ZIMSEC O Level Mathematics Paper 1 June 2001

Question 101

[1 marks]Number

Giving your answer as a common fraction in its lowest terms, find the value of

7\frac{2}{5} - 6\frac{2}{3}

Answer this when you sit the paper.

Question 102

[1 marks]Number

Giving your answer as a common fraction in its lowest terms, find the value of

0,45

\frac{5}{9}

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Question 103

[1 marks]Number

Express

\frac{15}{16}

as a terminating decimal.

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Question 201

[1 marks]Approximations & Estimations

Express

158,697

correct to the nearest hundredth.

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Question 202

[1 marks]Approximations & Estimations

Express

158,697

correct to two significant figures.

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Question 203

[1 marks]Number

Express 720 as a product of its prime factors.

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Question 301

[1 marks]Time

Find the sum of 2 days 15 hours and 3 days 21 hours, giving your answer in days and hours.

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Question 302

[2 marks]Number Bases

Express

34_5

(34 base five) as a number in base two.

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Question 401

[3 marks]Algebra

Simplify

\dfrac{a^2-b^2}{ab+a^2} \div \dfrac{ab-a^2}{2a^3}

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Question 501

[1 marks]Measures & Mensuration

Two similar cylinders have their volumes in the ratio 1:8. Write down the ratio of the areas of their circular surfaces.

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Question 502

[2 marks]Trigonometry, Bearing & Distances

A

B

and

C

are three points on level ground. The bearing of

C

from

B

138°

and

A\hat{B}C = 92°

. Calculate the bearing of

B

from

A

Answer this when you sit the paper.

Question 801

[1 marks]Laws of Indices

Evaluate

\left(\dfrac{1}{5}\right)^{-2}

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Question 802

[2 marks]Laws of Indices

Evaluate

-27^{\frac{2}{3}}

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Question 901

[2 marks]Measures & Mensuration

In the diagram,

ABE

and

DCF

are parallel straight lines,

ABCD

is a parallelogram,

DC = 7

cm,

EC = 8

cm and

E\hat{C}F = 65°

. Using the information given below where necessary, find the area of

\triangle DEC

. [

\sin 65° = 0,91

;

\cos 65° = 0,42

;

\tan 65° = 2,14

Answer this when you sit the paper.

Question 902

[1 marks]Measures & Mensuration

In the diagram,

ABE

and

DCF

are parallel straight lines,

ABCD

is a parallelogram,

DC = 7

cm,

EC = 8

cm and

E\hat{C}F = 65°

. Using the information given below where necessary, find the area of parallelogram

ABCD

. [

\sin 65° = 0,91

;

\cos 65° = 0,42

;

\tan 65° = 2,14

Answer this when you sit the paper.

Question 1001

[1 marks]Functional Graphs

In the diagram, line

l_1

and line

l_2

are parallel.

l_1

passes through

(0,4)

and

(3,0)

. Find the gradient of line

l_1

Answer this when you sit the paper.

Question 1002

[2 marks]Functional Graphs

In the diagram, line

l_1

and line

l_2

are parallel.

l_1

passes through

(0,4)

and

(3,0)

, and

l_2

passes through

(5,4)

. Find the equation of line

l_2

, giving your answer in the form

ax + by = c

where

a

b

and

c

are integers.

Answer this when you sit the paper.

Question 1101

[1 marks]Inequalities

The diagram shows an unshaded region bounded by the lines

2y = 7x+14

y+x=7

and

y=-4

. Write down the inequality (involving only

y

) that defines the unshaded region.

Answer this when you sit the paper.

Question 1102

[1 marks]Inequalities

The diagram shows an unshaded region bounded by the lines

2y = 7x+14

y+x=7

and

y=-4

. Write down the inequality relating

2y

and

7x+14

that defines the unshaded region.

Answer this when you sit the paper.

Question 1103

[1 marks]Inequalities

The diagram shows an unshaded region bounded by the lines

2y = 7x+14

y+x=7

and

y=-4

. Write down the inequality relating

y+x

and 7 that defines the unshaded region.

Answer this when you sit the paper.

