ZIMSEC O Level Mathematics Paper 1 November 2022

Question 101

[1 marks]Number

Express one million and one in figures.

Answer this when you sit the paper.

Question 102

[1 marks]Time

Express

1\frac{3}{4}

days in hours.

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Question 103

[1 marks]Points, Lines & Angles

Express

11,6°

in degrees and minutes.

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Question 201

[1 marks]Equations

Solve the equation

13x = 377

Answer this when you sit the paper.

Question 202

[1 marks]Vector Geometry

If vector

a + \begin{pmatrix}3\\4\end{pmatrix} = \begin{pmatrix}5\\0\end{pmatrix}

, find vector

a

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Question 203

[1 marks]Number

Write down the largest perfect square integer number less than 20.

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Question 301

[1 marks]Trigonometry, Bearing & Distances

Write the three figure bearing equivalent to North East.

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Question 302

[1 marks]Number

Write the first three positive odd integers.

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Question 303

[1 marks]Approximations & Estimations

Express

0,0456

correct to one significant figure.

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Question 401

[1 marks]Laws of Indices

Evaluate

\left(\frac{7}{8}\right)^{-1}

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Question 402

[2 marks]Logarithms

Evaluate

\log_5 80 - \log_5 16

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Question 501

[2 marks]Algebra

Simplify the expression

\frac{2x+3y}{6x+9y}

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Question 502

[2 marks]Number

Find

\sqrt{5\frac{4}{9}}

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Question 601

[3 marks]Equations

Solve the equation

2x^2 - 5x - 3 = 0

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Question 701

[1 marks]Functional Notation

Given that

f(d) = d^2 - 3d

, find

f(3)

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Question 702

[3 marks]Functional Notation

Given that

f(d) = d^2 - 3d

, find the values of

d

for which

f(d) = 10

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Question 801

[3 marks]Equations

Solve the simultaneous equations:

3m - n = -7

2m + n = 17

Answer this when you sit the paper.

Question 901

[1 marks]Number

Given that

\xi = \{x : 49 \leq x \leq 58\}

x \in \mathbb{Z}

, state from

\xi

a prime number.

Answer this when you sit the paper.

Question 902

[1 marks]Number

Given that

\xi = \{x : 49 \leq x \leq 58\}

x \in \mathbb{Z}

, state from

\xi

a multiple of 19.

Answer this when you sit the paper.

Question 903

[1 marks]Number

Given that

\xi = \{x : 49 \leq x \leq 58\}

x \in \mathbb{Z}

, state from

\xi

a square number.

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Question 1001

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

Find the next two terms in the sequence 1; 3; 6; 10; 15; ...

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Question 1002

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

Find the next two terms in the sequence 16; 4; 1;

\frac{1}{4}

; ...

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Question 1101

[2 marks]Number Bases

Given that

11_a = 9_{10}

, find the value of

a

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Question 1102

[2 marks]Number Bases

Convert

202_7

to a number in base 5.

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Question 1201

[2 marks]Number

Evaluate

\left(\frac{1}{3} + \frac{1}{4}\right)^2

Answer this when you sit the paper.

Question 1202

[2 marks]Number

Evaluate

1\frac{1}{4} \div 1\frac{1}{2}

, leaving the answer in its lowest terms.

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Question 1301

[1 marks]Polygons, Symmetry & Circles

State the number of lines of symmetry of a rhombus.

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Question 1302

[3 marks]Measures & Mensuration

The diagram shows triangle HIJ. Line HI is parallel to line KL, where L and K are midpoints of IJ and HJ respectively. The area of triangle HIJ is 48 cm

^2

. Calculate the area of the shaded quadrilateral HILK.

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Question 1401

[3 marks]Algebra

Factorise completely

36p^4 - 4q^2

Answer this when you sit the paper.

Question 1402

[2 marks]Algebra

Factorise completely

10my + 15ny + 6m + 9n

Answer this when you sit the paper.

Question 1501

[2 marks]Speed, distance and time

Convert a speed of 10 m/s to a speed in km/h.

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Question 1502

[2 marks]Matrices

Given that matrix

A = \begin{pmatrix}m & 6\\12 & 2m\end{pmatrix}

is singular, find the two possible values of

m

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Question 1601

[1 marks]Inequalities

A rectangle of length

x

metres and width

y

metres is drawn according to these conditions: the width is greater than one third of the length. Find an inequality that satisfies this condition.

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Question 1602

[3 marks]Inequalities

A rectangle of length

x

metres and width

y

metres is drawn according to these conditions: the perimeter is not less than 400 metres but less than 560 metres. Find an inequality which satisfies this condition.

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Question 1701

[2 marks]Inequalities

Given that

n - 4 > 7

, find the smallest possible value of

n

n

is an integer.

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Question 1702

[3 marks]Trigonometry, Bearing & Distances

A triangle ABC is such that

AB = 3

cm,

AC = 5

cm,

BC = x

cm and

B\hat{A}C = 120°

. Use as much of the information given below as is necessary to answer the question. [

\sin 60° = \frac{\sqrt3}{2}

;

\cos 60° = \frac{1}{2}

;

\tan 60° = \sqrt3

] Find the value of

x

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Question 1801

[2 marks]Vector Geometry

The magnitude of vector

\begin{pmatrix}x\\3\end{pmatrix}

is 5. Find the possible values of

x

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Question 1802

[1 marks]Sets

The universal set

\xi

has subsets A, B and C such that

\xi = \{1;2;3;4;5;6;7;8;9\}

A = \{x : x \text{ is a factor of } 8\}

B = \{2;4;8\}

C = \{x : x \text{ is a perfect square number}\}

. List all elements of subset C.

