ZIMSEC O Level Mathematics Paper 1 June 2023

Question 101

[1 marks]Approximations & Estimations

Express 54,497 correct to the nearest tenth.

Answer this when you sit the paper.

Question 102

[1 marks]Ordinary & Standard Form

Express 0,000342 in standard form.

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Question 103

[1 marks]Approximations & Estimations

Express 478,367 correct to two significant figures.

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Question 201

[1 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{2}{7} + \dfrac{1}{3}

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

Answer this when you sit the paper.

Question 202

[1 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{2}{5} \div 10

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

Answer this when you sit the paper.

Question 203

[1 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{18}{35} \times \dfrac{14}{27}

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

Answer this when you sit the paper.

Question 301

[1 marks]Fractions, Decimals & Percentages

Evaluate

0,024 \times 0,3

, giving the answer as an exact decimal.

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Question 302

[1 marks]Fractions, Decimals & Percentages

Evaluate

(0,4)^3

, giving the answer as an exact decimal.

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Question 303

[1 marks]Fractions, Decimals & Percentages

Express 0,224 as a percentage.

Answer this when you sit the paper.

Question 401

[1 marks]Sets

The universal set is

\xi = \{75; 76; 77; 78; 79; 80\}

and M is the set of even numbers in

\xi

. List the elements of set M.

Answer this when you sit the paper.

Question 402

[1 marks]Sets

The universal set is

\xi = \{75; 76; 77; 78; 79; 80\}

and R is the set of multiples of 4 in

\xi

. List the elements of set R.

Answer this when you sit the paper.

Question 403

[1 marks]Sets

The universal set is

\xi = \{75; 76; 77; 78; 79; 80\}

M = \{76; 78; 80\}

and

R = \{76; 80\}

. Find

n(M' \cup R)

Answer this when you sit the paper.

Question 501

[1 marks]Algebraic Expressions

Simplify

2(a - 2) - 4(a + 3)

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Question 502

[2 marks]Algebraic Fractions

Express

\dfrac{3}{m-2} - \dfrac{2}{4m+3}

as a single fraction.

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Question 601

[1 marks]Polygons, Symmetry & Circles

State the special name of a quadrilateral with four lines of symmetry.

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Question 602

[2 marks]Polygons, Symmetry & Circles

A quadrilateral has interior angles of

x°

2x°

(x + 10)°

and

(x + 50)°

. Calculate the value of

x

Answer this when you sit the paper.

Question 701

[2 marks]Variation

P

varies directly as the cube of

r

. Given that

P = 2

when

r = 4

, find the formula connecting

P

and

r

Answer this when you sit the paper.

Question 702

[1 marks]Variation

Given that

P = \dfrac{r^3}{32}

, find the value of

P

when

r = 8

Answer this when you sit the paper.

Question 801

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

Given that

m + 3n = 5

and

m^2 - 9n^2 = -15

, find the numerical value of

m - 3n

Answer this when you sit the paper.

Question 802

[2 marks]Simultaneous Equations

Given that

m + 3n = 5

and

m - 3n = -3

, find the numerical values of

m

and

n

Answer this when you sit the paper.

Question 901

[2 marks]Change of Subject of Formula

Given that

p = \dfrac{q}{q+m}

, make

m

the subject of the formula.

Answer this when you sit the paper.

Question 902

[1 marks]Substitution

Given that

m = \dfrac{q(1-p)}{p}

, find

m

when

q = 3

and

p = 2

Answer this when you sit the paper.

Question 1001

[1 marks]Circle Geometry

In the diagram, Q, S and R are on the circumference of a circle centre O and PQT is a tangent to the circle at Q.

P\hat{Q}S = m°

O\hat{Q}S = n°

Q\hat{O}R = p°

Q\hat{S}R = 70°

and

O\hat{R}S = 25°

. Calculate the value of

m

Answer this when you sit the paper.

Question 1002

[1 marks]Circle Geometry

In the diagram, Q, S and R are on the circumference of a circle centre O and PQT is a tangent to the circle at Q.

P\hat{Q}S = m°

O\hat{Q}S = n°

Q\hat{O}R = p°

Q\hat{S}R = 70°

and

O\hat{R}S = 25°

. Calculate the value of

n

Answer this when you sit the paper.

Question 1003

[1 marks]Circle Geometry

In the diagram, Q, S and R are on the circumference of a circle centre O and PQT is a tangent to the circle at Q.

P\hat{Q}S = m°

O\hat{Q}S = n°

Q\hat{O}R = p°

Q\hat{S}R = 70°

and

O\hat{R}S = 25°

. Calculate the value of

p

Answer this when you sit the paper.