Question 1201

[3 marks]Trigonometry, Bearing & Distances

In the diagram,

AB = 11

cm,

BC = 7

cm and

AC = 6

cm. Calculate the value of

\cos A\hat{C}B

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

Answer this when you sit the paper.

Question 1301

[3 marks]Equations

Solve the simultaneous equations

2x - 3y = 13

3x + 2y = 0

Answer this when you sit the paper.

Question 1401

[2 marks]Approximations & Estimations

Estimate, to the nearest whole number, the value of

\dfrac{7,9 \times \sqrt{80,6}}{1,8 \times 3,1}

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Question 1402

[2 marks]Approximations & Estimations

The length of a square is given as 10 cm correct to one significant figure. Find the smallest possible area of the square.

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Question 1501

[1 marks]Ordinary & Standard Form

Given that

m = 4,8 \times 10^3

and

n = 1,2 \times 10^{-5}

, find

5m

, giving your answer in standard form.

Answer this when you sit the paper.

Question 1502

[1 marks]Ordinary & Standard Form

Given that

m = 4,8 \times 10^3

and

n = 1,2 \times 10^{-5}

, find

n^2

, giving your answer in standard form.

Answer this when you sit the paper.

Question 1503

[2 marks]Ordinary & Standard Form

Given that

m = 4,8 \times 10^3

and

n = 1,2 \times 10^{-5}

, find

\dfrac{n}{m}

, giving your answer in standard form.

Answer this when you sit the paper.

Question 1601

[2 marks]Algebra

Expand and simplify

(x + 2)(5 + 2x - x^2)

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Question 1602

[2 marks]Algebra

Factorise completely

3x^2 - 6x - ax + 2a

Answer this when you sit the paper.

Question 1701

[1 marks]Circle Geometry

In the diagram,

PA

and

PB

are tangents to the circle centre

O

Q

is a point on the minor arc

AB

and

A\hat{O}B = 140°

. Find

O\hat{B}P

Answer this when you sit the paper.

Question 1702

[1 marks]Circle Geometry

In the diagram,

PA

and

PB

are tangents to the circle centre

O

Q

is a point on the minor arc

AB

and

A\hat{O}B = 140°

. Find

A\hat{P}B

Answer this when you sit the paper.

Question 1703

[2 marks]Circle Geometry

In the diagram,

PA

and

PB

are tangents to the circle centre

O

Q

is a point on the minor arc

AB

and

A\hat{O}B = 140°

. Find

A\hat{Q}B

Answer this when you sit the paper.

Question 1801

[2 marks]Matrices

A = \begin{pmatrix} 7 & -2 \\ 4 & -1 \end{pmatrix}

B = \begin{pmatrix} -1 & 2 \\ -4 & 7 \end{pmatrix}

. Find

AB

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Question 1802

[2 marks]Matrices

M = \begin{pmatrix} -3 & -5 \\ 2 & 6 \end{pmatrix}

. Find the inverse of

M

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Question 1901

[2 marks]Number

It is given that

\mathbf{a} = \begin{pmatrix} 11 \\ -7 \end{pmatrix}

\sqrt{17} = 4,123

and

\sqrt{1,7} = 1,304

. Find

\sqrt{0,17}

Answer this when you sit the paper.

Question 1902

[2 marks]Vector Geometry

It is given that

\mathbf{a} = \begin{pmatrix} 11 \\ -7 \end{pmatrix}

\sqrt{17} = 4,123

and

\sqrt{1,7} = 1,304

. Find the magnitude of

\mathbf{a}

correct to two significant figures.

Answer this when you sit the paper.

Question 2001

[2 marks]Algebra

In a regular polygon of

n

sides, the size of each interior angle

x°

is given by the formula

x = 180 - \dfrac{360}{n}

. Make

n

the subject of the formula.

Answer this when you sit the paper.

Question 2002

[2 marks]Polygons, Symmetry & Circles

In a regular polygon of

n

sides, the size of each interior angle

x°

is given by the formula

x = 180 - \dfrac{360}{n}

. Calculate the number of sides of a regular polygon whose interior angle is

150°

Answer this when you sit the paper.