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Question 1803

[1 marks]Sets

The universal set

\xi

has subsets A, B and C such that

\xi = \{1;2;3;4;5;6;7;8;9\}

A = \{x : x \text{ is a factor of } 8\}

B = \{2;4;8\}

C = \{x : x \text{ is a perfect square number}\}

. Find

n(A \cup B)

Answer this when you sit the paper.

Question 1804

[1 marks]Sets

The universal set

\xi

has subsets A, B and C such that

\xi = \{1;2;3;4;5;6;7;8;9\}

A = \{x : x \text{ is a factor of } 8\}

B = \{2;4;8\}

C = \{x : x \text{ is a perfect square number}\}

. Write down the relationship between sets A and B in set notation.

Answer this when you sit the paper.

Question 1901

[1 marks]Statistics & Probability

The midday temperature, in degrees Celsius, for ten days in September in a certain town were recorded as follows: 18; 20; 22; 23; 26; 28; 22; 18; 18; 17. State the modal temperature.

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Question 1902

[1 marks]Statistics & Probability

The midday temperature, in degrees Celsius, for ten days in September in a certain town were recorded as follows: 18; 20; 22; 23; 26; 28; 22; 18; 18; 17. Find the median temperature.

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Question 1903

[1 marks]Statistics & Probability

The midday temperature, in degrees Celsius, for ten days in September in a certain town were recorded as follows: 18; 20; 22; 23; 26; 28; 22; 18; 18; 17. Find the temperature range.

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Question 1904

[2 marks]Statistics & Probability

The midday temperature, in degrees Celsius, for ten days in September in a certain town were recorded as follows: 18; 20; 22; 23; 26; 28; 22; 18; 18; 17. Calculate the mean temperature.

Answer this when you sit the paper.

Question 2001

[1 marks]Points, Lines & Angles

The diagram shows two parallel lines AB and CD. Line QN cuts the parallel lines at Q and N. Line PM cuts QN at P and AB at M.

C\hat{Q}P = 4d°

Q\hat{P}M = 3d°

and

P\hat{M}N = d°

. Express

M\hat{N}P

in terms of

d

Answer this when you sit the paper.

Question 2002

[2 marks]Points, Lines & Angles

The diagram shows two parallel lines AB and CD. Line QN cuts the parallel lines at Q and N. Line PM cuts QN at P and AB at M.

C\hat{Q}P = 4d°

Q\hat{P}M = 3d°

and

P\hat{M}N = d°

. Calculate the value of

d

Answer this when you sit the paper.

Question 2003

[1 marks]Circle Geometry

The diagram shows points A, B, C and D on the circumference of a circle centre O. AB and DC are chords and AC is the diameter of the circle. Point F is on AB produced.

F\hat{B}O = 142°

. Calculate

B\hat{A}C

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Question 2004

[2 marks]Circle Geometry

The diagram shows points A, B, C and D on the circumference of a circle centre O. AB and DC are chords and AC is the diameter of the circle. Point F is on AB produced.

F\hat{B}O = 142°

. Calculate

B\hat{O}C

Answer this when you sit the paper.

Question 2101

[2 marks]Polygons, Symmetry & Circles

The interior angle of a regular polygon is

13x°

and the exterior angle is

2x°

. Calculate the value of

x

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Question 2102

[2 marks]Polygons, Symmetry & Circles

The interior angle of a regular polygon is

13x°

and the exterior angle is

2x°

, where

x = 12

. Find the number of sides of the regular polygon.

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Question 2103

[2 marks]Probability

A bag contains 20 balls all identical except for colour. There are 3 green balls, 5 red balls and 12 brown balls. One ball is picked at random from the bag, its colour noted and is replaced. A second ball is picked at random and its colour noted and is replaced. Calculate the probability that both balls are of the same colour.

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Question 2201

[1 marks]Functional Notation

The velocity,

v

m/s, of a moving particle after

t

seconds is given by the equation

v = 5 + 4t - t^2

. Calculate the value of

v

when

t = 3

seconds.

Answer this when you sit the paper.

Question 2202

[3 marks]Functional Notation

The velocity,

v

m/s, of a moving particle after

t

seconds is given by the equation

v = 5 + 4t - t^2

. Calculate the value of

t

when

v = 0

Answer this when you sit the paper.

Question 2203

[2 marks]Algebra

Make

h

the subject in the formula

A = 2\pi r^2 + 2\pi rh

Answer this when you sit the paper.

Question 2301

[4 marks]Measures & Mensuration

ABCD is an isosceles trapezium with

AB = 5

cm,

DC = 17

cm and

AD = BC

. AB is parallel to DC. The perimeter of the trapezium is 42 cm. Calculate the perpendicular distance between the two parallel sides.

Answer this when you sit the paper.

Question 2302

[2 marks]Measures & Mensuration

ABCD is an isosceles trapezium with

AB = 5

cm,

DC = 17

cm and

AD = BC

. AB is parallel to DC. The perimeter of the trapezium is 42 cm. Calculate the area of the trapezium ABCD.

Answer this when you sit the paper.

Question 2401

[2 marks]Fractions, Decimals & Percentages

A dealer made a profit of 20% on the buying price by selling a double bed for $180,00. Calculate the buying price.

Answer this when you sit the paper.

Question 2402

[2 marks]Fractions, Decimals & Percentages

A dealer made a profit of 20% on the buying price by selling a double bed for $180,00. Calculate the selling price if the same bed had been sold at a loss of 20%.

Answer this when you sit the paper.

Mathematics Paper 1 November 2022

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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 501

Question 502

Question 601

Question 701

Question 702

Question 801

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1202

Question 1301

Question 1302

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1804

Question 1901

Question 1902

Question 1903

Question 1904

Question 2001

Question 2002

Question 2003

Question 2004

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2401

Question 2402

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