]Probability and Functional Graphs

A class has 16 boys and 10 girls. Two learners are chosen one after the other, without replacement, to represent the school. Find the probability that both are of the same sex. Give the answer as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 1002

[2 marks]Probability and Functional Graphs

For the function

y = 2x^2 - x - 6

, one value of

y

is missing at

x = -2

and another at

x = 3

. Find both values.

A $4$ at $x = -2$ and $9$ at $x = 3$
B $0$ at $x = -2$ and $15$ at $x = 3$
C $-4$ at $x = -2$ and $9$ at $x = 3$ , treating $2x^2$ as $(2x)^2$
D $8$ at $x = -2$ and $21$ at $x = 3$ , dropping the $-x$ term

Question 1003

[2 marks]Probability and Functional Graphs

Find the values of

x

at which the curve

y = 2x^2 - x - 6

meets the

x

axis.

A $x = -1,5$ and $x = 2$
B $x = -6$ and $x = 1$ , taking them from the constant term
C $x = 0,25$ alone, which is where the curve turns
D $x = 1,5$ and $x = 2$ , reading the signs the wrong way round

Question 1004

[2 marks]Probability and Functional Graphs

Find the minimum value of

y = 2x^2 - x - 6

Answer this when you sit the paper.

Question 1005

[3 marks]Probability and Functional Graphs

Find the gradient of the curve

y = 2x^2 - x - 6

at the point where

x = -3

Answer this when you sit the paper.

Question 1101

[2 marks]Pie Charts and Vector Geometry

In a pie chart of 192 learners' favourite subjects, the sector for Shona has an angle of

120^\circ

. Find the number of learners who preferred Shona.

Answer this when you sit the paper.

Question 1102

[2 marks]Pie Charts and Vector Geometry

In a pie chart of 192 learners' favourite subjects, the sector for Accounts is marked with a right angle. Find the number of learners who preferred Accounts.

Answer this when you sit the paper.

Question 1103

[2 marks]Pie Charts and Vector Geometry

In a pie chart of 192 learners' favourite subjects, 40 learners preferred Commerce and the Commerce sector has an angle of

p^\circ

. Find the value of

p

Answer this when you sit the paper.

Question 1104

[2 marks]Pie Charts and Vector Geometry

In a pie chart of 192 learners' favourite subjects the sectors are Shona

120^\circ

, Accounts

90^\circ

, Commerce

75^\circ

, History (chosen by 32 learners) and Others. Find the angle of the sector for Others.

Answer this when you sit the paper.

Question 1105

[2 marks]Pie Charts and Vector Geometry

ABCD

is a trapezium with

AB

parallel to

DC

\overrightarrow{AB} = 6a

\overrightarrow{DC} = 2a

and

\overrightarrow{DA} = 3b

. Express

\overrightarrow{BC}

in terms of

a

and

b

A $-4a + 3b$
B $4a + 3b$
C $-8a - 3b$
D $-4a - 3b$

Question 1106

[2 marks]Pie Charts and Vector Geometry

ABCD

is a trapezium with

AB

parallel to

DC

\overrightarrow{AB} = 6a

\overrightarrow{DC} = 2a

and

\overrightarrow{DA} = 3b

AC

and

BD

meet at

P

, where

AP:PC = 3:1

. Express

\overrightarrow{DP}

in terms of

a

and

b

Answer this when you sit the paper.

Question 1201

[2 marks]Matrices, Quadratic Equations, Polygons and Inequalities

Given that

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

and

B = \begin{pmatrix} -1 \\ 4 \end{pmatrix}

, evaluate

AB

Answer this when you sit the paper.

Question 1202

[2 marks]Matrices, Quadratic Equations, Polygons and Inequalities

A matrix

A

has order

2 \times 2

and a matrix

B

has order

2 \times 1

. State the order of the product

AB

AThe product cannot be formed, since the two orders differ
B $2 \times 1$
C $1 \times 2$
D $2 \times 2$

Question 1203

[3 marks]Matrices, Quadratic Equations, Polygons and Inequalities

The function

f

is given by

f(x) = 3x^2 - 5x - 1

. Solve the equation

f(x) = -3

Answer this when you sit the paper.

Question 1204

[3 marks]Matrices, Quadratic Equations, Polygons and Inequalities

The interior angles of a hexagon are

82^\circ

94^\circ

109^\circ

x^\circ

2x^\circ

and

3x^\circ

. Find the value of

x

Answer this when you sit the paper.

Question 1205

[2 marks]Matrices, Quadratic Equations, Polygons and Inequalities

Solve the inequality

5 - x > 3x + 2

A $x > 0,75$
B $x > \frac{7}{2}$ , from collecting the constants on the wrong side
C $x < 0,75$
D $x < -0,75$

Mathematics Paper 2 June 2023

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 305

Question 401

Question 402

Question 403

Question 404

Question 501

Question 502

Question 503

Question 504

Question 505

Question 506

Question 601

Question 602

Question 603

Question 604

Question 605

Question 701

Question 702

Question 703

Question 704

Question 705

Question 706

Question 801

Question 802

Question 803

Question 804

Question 901

Question 902

Question 903

Question 904

Question 905

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1101

Question 1102

Question 1103

Question 1104

Question 1105

Question 1106

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

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