ZIMSEC O Level Mathematics Paper 1 June 2024

Question 101

[1 marks]Fractions, Decimals & Percentages

Simplify

0 - (-3)

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Question 102

[1 marks]Fractions, Decimals & Percentages

Express

\dfrac{8}{3}

as a recurring decimal.

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Question 103

[1 marks]Rational, Irrational Numbers & Surds

Find

\sqrt{1\frac{11}{25}}

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Question 201

[1 marks]Fractions, Decimals & Percentages

Simplify

2\frac{2}{3} \div 2

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Question 202

[1 marks]Fractions, Decimals & Percentages

Find the value of

9 + 6 \div 3

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Question 203

[1 marks]Fractions, Decimals & Percentages

Evaluate

0,032 \div 0,4

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Question 301

[1 marks]Ratios, Rates & Proportions

Three learners A, B and C contributed

20,

30 and $50 respectively. Write down the ratio of the money they contributed in ascending order, in its simplest form.

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Question 302

[2 marks]Ratios, Rates & Proportions

Three learners A, B and C contributed

20,

30 and $50 respectively and bought a packet of 150 sweets worth $100. If they shared the sweets in the ratio of the money they contributed, calculate the number of sweets C got.

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Question 501

[1 marks]Circle Geometry

In the diagram, P, Q and R are on the circumference of a circle centre O. The reflex angle

P\hat{O}R

on the side containing Q is 300°, and

Q\hat{P}O = Q\hat{R}O = x°

. Find

P\hat{Q}R

, in degrees.

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Question 502

[2 marks]Circle Geometry

In the diagram, P, Q and R are on the circumference of a circle centre O. The reflex angle

P\hat{O}R

on the side containing Q is 300°, and

Q\hat{P}O = Q\hat{R}O = x°

. Find

x

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Question 601

[3 marks]Simultaneous Equations

Solve the simultaneous equations

x = 3 - 3y

and

2y = x - 8

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Question 701

[3 marks]Measures & Mensuration

A rectangular wall measuring 6 m by 5 m has a window measuring 1,5 m by 1,2 m. The wall needs to be painted. Calculate the area, in square metres, of the wall to be painted.

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Question 801

[1 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 20,\ x

is an integer

\}

and

B = \{x : x

is a perfect cube

\}

. List all elements of B.

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Question 802

[1 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 20,\ x

is an integer

\}

A = \{x : x < 10\}

and

B = \{x : x

is a perfect cube

\}

. List all elements of

A \cap B

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Question 803

[1 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 20,\ x

is an integer

\}

A = \{1; 2; ...; 9\}

and

B = \{1; 8\}

. State the relationship between sets A and B.

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Question 901

[1 marks]Ordinary & Standard Form

Express

732 \times 10^{-1}

in standard form.

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Question 902

[2 marks]Ordinary & Standard Form

Three towns A, B and C are situated along a straight road, such that town C is

(4 \times 10^2)

km from town A and town B is

(1,88 \times 10^2)

km from town A. Find the distance of town B from town C, giving the answer in standard form.

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Question 1001

[1 marks]Approximations & Estimations

Round off

9\,995,85 correct to the nearest

10.

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Question 1002

[1 marks]Approximations & Estimations

Round off

3\frac{1}{5}

cm correct to the nearest centimetre.

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Question 1003

[1 marks]Prime Numbers, Sequences & Types of Numbers

Express 432 as a product of its prime factors.

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Question 1004

[1 marks]Prime Numbers, Sequences & Types of Numbers

Given that

432 = 2^4 \times 3^3

, find the smallest number by which 432 must be multiplied to get a result which is a perfect square.

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Question 1101

[2 marks]Consumer Arithmetic

A greengrocer bought 80 oranges for $640 and sold them at $15 each. Find the percentage profit made.

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Question 1102

[2 marks]Consumer Arithmetic

A woman invested $4 000 in a bank at 3% simple interest and the money earned an interest of $240. Find the time, in years, her money was in the bank.

