ZIMSEC O Level Mathematics Paper 1 November 2024

Question 101

[1 marks]Approximations and Estimations

Express 0, 09874 correct to the nearest tenth.

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Question 102

[1 marks]Approximations and Estimations

Express 0, 09874 correct to 2 significant figures.

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Question 103

[1 marks]Ordinary and Standard Form

Express 0, 09874 in standard form.

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Question 201

[2 marks]Number

Express 1 225 as a product of its prime factors in index form.

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Question 202

[1 marks]Number

Express 1 225 as a product of its prime factors in index form. Hence or otherwise find

\sqrt{1\ 225}

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Question 301

[3 marks]Ratios, Rates & Proportions

Kate, James and Jack shared

\$3\ 042

in the ratio 4 : 3 : 2 respectively. Find how much Kate got more than Jack.

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Question 401

[1 marks]Change of Units

In a school, lessons start at quarter to 8 in the morning and end at 3. 15 pm. Express 3. 15 pm in 24 hour notation.

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Question 402

[2 marks]Change of Units

In a school, lessons start at quarter to 8 in the morning and end at 3. 15 pm. Find total time for lessons on each day.

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Question 501

[1 marks]Similarity and Congruency

XQZ and YPZ are straight lines meeting at Z. XY and QP are parallel.

XY = 6

cm,

QP = 4

cm and

XQ = 9

cm. QZ =

x

cm. Name two triangles that are similar.

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Question 502

[3 marks]Similarity and Congruency

XQZ and YPZ are straight lines meeting at Z. XY and QP are parallel.

XY = 6

cm,

QP = 4

cm and

XQ = 9

cm. QZ =

x

cm. Hence find the length of QZ.

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Question 601

[1 marks]Statistics

The table below shows the number of learners in each age group of a class. Age (years): 13, 14, 15. Number of learners: 9, 26, 5. Use the table to find the total number of learners in the class.

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Question 602

[1 marks]Probability

The table below shows the number of learners in each age group of a class. Age (years): 13, 14, 15. Number of learners: 9, 26, 5. Use the table to find the probability that a learner chosen at random is 13 years old.

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Question 603

[2 marks]Probability

The table below shows the number of learners in each age group of a class. Age (years): 13, 14, 15. Number of learners: 9, 26, 5. Use the table to find the probability that if two learners are chosen at random, the first is aged 13 years and the second is aged 15 years.

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Question 701

[2 marks]Vector Geometry

Find vector

\vec{p}

such that

\begin{pmatrix} 1 \\ 3 \end{pmatrix} - \vec{p} = \begin{pmatrix} 9 \\ -3 \end{pmatrix}

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Question 702

[2 marks]Vector Geometry

Given that

\begin{pmatrix} 1 \\ 3 \end{pmatrix} - \vec{p} = \begin{pmatrix} 9 \\ -3 \end{pmatrix}

, hence find

|\vec{p}|

, the magnitude of vector p.

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Question 801

[3 marks]Inequalities

Solve the inequality

3x - 2 < 10 + x < 5x + 2

giving the answer in the form

a < x < b

, where

a

and

b

are numbers.

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Question 802

[1 marks]Inequalities

The inequality

3x - 2 < 10 + x < 5x + 2

has solution

2 < x < 6

. Hence find a perfect square number which satisfies the given inequality.

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Question 901

[1 marks]Circle Geometry

M, N and Q are three points on the circumference of circle O and diameter QN. PR is a tangent to the circle at Q. Given that

M\hat{Q}R = 42^\circ

. Find

Q\hat{N}M

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Question 902

[1 marks]Circle Geometry

M, N and Q are three points on the circumference of circle O and diameter QN. PR is a tangent to the circle at Q. Given that

M\hat{Q}R = 42^\circ

. Find

Q\hat{M}N

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Question 903

[2 marks]Circle Geometry

M, N and Q are three points on the circumference of circle O and diameter QN. PR is a tangent to the circle at Q. Given that

M\hat{Q}R = 42^\circ

. Find

M\hat{O}Q

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Question 1001

[2 marks]Measures and Mensuration

A cylindrical floor polish tin is 14cm in diameter and 5cm deep. In this question take

\pi

to be

3\frac{1}{7}

. Calculate the volume of the tin.

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Question 1002

[2 marks]Measures and Mensuration

A cylindrical floor polish tin is 14cm in diameter and 5cm deep. In this question take

\pi

to be

3\frac{1}{7}

. When full the tin contains 840g of floor polish. Calculate the density of the polish in g/cm

^3

to 2 decimal places.

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Question 1101

[1 marks]Change of Units

Express 2,35 hours in hours and minutes.

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Question 1102

[3 marks]Number Bases

Simplify

413_5 + 1011_2

giving the answer in base ten.

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Question 1201

[1 marks]Ratios, Rates & Proportions

A map is drawn to a scale of 1cm to 5 kilometres. Express the scale in the form 1 : n

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Question 1202

[2 marks]Ratios, Rates & Proportions

A map is drawn to a scale of 1cm to 5 kilometres. Find the actual distance in kilometres between two points which are 3,6 cm apart on the map.

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Question 1203

[2 marks]Ratios, Rates & Proportions

A map is drawn to a scale of 1cm to 5 kilometres. If the actual area of a city is 125 km

^2

, find the area of the city on the map.

