ZIMSEC O Level Mathematics Paper 1 June 2000

Question 101

[1 marks]Number

Express 2,5 mm as a fraction of 50 cm in its lowest terms.

Answer this when you sit the paper.

Question 102

[1 marks]Number

Express 0,84 as a percentage.

Answer this when you sit the paper.

Question 103

[1 marks]Number

Express 1,4 m

^2

in cm

^2

Answer this when you sit the paper.

Question 201

[1 marks]Laws of Indices

Evaluate

5^{2/3} \times 5^{1/3}

Answer this when you sit the paper.

Question 202

[1 marks]Laws of Indices

Evaluate

16^{3/4}

Answer this when you sit the paper.

Question 203

[1 marks]Laws of Indices

Evaluate

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

Answer this when you sit the paper.

Question 301

[1 marks]Rational, Irrational Numbers & Surds

Given that

\sqrt{7} = 2,646

and

\sqrt{70} = 8,367

, calculate

\sqrt{7000}

Answer this when you sit the paper.

Question 302

[2 marks]Rational, Irrational Numbers & Surds

Given that

\sqrt{7} = 2,646

and

\sqrt{70} = 8,367

, calculate

\sqrt{0,07}

Answer this when you sit the paper.

Question 401

[1 marks]Algebra

Expand and simplify

(x-3)^2

Answer this when you sit the paper.

Question 402

[2 marks]Algebra

Expand and simplify

5(4x-7) - 6(3x-2)

Answer this when you sit the paper.

Question 501

[1 marks]Trigonometry, Bearing & Distances

Given that the bearing of

B

from

A

138°

, write down the bearing of

A

from

B

, expressing your answer as a three-figure bearing.

Answer this when you sit the paper.

Question 502

[2 marks]Scales & Simple Map Problems

The road from

A

B

is represented on a map, drawn to a scale of 1:50 000, by a line of length 12 cm. Find the length, in kilometres, of the road.

Answer this when you sit the paper.

Question 601

[1 marks]Number Bases

Express

2^5 + 2^4 + 2^2 + 1

as a number in base 2.

Answer this when you sit the paper.

Question 602

[1 marks]Number Bases

Given that

31_n = 16_{10}

for some base

n

, form an equation in

n

Answer this when you sit the paper.

Question 603

[1 marks]Number Bases

Given that

31_n = 16_{10}

for some base

n

, find the value of

n

Answer this when you sit the paper.

Question 701

[1 marks]Statistics & Probability

Mary drew the pie chart shown to illustrate the time she spent on her homework in one week. The chart shows Mathematics as a right angle (90°), Science as

50°

, English as

3x°

and Other subjects as

(60+x)°

. Calculate the value of

x

Answer this when you sit the paper.

Question 702

[1 marks]Statistics & Probability

Mary drew the pie chart shown to illustrate the time she spent on her homework in one week (Mathematics 90°, Science 50°, English

3x°

, Other subjects

(60+x)°

, with

x=40

). She spent 75 minutes doing Science. Calculate the total time, in hours, she spent doing her homework.

Answer this when you sit the paper.

Question 703

[1 marks]Statistics & Probability

Mary drew the pie chart shown to illustrate the time she spent on her homework in one week (Mathematics 90°, Science 50°, English

3x°

, Other subjects

(60+x)°

, with

x=40

). Find the percentage of the time she spent on English.

Answer this when you sit the paper.

Question 801

[3 marks]Equations

Solve the simultaneous equations

2x + 3y + 5 = 0

and

3x - 2y = 12

Answer this when you sit the paper.

Question 901

[1 marks]Polygons, Symmetry & Circles

ABCDEFGHI is a regular nonagon with centre O. State the order of rotational symmetry of the nonagon.

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Question 902

[1 marks]Polygons, Symmetry & Circles

ABCDEFGHI is a regular nonagon with centre O. Calculate the size of one of the interior angles of the nonagon.

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Question 903

[1 marks]Polygons, Symmetry & Circles

ABCDEFGHI is a regular nonagon with centre O. Calculate

B\hat{O}F

Answer this when you sit the paper.

Question 1001

[1 marks]Logarithms

Evaluate

\log_{10}16 \div \log_{10}2

Answer this when you sit the paper.

Question 1002

[2 marks]Logarithms

Evaluate

2\log_{10}5 + \log_{10}36 - \log_{10}9

Answer this when you sit the paper.

Question 1101

[1 marks]Inequalities

Two types of factory machines are available for sale. Type A needs 3 m

^2

floor space and costs \$20 000 each; type B needs 2 m

^2

and costs \$45 000 each. A factory manager decides to buy

x

machines of type A and

y

machines of type B, where

x \geq 0

and

y \geq 0

. If there is 40 m

^2

of floor space available, write down an inequality in

x

and

y

Answer this when you sit the paper.