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Question 1201

[1 marks]Change of Units

Write 0545 as a time in 12 hour notation.

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Question 1202

[1 marks]Change of Units

Lessons commence at 0715. Learner P arrived at school at 0725. Find the time by which learner P was late for the lessons.

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Question 1203

[2 marks]Ratios, Rates & Proportions

Learner P walks 5 km to school. On one day the learner left home at 0545 and arrived at school at 0725. Calculate the average speed, in km/h, at which learner P was walking on that day.

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Question 1301

[1 marks]Points, Lines & Angles

In the diagram, triangle PSR is such that QT is parallel to RS,

Q\hat{R}S = 50°

Q\hat{S}R = 30°

and PQ = QS. Find

S\hat{Q}T

, in degrees.

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Question 1302

[1 marks]Points, Lines & Angles

In the diagram, triangle PSR is such that QT is parallel to RS,

Q\hat{R}S = 50°

Q\hat{S}R = 30°

and PQ = QS. Find

T\hat{Q}P

, in degrees.

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Question 1303

[2 marks]Points, Lines & Angles

In the diagram, triangle PSR is such that QT is parallel to RS,

Q\hat{R}S = 50°

Q\hat{S}R = 30°

and PQ = QS. Find

P\hat{T}Q

, in degrees.

Answer this when you sit the paper.

Question 1401

[2 marks]Probability

Two learners P and Q write a Mathematics test. The probability that P passes is

\frac{3}{5}

and the probability that Q passes is

\frac{2}{3}

. Write down the probability that P fails and the probability that Q fails.

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Question 1402

[2 marks]Probability

Two learners P and Q write a Mathematics test. The probability that P passes is

\frac{3}{5}

and the probability that Q passes is

\frac{2}{3}

. Find the probability that only one of the learners passes the test.

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Question 1501

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

Factorise completely

4x - 2y

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Question 1502

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

Factorise completely

4x^2 - y^2

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Question 1503

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

Find the L.C.M of

4x - 2y

and

4x^2 - y^2

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Question 1601

[1 marks]Variation

A table shows the distance D, in km, covered per given number of litres

l

of fuel: 0,5 litres covers 7,5 km, 10 litres covers 150 km, 30 litres covers 450 km and 50 litres covers 750 km. State the type of variation connecting the two quantities.

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Question 1602

[2 marks]Variation

The distance D, in km, covered on

l

litres of fuel is such that 10 litres covers 150 km and 30 litres covers 450 km. Express D in terms of

l

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Question 1603

[2 marks]Variation

The distance D, in km, covered on

l

litres of fuel is given by

D = 15l

. Calculate the amount of fuel, in litres, that will be required for a distance of 480 km.

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Question 1701

[2 marks]Trigonometry, Bearing & Distances

School F is 8 km due north of school E. School G is 5 km from school E on a bearing of 240°. Find the compass bearing of school E from school G.

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Question 1702

[3 marks]Trigonometry, Bearing & Distances

School F is 8 km due north of school E. School G is 5 km from school E on a bearing of 240°. Calculate the distance of school F from school G, leaving the answer in surd form.

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Question 1801

[1 marks]Matrices

Given that

\begin{pmatrix} 1 & 2 \\ 6 & 3 \end{pmatrix} - \begin{pmatrix} 4 & 7 \\ 3y & 10 \end{pmatrix} = \begin{pmatrix} -3 & -5 \\ 9 & -7 \end{pmatrix}

, find the value of

y

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Question 1802

[2 marks]Matrices

Simplify

\begin{pmatrix} 2 \\ 3 \end{pmatrix}\begin{pmatrix} 1 & -3 \end{pmatrix}

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Question 1803

[2 marks]Matrices

Given that

\begin{pmatrix} 1 & -x \\ -2 & 9 \end{pmatrix}

is the inverse of

\begin{pmatrix} 9 & x \\ 2 & 1 \end{pmatrix}

, find the value of

x

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Question 1901

[1 marks]Number Bases

Write down the value of 1 in the number

610_7

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Question 1902

[1 marks]Number Bases

Evaluate

1\,016_9 + 881_9

, giving the answer in base 9.