Question 2101

[1 marks]Geometrical Transformation

The diagram shows

\triangle ABC

with

A(-3,-1)

B(-1,-1)

C(-1,-3)

. Find the coordinates of

P

Q

and

R

, the images of

A

B

and

C

respectively under a translation of vector

\begin{pmatrix} 7 \\ 4 \end{pmatrix}

Answer this when you sit the paper.

Question 2102

[3 marks]Geometrical Transformation

The diagram shows

\triangle ABC

and

\triangle DEF

. Describe fully the single transformation that maps

\triangle ABC

onto

\triangle DEF

Answer this when you sit the paper.

Question 2201

[2 marks]Scales & Simple Map Problems

The scale of a map is given as 1:50 000. Calculate the length of a line on the map that represents a road 6,4 km long.

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Question 2202

[3 marks]Scales & Simple Map Problems

The scale of a map is given as 1:50 000. Calculate the area, in hectares, of a piece of land represented on the map by an area of 3 cm². [1 hectare = 10 000 m².]

Answer this when you sit the paper.

Question 2301

[1 marks]Variation

m

is directly proportional to

n^2

and

m = 28

when

n = 2

. Write down an expression for

m

in terms of

n

and a constant

k

Answer this when you sit the paper.

Question 2302

[2 marks]Variation

m

is directly proportional to

n^2

and

m = 28

when

n = 2

, so that

m = kn^2

. Calculate the value of

k

Answer this when you sit the paper.

Question 2303

[2 marks]Variation

m

is directly proportional to

n^2

, so that

m = 7n^2

. Calculate the values of

n

when

m = 63

Answer this when you sit the paper.

Question 2401

[1 marks]Logarithms

Given that

\log 216 = 2,334

and

\log 3 = 0,477

, find

\log 2,16

Answer this when you sit the paper.

Question 2402

[2 marks]Logarithms

Given that

\log 216 = 2,334

and

\log 3 = 0,477

, find

\log 6

Answer this when you sit the paper.

Question 2403

[2 marks]Logarithms

Given that

\log 216 = 2,334

and

\log 3 = 0,477

, find

\log 72

Answer this when you sit the paper.

Question 2501

[1 marks]Simultaneous Equations

The graph of

x + 2y + p = 0

and the graph of

3x + qy = 9

intersect at the point

(-2, 3)

. Find the value of

p

Answer this when you sit the paper.

Question 2502

[1 marks]Simultaneous Equations

The graph of

x + 2y + p = 0

and the graph of

3x + qy = 9

intersect at the point

(-2, 3)

. Find the value of

q

Answer this when you sit the paper.

Question 2503

[2 marks]Algebra

Factorise

4x^2 - 12x + 9

Answer this when you sit the paper.

Question 2504

[2 marks]Algebra

Given that

4x^2 - 12x + 9 = (2x-3)^2

, solve the equation

4x^2 - 12x + 9 = 16

Answer this when you sit the paper.

Question 2601

[1 marks]Functional Graphs

The diagram shows the velocity-time graph of a car during a period of 20 minutes: velocity falls from 90 km/h to 30 km/h during the first 5 minutes, stays at 30 km/h from 5 to 15 minutes, then rises back to 90 km/h from 15 to 20 minutes. Find the retardation, in km/h per minute, during the first 5 minutes.

Answer this when you sit the paper.

Question 2602

[2 marks]Functional Graphs

The diagram shows the velocity-time graph of a car during a period of 20 minutes: velocity falls from 90 km/h to 30 km/h during the first 5 minutes, stays at 30 km/h from 5 to 15 minutes, then rises back to 90 km/h from 15 to 20 minutes. Find the distance, in kilometres, travelled at constant velocity.

Answer this when you sit the paper.

Question 2603

[2 marks]Functional Graphs

Answer this when you sit the paper.

Question 2604

[3 marks]Functional Graphs

Answer this when you sit the paper.

Mathematics Paper 1 June 2001

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 401

Question 501

Question 502

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1002

Question 1101

Question 1102

Question 1103

Question 1201

Question 1301

Question 1401

Question 1402

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1701

Question 1702

Question 1703

Question 1801

Question 1802

Question 1901

Question 1902

Question 2001

Question 2002

Question 2101

Question 2102

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2504

Question 2601

Question 2602

Question 2603

Question 2604

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