ZIMSEC O Level Mathematics Paper 1 November 2021

Question 101

[1 marks]Approximations & Estimations

Express 30,098 correct to the nearest tenth.

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Question 102

[1 marks]Approximations & Estimations

Express 30,098 correct to four significant figures.

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Question 103

[1 marks]Ordinary & Standard Form

Express 30,098 in standard form.

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Question 201

[1 marks]Number

Express

4\frac{2}{3}

as a recurring decimal.

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Question 202

[2 marks]Number

Find the value of

10 - 10 \div 2 + 2 \times 2

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Question 301

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

Write down the next term in the sequence 2; 3; 5; 8; 12; ....

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Question 302

[2 marks]Number

Simplify

\frac{20-8}{20+8}

, giving your answer as a common fraction in its simplest form.

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Question 401

[1 marks]Number

List the prime numbers between 14 and 20.

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Question 402

[1 marks]Number

Write the number 801 008 in words.

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Question 403

[1 marks]Time

Express 6,65 hours in hours and minutes.

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Question 501

[2 marks]Number

List the first three values of

x

such that

1 \leq x \leq 4

where

x

is a natural number.

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Question 502

[2 marks]Number

Express 270 as a product of its prime factors in index form.

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Question 601

[1 marks]Trigonometry, Bearing & Distances

If the bearing of P from Q is

054°

, find the bearing of Q from P.

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Question 602

[2 marks]Polygons, Symmetry & Circles

Calculate the number of sides of a regular polygon with interior angles of

162°

each.

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Question 701

[3 marks]Algebra

Express

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

as a single fraction in its simplest form.

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Question 801

[1 marks]Number Bases

Write down the largest four-digit number in base 5.

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Question 802

[2 marks]Number Bases

Convert

111_8

to a number in base 7.

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Question 901

[3 marks]Algebra

Factorise completely

x^2(y+1) - y - 1

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Question 1001

[1 marks]Logarithms

Evaluate

\log_4 64

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Question 1002

[2 marks]Logarithms

Evaluate

\frac{\log 8}{\log 16}

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Question 1101

[3 marks]Algebra

Solve the simultaneous equations:

2x + y = 4

5y - 4x = 13

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Question 1201

[1 marks]Algebra

For the expressions

10(x+1)

and

8(x+1)^2

, find the H.C.F.

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Question 1202

[2 marks]Algebra

For the expressions

10(x+1)

and

8(x+1)^2

, find the L.C.M.

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Question 1301

[3 marks]Trigonometry, Bearing & Distances

A triangle has sides of lengths 5 cm, 8 cm and 12 cm. Find the cosine of the smallest angle as a common fraction in its simplest form.

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Question 1401

[2 marks]Laws of Indices

Solve the equation

5^x = 125

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Question 1402

[2 marks]Laws of Indices

Simplify

\left(\frac{98}{32}\right)^{-\frac{1}{2}}

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Question 1501

[2 marks]Inequalities

Given that

-2 \leq x \leq 5

and

3 \leq y \leq 10

, calculate the greatest possible value of

y^2 - x^2

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Question 1502

[2 marks]Inequalities

Given that

-2 \leq x \leq 5

and

3 \leq y \leq 10

, calculate the least possible value of

xy

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Question 1601

[3 marks]Inequalities

Solve the simultaneous inequalities

2x - 6 \leq 4x < 10 - x

. Leave the answer in the form

a \leq x < b

, where

a

and

b

are integers.

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Question 1701

[2 marks]Algebra

Given that

v^2 = u^2 + 2as

, make

a

the subject of the formula.

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Question 1702

[2 marks]Algebra

Given that

v^2 = u^2 + 2as

, find

a

when

s = 5

u = 2

and

v = 2

Answer this when you sit the paper.

Question 1801

[1 marks]Variation

D

varies jointly as

S

and

T

. Find an equation connecting

D

S

T

and a constant

k

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Question 1802

[1 marks]Variation

D

varies jointly as

S

and

T

, so that

D = kST

. Find the value of

k

given that

D = 24

when

S = 4

and

T = 2

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Question 1803

[2 marks]Variation

D

varies jointly as

S

and

T

, so that

D = kST

with

k = 3

. Find the value of

T

given that

D = 50

and

S = 10

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Question 1902

[1 marks]Sets

The universal set

\xi

has subsets A and B such that

n(\xi) = 45

n(A) = 25

n(A' \cap B) = 9

and

n(A \cap B) = n(A \cup B)'