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Question 1903

[3 marks]Number Bases

Evaluate

140_5 - 123_5

, giving the answer in base 2.

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Question 2001

[1 marks]Travel Graphs

A man went for a walk, leaving home at 9.30 am. His displacement-time graph runs for 4 hours in total. Find the time he arrived back home.

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Question 2002

[1 marks]Travel Graphs

A man went for a walk. His displacement-time graph shows him reaching 6 km from home and then returning home. Find the total distance, in kilometres, he walked.

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Question 2003

[2 marks]Travel Graphs

A man walked a total distance of 12 km in a journey lasting 4 hours. Find his average speed, in km/h, for the whole journey.

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Question 2004

[1 marks]Travel Graphs

A man's displacement-time graph is horizontal at a distance of 6 km from home between 2,5 hours and 3,5 hours after he set off. Find the amount of time the man rested.

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Question 2101

[1 marks]Laws of Indices

Evaluate

2^3 + 2^2

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Question 2102

[1 marks]Laws of Indices

Evaluate

-\left(7x^2\right)^0

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Question 2103

[1 marks]Laws of Indices

Evaluate

\left(2^3\right)^{-\frac{2}{3}}

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Question 2104

[3 marks]Laws of Indices

Solve the equation

3^x \times 3^{2x} = 27

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Question 2201

[1 marks]Similarity & Congruency

In the diagram,

E\hat{A}C = B\hat{D}C

AB = x

cm,

BC = 3

cm,

DC = 4

cm and

ED = 2

cm. Name a triangle which is similar to triangle ACE.

Answer this when you sit the paper.

Question 2202

[2 marks]Similarity & Congruency

In the diagram,

E\hat{A}C = B\hat{D}C

AB = x

cm,

BC = 3

cm,

DC = 4

cm and

ED = 2

cm. Find

x

Answer this when you sit the paper.

Question 2203

[3 marks]Similarity & Congruency

In the diagram,

E\hat{A}C = B\hat{D}C

BC = 3

cm,

DC = 4

cm,

ED = 2

cm and the area of triangle ACE is

24\ \text{cm}^2

. Calculate the area, in square centimetres, of quadrilateral ABDE.

Answer this when you sit the paper.

Question 2301

[3 marks]Polygons, Symmetry & Circles

An 11 sided polygon has 9 of its exterior angles each

x°

and 2 each

y°

. The sum of the 9 interior angles adjacent to the angles

x°

is 1152° more than the sum of the 2 interior angles adjacent to the angles

y°

. Form two simultaneous equations in

x

and

y

Answer this when you sit the paper.

Question 2302

[3 marks]Simultaneous Equations

Solve the simultaneous equations

9x + 2y = 360

and

9x - 2y = 108

Answer this when you sit the paper.

Question 2401

[2 marks]Co-ordinate Geometry

A straight line

l

passes through the point

(2; -3)

and has gradient 3. Find the equation of line

l

in the form

y = mx + c

Answer this when you sit the paper.

Question 2402

[1 marks]Co-ordinate Geometry

State the relationship between the line

y = 3x - 9

and the line whose equation is

y = 3x - 1

Answer this when you sit the paper.

Question 2403

[3 marks]Functional Notation

Given that

f(x) = 2x + k^2

and that

f(2) = 29

, find the two possible values of

k

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Mathematics Paper 1 June 2024

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 501

Question 502

Question 601

Question 701

Question 801

Question 802

Question 803

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1004

Question 1101

Question 1102

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1303

Question 1401

Question 1402

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2003

Question 2004

Question 2101

Question 2102

Question 2103

Question 2104

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2401

Question 2402

Question 2403

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The answers, and why they are the answers

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