Question 1102

[2 marks]Inequalities

Two types of factory machines are available for sale. Type A needs 3 m

^2

floor space and costs \$20 000 each; type B needs 2 m

^2

and costs \$45 000 each. A factory manager decides to buy

x

machines of type A and

y

machines of type B. If the manager has \$400 000 to spend, write down, in its simplest form, another inequality in

x

and

y

Answer this when you sit the paper.

Question 1201

[1 marks]Probability

A bag contains 6 red balls and 9 green balls which are all identical except for colour. Find, as a fraction in its lowest terms, the probability that a ball, taken at random from the bag, is red.

Answer this when you sit the paper.

Question 1202

[2 marks]Probability

A bag contains 6 red balls and 9 green balls which are all identical except for colour. The ball is returned into the bag. Two balls are then taken at random, one after the other without replacement, from the bag. Find the probability that they are of different colours.

Answer this when you sit the paper.

Question 1301

[1 marks]Algebra

Given that

x + y = 12

and

x^2 - y^2 = 30

, evaluate

x - y

Answer this when you sit the paper.

Question 1302

[2 marks]Equations

Solve the equation

(t-6)^2 = 25

Answer this when you sit the paper.

Question 1401

[1 marks]Ratios, Rates & Proportions

A tourist from England visited Zimbabwe bringing with him £2000 (two thousand pounds) which he exchanged for Zimbabwean dollars at the rate of £1 to Z$30. Calculate the amount he received in Zimbabwean dollars.

Answer this when you sit the paper.

Question 1402

[2 marks]Ratios, Rates & Proportions

A tourist from England exchanged £2000 for Zimbabwean dollars at £1 to Z

30, receiving Z

60 000. After visiting various resort centres in Zimbabwe he had spent Z$40 500. He then exchanged the remainder of his money for pounds. Find how many pounds he received.

Answer this when you sit the paper.

Question 1501

[1 marks]Time

Tafadzwa left Mutare at 1.10 p.m. by car and arrived in Masvingo 3¼ hours later. He rested for ½ an hour and then travelled to Beit Bridge in 3½ hours. Find the time, on the 24 hour clock, when Tafadzwa arrived in Beit Bridge.

Answer this when you sit the paper.

Question 1502

[2 marks]Speed, distance and time

Tafadzwa left Mutare at 1.10 p.m. by car and arrived in Beit Bridge at 2025 hours, via Masvingo, with a ½ hour rest along the way. His average speed for the whole journey (door to door) was 80 km/h. Find the distance from Mutare to Beit Bridge.

Answer this when you sit the paper.

Question 1601

[1 marks]Approximations & Estimations

Express 5,9964 correct to 2 decimal places.

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Question 1602

[2 marks]Ordinary & Standard Form

Simplify

(3,5 \times 10^5) \div (7 \times 10^2)

, giving the answer in standard form.

Answer this when you sit the paper.

Question 1701

[1 marks]Number

Divide

3\frac{1}{2}

5\frac{1}{4}

, giving the answer as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 1702

[2 marks]Number

Simplify

\frac{5+10}{5 \times 10}

as far as possible.

Answer this when you sit the paper.

Question 1801

[2 marks]Algebra

Express

\frac{3}{x-2} - \frac{2}{x}

as a single fraction.

Answer this when you sit the paper.

Question 1802

[2 marks]Matrices

Given that the matrix

\begin{pmatrix} y+2 & 3 \\ y-1 & 4 \end{pmatrix}

has determinant 4, find the value of

y

Answer this when you sit the paper.

Question 1901

[1 marks]Inequalities

Solve the inequality

14 \geq 2 - 3x

Answer this when you sit the paper.

Question 1902

[1 marks]Approximations & Estimations

The length,

l

cm, of a side of a square is given as 6 cm, correct to 1 significant figure. Write down the upper bound of

l

Answer this when you sit the paper.

Question 1903

[2 marks]Approximations & Estimations

The length,

l

cm, of a side of a square is given as 6 cm, correct to 1 significant figure. The area of the square is

A

^2

. Calculate the least possible value of

A

Answer this when you sit the paper.

Question 2001

[2 marks]Measures & Mensuration

In this question take

\pi

to be

\frac{22}{7}

. A circular cylinder has height 21 cm. Its volume is 1650 cm

^3

. Calculate the radius of the cylinder.

Answer this when you sit the paper.

Question 2002

[2 marks]Measures & Mensuration

In this question take

\pi

to be

\frac{22}{7}

. A circular cylinder has height 21 cm and volume 1650 cm

^3

(radius 5 cm). Calculate the volume of a similar body of height 7 cm.

Answer this when you sit the paper.

Question 2101

[1 marks]Circle Geometry

In the diagram,

A

B

and

C

are points on the circumference of a circle, centre

O

TA

and

TB

are tangents to the circle.