. Find

n(B)

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Question 2001

[1 marks]Functional Notation

Given that

f(x) = \frac{3}{x+2}

x \neq -2

, find

f(-1)

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Question 2002

[3 marks]Functional Notation

Given that

f(x) = \frac{3}{x+2}

x \neq -2

, find the value of

x

for which

f(x) = -\frac{3}{4}

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Question 2101

[2 marks]Speed, distance and time

The diagram shows a speed-time graph of a moving object. The object decelerates uniformly at

3\text{ m/s}^2

from a speed of

V

m/s to a speed of 15 m/s in 5 seconds. It maintains the speed of 15 m/s for a further 5 seconds. It then decelerates uniformly until it comes to rest after 3 seconds. Calculate

V

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Question 2102

[1 marks]Speed, distance and time

The diagram shows a speed-time graph of a moving object. The object decelerates uniformly at

3\text{ m/s}^2

from a speed of

V

m/s to a speed of 15 m/s in 5 seconds, maintains 15 m/s for a further 5 seconds, then decelerates uniformly to rest over the last 3 seconds. Calculate the deceleration in the last 3 seconds.

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Question 2103

[2 marks]Speed, distance and time

The diagram shows a speed-time graph of a moving object. The object decelerates uniformly at

3\text{ m/s}^2

from a speed of

V

m/s to a speed of 15 m/s in 5 seconds, maintains 15 m/s for a further 5 seconds, then decelerates uniformly to rest over the last 3 seconds. Calculate the distance travelled in the last 8 seconds.

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Question 2201

[2 marks]Fractions, Decimals & Percentages

By selling an article for \$20,00 a dealer made a profit of 25%. Calculate the cost price of the article.

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Question 2202

[3 marks]Algebra

Given that

\frac{7t-s}{2} = \frac{s-5t}{3}

, find the ratio

t : s

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Question 2301

[1 marks]Functional Graphs

A straight line,

l

, passes through the origin and the point

(1;2)

. Find the gradient of line

l

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Question 2302

[2 marks]Functional Graphs

A straight line,

l

, passes through the origin and the point

(1;2)

. Find the equation of the line

l

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Question 2303

[2 marks]Functional Graphs

A straight line,

l

, passes through the origin and the point

(1;2)

. Find the equation of the straight line through point

(0;-1)

which is parallel to line

l

Answer this when you sit the paper.

Question 2401

[2 marks]Scales & Simple Map Problems

On a map the distance between point A and point B is 10 cm. The actual distance is

2\frac{1}{2}

km. Find the scale on the map, giving the answer in the form

1:n

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Question 2402

[1 marks]Scales & Simple Map Problems

A map has a scale of 1:25 000. Calculate the actual distance, in metres, between 2 places which are 3 cm apart on the map.

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Question 2403

[2 marks]Scales & Simple Map Problems

A map has a scale of 1:25 000. Calculate the actual area, in km

^2

, represented by an area of 8 cm

^2

on the map.

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Question 2501

[2 marks]Vector Geometry

Given that

\vec{OA} = \binom{-2}{1}

and

\vec{OB} = \binom{1}{-2}

, where O is the origin, find

\vec{AB}

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Question 2502

[2 marks]Vector Geometry

Given that

\vec{OA} = \binom{-2}{1}

and

\vec{OB} = \binom{1}{-2}

, where O is the origin, find

|\vec{AB}|

, leaving the answer in surd form.

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Question 2503

[2 marks]Vector Geometry

Given that

\vec{OA} = \binom{-2}{1}

and

\vec{OB} = \binom{1}{-2}

, where O is the origin, find

\vec{OM}

, where M is the midpoint of AB.

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Question 2601

[2 marks]Matrices

Given that matrix

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

and matrix

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

, find the determinant of matrix C.

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Question 2602

[2 marks]Matrices

Given that matrix

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

and matrix

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

, find

A - 3C

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Question 2603

[2 marks]Matrices

Given that matrix

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

, find matrix B if

B = A\binom{5}{6}

Answer this when you sit the paper.

Mathematics Paper 1 November 2021

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 302

Question 401

Question 402

Question 403

Question 501

Question 502

Question 601

Question 602

Question 701

Question 801

Question 802

Question 901

Question 1001

Question 1002

Question 1101

Question 1201

Question 1202

Question 1301

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1902

Question 2001

Question 2002

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

Question 2603

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