Question 1101

[1 marks]Number Bases

Evaluate

766_9 + 143_9

, giving the answer in base 9.

Answer this when you sit the paper.

Question 1102

[2 marks]Number Bases

Convert

35_6

to a number in base 2.

Answer this when you sit the paper.

Question 1103

[1 marks]Functional Notation

Given that

f(x) = (4 - x)(x - 0,5)

, find

f(0)

Answer this when you sit the paper.

Question 1201

[1 marks]Inequalities & Linear Programming

In the diagram, the unshaded region R is bounded on the left by the solid vertical line through

x = 1

. 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, the unshaded region R is bounded below by the solid horizontal line through

y = 2

. 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, the unshaded region R is bounded above by the solid line through

(0; 6)

and

(6; 0)

. Write down the inequality whose boundary is that line.

Answer this when you sit the paper.

Question 1301

[1 marks]Similarity & Congruency

Two similar cylinders have heights of 16 cm and 48 cm. Write down, in its simplest form, the ratio of their heights.

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Question 1302

[1 marks]Similarity & Congruency

Two similar cylinders have heights of 16 cm and 48 cm. Write down, in its simplest form, the ratio of their volumes.

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Question 1303

[2 marks]Similarity & Congruency

Two similar cylinders have heights of 16 cm and 48 cm. The curved surface area of the larger cylinder is

500\ \text{cm}^2

. Calculate the curved surface area, in square centimetres, of the smaller cylinder.

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Question 1401

[2 marks]Ratios, Rates & Proportions

A sum of money is shared in the ratio 2 : 3 : 4. The smallest share is $160,00. Calculate the total amount of money shared.

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Question 1402

[2 marks]Consumer Arithmetic

Find the time, in years, taken for $4 000,00 to earn a simple interest of $400,00 at a rate of 5% per annum.

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Question 1501

[2 marks]Linear Equations

Solve the equation

3(x - 2) = 5x + 3

Answer this when you sit the paper.

Question 1502

[2 marks]Quadratic Equations

Solve the equation

\left(q - \dfrac{2}{9}\right)^2 = \dfrac{49}{81}

Answer this when you sit the paper.

Question 1601

[3 marks]Approximations & Estimations

Evaluate

\dfrac{0,0469 \times 2,13}{2,28 + 3,83 \times 2,06}

by first estimating each number to one significant figure.

Answer this when you sit the paper.

Question 1602

[2 marks]Laws of Indices

Solve the equation

27 = 3^{2d+1}

Answer this when you sit the paper.

Question 1701

[1 marks]Vector Geometry

Points

E

F

and

G

have coordinates

(4; 8)

(-4; 0)

and

(-6; 4)

respectively. Express

\vec{EF}

as a column vector.

Answer this when you sit the paper.

Question 1702

[1 marks]Vector Geometry

Points

F

and

G

have coordinates

(-4; 0)

and

(-6; 4)

respectively. Express

-\dfrac{1}{2}\vec{GF}

as a column vector.

Answer this when you sit the paper.

Question 1703

[1 marks]Vector Geometry

Points

E

F

and

G

have coordinates

(4; 8)

(-4; 0)

and

(-6; 4)

respectively. Express

\vec{EF} + \vec{FG}

as a column vector.

Answer this when you sit the paper.

Question 1704

[2 marks]Vector Geometry

The point

E

has coordinates

(4; 8)

and O is the origin. Find

\left|\vec{OE}\right|

, leaving the answer in surd form.

Answer this when you sit the paper.

Question 1801

[2 marks]Change of Units

Convert

2\ \text{g/cm}^3

\text{kg/m}^3

Answer this when you sit the paper.

Question 1802

[1 marks]Scales & Simple Map Problems

A map of a town is drawn to a scale of 1 cm to 9,5 km. Calculate the actual length, in kilometres, of a road that is 3 cm long on the map.

Answer this when you sit the paper.

Question 1803

[2 marks]Scales & Simple Map Problems

A map of a town is drawn to a scale of 1 cm to 9,5 km. Calculate the area, in square centimetres, on the map of a town that has an actual area of

361\ \text{km}^2

Answer this when you sit the paper.

Question 1901

[1 marks]Trigonometry, Bearing & Distances

Village A is on a bearing of 092° from village B. Calculate the three figure bearing of village B from village A.

Answer this when you sit the paper.

Question 1902

[2 marks]Measures & Mensuration

OPQ is a sector with centre O and radius 9 cm, and

P\hat{O}Q = 84°

. Taking

\pi

to be

\frac{22}{7}

, calculate the length, in centimetres, of arc PQ.

Answer this when you sit the paper.