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Question 1301

[2 marks]Variation

y

varies jointly as the square of

x

and directly with

z

. When

x = 2

and

z = 3

y = 4\frac{1}{2}

. Find the relationship between

y

x

and

z

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Question 1302

[3 marks]Variation

y

varies jointly as the square of

x

and directly with

z

. When

x = 2

and

z = 3

y = 4\frac{1}{2}

. Find

y

when

x = 5

and

z = 4

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Question 1401

[2 marks]Functional Notation

Given that

f(x) = 2^{3x-1}

find

f(1)

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Question 1402

[3 marks]Functional Notation

Given that

f(x) = 2^{3x-1}

find the value of

x

for which

f(x) = 32

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Question 1501

[3 marks]Functional Graphs

Line

n

passing through point P has equation

2y = x + 6

. Line

l

passes through the origin and is parallel to line

n

. Find the distance OP.

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Question 1502

[2 marks]Functional Graphs

Line

n

passing through point P has equation

2y = x + 6

. Line

l

passes through the origin and is parallel to line

n

. Find the equation of line

l

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Question 1601

[3 marks]Algebraic Expressions

Express

\frac{2}{a} - \frac{5}{2 - 5a}

as a single fraction in its simplest form.

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Question 1602

[2 marks]Algebraic Expressions

Given that

a = 1

b = 0

and

c = -2

, evaluate

\frac{b - c}{3a}

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Question 1701

[1 marks]Bearing & Distances

Three towns X, Y and Z are on level ground such that Y is

8km

to the east of X. Z is due south of Y. Z is on a bearing of

S60^\circ E

and

10km

from X. Find the three figure bearing of Z from X

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Question 1702

[1 marks]Bearing & Distances

Three towns X, Y and Z are on level ground such that Y is

8km

to the east of X. Z is due south of Y. Z is on a bearing of

S60^\circ E

and

10km

from X. Find the compass bearing of X from Z

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Question 1703

[3 marks]Bearing & Distances

Three towns X, Y and Z are on level ground such that Y is

8km

to the east of X. Z is due south of Y. Z is on a bearing of

S60^\circ E

and

10km

from X. Calculate the distance that Z is south of Y.

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Question 1801

[2 marks]Matrices

Matrix

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

, Matrix

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

. Simplify

A + \frac{1}{2}B

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Question 1802

[3 marks]Matrices

Matrix

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

, Matrix

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

. Find the inverse of matrix

B

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Question 1901

[1 marks]Statistics

The table below shows the number of children in a hospital by age. Age (years): 1, 2, 3, 4, 5, 6, 7, 8. Number of children: 3, 4, 5, 6, 7, 6, 5, 4. Use the table to find the modal age of the children.

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Question 1902

[2 marks]Statistics

The table below shows the number of children in a hospital by age. Age (years): 1, 2, 3, 4, 5, 6, 7, 8. Number of children: 3, 4, 5, 6, 7, 6, 5, 4. Use the table to find the number of children in the hospital.

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Question 1903

[3 marks]Statistics

The table below shows the number of children in a hospital by age. Age (years): 1, 2, 3, 4, 5, 6, 7, 8. Number of children: 3, 4, 5, 6, 7, 6, 5, 4. Calculate the mean age of the children.

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Question 2001

[2 marks]Linear Equations

Solve the equation

2(3x - 1) - 10 = 0

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Question 2002

[4 marks]Quadratic Equations

Solve the equation

(x - 2)^2 = \frac{1}{4}

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Question 2101

[2 marks]Travel Graphs

The speed - time graph shows how an object travels at a constant speed of 40m/s in 6 seconds and then slows down uniformly, coming to rest after 2 seconds. Use the graph to calculate the uniform deceleration of the object in the last 2 seconds.

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Question 2102

[2 marks]Travel Graphs

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Question 2103

[2 marks]Travel Graphs

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Question 2201

[2 marks]Sets

The universal set

\xi

, has subsets A and B such that;

\xi = \{3; 6; 9; 12 \ldots ; 30\}

, A = { numbers less than 20 }, B = { factors of 30 }. List the elements of set A.

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Question 2202

[2 marks]Sets

The universal set

\xi

, has subsets A and B such that;

\xi = \{3; 6; 9; 12 \ldots ; 30\}

, A = { numbers less than 20 }, B = { factors of 30 }. Find

n(B')

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Question 220301

[1 marks]Sets

The universal set is

\xi = \{3; 6; 9; 12; \ldots ; 30\}

, the multiples of 3 from 3 to 30. Set B is the set of factors of 30 that lie in

\xi

. List the members of B.

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Question 220302

[1 marks]Sets

The universal set is

\xi = \{3; 6; 9; 12; \ldots ; 30\}

, the multiples of 3 from 3 to 30. Set A holds the members less than 20 and set B the factors of 30. Which members lie in both A and B?

A9, 12 and 18
B3, 6 and 15
C3, 6, 9 and 15
D3, 6, 15 and 30

Question 220303

[1 marks]Sets

The universal set is

\xi = \{3; 6; 9; 12; \ldots ; 30\}

, the multiples of 3 from 3 to 30. Set A holds the members less than 20 and set B the factors of 30. Which members lie outside both A and B?

A21, 24 and 27
B9, 12 and 18
C21, 24, 27 and 30
D30 only

Mathematics Paper 1 November 2024

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1702

Question 1703

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 220301

Question 220302

Question 220303

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