Question 1903

[2 marks]Measures & Mensuration

OPQ is a sector with centre O and radius 9 cm, and

P\hat{O}Q = 84°

. Taking

\pi

to be

\frac{22}{7}

, calculate the area, in square centimetres, of the sector OPQ.

Answer this when you sit the paper.

Question 2001

[1 marks]Statistics & Probability

A table shows the enrollment at a certain school: Form 1 has 128 learners, Form 2 has 127, Form 3 has 125 and Form 4 has 120. State the modal form.

Answer this when you sit the paper.

Question 2002

[2 marks]Statistics & Probability

A table shows the enrollment at a certain school: Form 1 has 128 learners, Form 2 has 127, Form 3 has 125 and Form 4 has 120. Calculate the mean number of learners per form.

Answer this when you sit the paper.

Question 2003

[2 marks]Statistics & Probability

A school has 500 learners, of whom 125 are in form 3. Two learners are chosen at random from the school. Calculate the probability that both learners are in form 3.

Answer this when you sit the paper.

Question 2101

[1 marks]Similarity & Congruency

In the diagram, XDF and YEG are two straight lines which intersect at O, and XY, ED and GF are parallel lines with

OX = OD = 7

cm and

DF = 3

cm. Name, in correct order, the triangle which is similar but not congruent to triangle XOY.

Answer this when you sit the paper.

Question 2102

[1 marks]Similarity & Congruency

In the diagram, XDF and YEG are two straight lines which intersect at O, and XY, ED and GF are parallel lines with

OX = OD = 7

cm and

DF = 3

cm. Name, in correct order, the triangle which is congruent to triangle XOY.

Answer this when you sit the paper.

Question 2103

[3 marks]Similarity & Congruency

In the diagram, XDF and YEG are two straight lines which intersect at O, and XY, ED and GF are parallel lines with

OX = OD = 7

cm,

DF = 3

cm,

ED = (x + 2)

cm and

GF = (2x - 4)

cm. Calculate the length of FG, in centimetres.

Answer this when you sit the paper.

Question 2201

[3 marks]Matrices

Matrix

M = \begin{pmatrix} 5 & -3 \\ -2 & 2 \end{pmatrix}

. Find

M^{-1}

, the inverse of matrix M.

Answer this when you sit the paper.

Question 2202

[3 marks]Matrices

Matrix

N = \begin{pmatrix} y^2 & 6 \\ 3 & 2 \end{pmatrix}

is singular. Find the possible values of

y

Answer this when you sit the paper.

Question 2301

[1 marks]Trigonometry, Bearing & Distances

In the diagram, PQRS is a trapezium with PS parallel to QR,

P\hat{Q}R = P\hat{R}S = 90°

PQ = 24

cm,

QR = 32

cm and

PR = 40

cm. Express

\tan R\hat{P}S

as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 2302

[2 marks]Trigonometry, Bearing & Distances

In the diagram, PQRS is a trapezium with PS parallel to QR,

P\hat{Q}R = P\hat{R}S = 90°

PQ = 24

cm,

QR = 32

cm and

PR = 40

cm. Calculate the length of RS, in centimetres.

Answer this when you sit the paper.

Question 2303

[2 marks]Measures & Mensuration

In the diagram, PQRS is a trapezium with PS parallel to QR,

P\hat{Q}R = P\hat{R}S = 90°

PQ = 24

cm,

QR = 32

cm,

PR = 40

cm and

RS = 30

cm. Calculate the area, in square centimetres, of trapezium PQRS.

Answer this when you sit the paper.

Question 2401

[3 marks]Geometrical Transformation

Triangle X has vertices

(2; 2)

(4; 2)

and

(4; 3)

. Triangle A is the image of triangle X under a translation of

\begin{pmatrix} -2 \\ 3 \end{pmatrix}

. Write down the vertices of triangle A.

Answer this when you sit the paper.

Question 2402

[3 marks]Geometrical Transformation

Triangle X has vertices

(2; 2)

(4; 2)

and

(4; 3)

. Triangle B is the image of triangle X under a rotation of 180° with centre

Q(4; 4)

. Write down the vertices of triangle B.

Answer this when you sit the paper.

Question 2403

[3 marks]Geometrical Transformation

Triangle X has vertices

(2; 2)

(4; 2)

and

(4; 3)

, and triangle C has vertices

(-4; 2)

(-2; 2)

and

(-5; 3)

. Describe fully the single transformation which maps triangle X onto triangle C.

Answer this when you sit the paper.

Mathematics Paper 1 June 2023

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 303

Question 401

Question 402

Question 403

Question 501

Question 502

Question 601

Question 602

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1101

Question 1102

Question 1103

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1303

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1702

Question 1703

Question 1704

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

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The answers, and why they are the answers

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