A\hat{C}B = 56°

and

C\hat{B}O = 48°

. Calculate

A\hat{O}B

Answer this when you sit the paper.

Question 2102

[1 marks]Circle Geometry

In the diagram,

A

B

and

C

are points on the circumference of a circle, centre

O

TA

and

TB

are tangents to the circle.

A\hat{C}B = 56°

and

C\hat{B}O = 48°

. Calculate

A\hat{B}T

Answer this when you sit the paper.

Question 2103

[2 marks]Circle Geometry

In the diagram,

A

B

and

C

are points on the circumference of a circle, centre

O

TA

and

TB

are tangents to the circle.

A\hat{C}B = 56°

and

C\hat{B}O = 48°

. Calculate

C\hat{A}T

Answer this when you sit the paper.

Question 2202

[3 marks]Rational, Irrational Numbers & Surds

The side of an equilateral triangle is 12 cm. Find the perpendicular height of the triangle in the form

m\sqrt{n}

, where

m

and

n

are integers and

n

is as small as possible.

Answer this when you sit the paper.

Question 2301

[1 marks]Similarity & Congruency

In the diagram,

AFGD

is a straight line.

AB

is parallel to

ED

and

EF

is parallel to

GB

EF = 6

cm,

AF = FG = GD = 5

cm and

E\hat{F}D = 64°

. Name, in correct order, two triangles which are congruent.

Answer this when you sit the paper.

Question 2302

[2 marks]Measures & Mensuration

In the diagram,

AFGD

is a straight line,

AB

parallel to

ED

EF

parallel to

GB

EF = 6

cm,

AF = FG = GD = 5

cm and

E\hat{F}D = 64°

. Using as much of the information given as is necessary, calculate the area of triangle

AGB

. [

\tan 64° = 2,05

;

\sin 64° = 0,90

;

\cos 64° = 0,44

Answer this when you sit the paper.

Question 2303

[1 marks]Measures & Mensuration

In the diagram,

AFGD

is a straight line,

AB

parallel to

ED

EF

parallel to

GB

EF = 6

cm,

AF = FG = GD = 5

cm and

E\hat{F}D = 64°

, with the area of triangle

AGB = 27

^2

. Hence, or otherwise, find the area of triangle

ABD

Answer this when you sit the paper.

Question 2401

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

Identical sticks are used to make a sequence of triangular patterns (Pattern 1: 3 sticks, 1 triangle, 0 inside sticks; Pattern 2: 9 sticks, 4 triangles, 3 inside sticks; Pattern 3: 18 sticks, 9 triangles, 9 inside sticks; Pattern 4: 30 sticks, 16 triangles, 18 inside sticks; Pattern 5:

x

sticks,

y

triangles,

z

inside sticks). By considering the number patterns in the table, write down the value of

x

Answer this when you sit the paper.

Question 2402

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

x

sticks,

y

triangles,

z

inside sticks). Write down the value of

y

Answer this when you sit the paper.

Question 2403

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

x

sticks,

y

triangles,

z

inside sticks). Write down the value of

z

Answer this when you sit the paper.

Question 2404

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

Identical sticks are used to make a sequence of triangular patterns as above. Find the number of sticks needed to make pattern 10 in the sequence.

Answer this when you sit the paper.

Question 2501

[2 marks]Number

Three companies, Comfort Cars, Reliable Services and Luxury Cruisers, offer cars for hire. Comfort Cars: \$660/day, nil per km. Reliable Services: nil per day, \$4,50/km. Luxury Cruisers: \$300/day, \$2,50/km. Mrs Tatenda hired a car for 2 days to drive 400 km. Find the cost if she hired the car from Luxury Cruisers.

Answer this when you sit the paper.

Question 2502

[3 marks]Number

Three companies, Comfort Cars, Reliable Services and Luxury Cruisers, offer cars for hire. Comfort Cars: \$660/day, nil per km. Reliable Services: nil per day, \$4,50/km. Mr Kudzai wishes to hire a car for 3 days. He finds that Comfort Cars and Reliable Services would make equal charges. Find the distance he intends to drive.

Answer this when you sit the paper.

Question 2602

[2 marks]Geometrical Transformation

The diagram shows quadrilaterals

A

B

and

C

(as drawn,

A

and

B

are right-triangular shapes and

C

is a trapezium). A shear maps quadrilateral

A

onto quadrilateral

B

. Describe fully this shear.

Answer this when you sit the paper.

Question 2603

[2 marks]Geometrical Transformation

The diagram shows quadrilaterals

A

B

and

C

. Describe fully the single transformation which maps quadrilateral

A

onto quadrilateral

C

Answer this when you sit the paper.

Question 2701

[1 marks]Kinematics

The diagram shows the velocity-time graph of a car during a period of 14 seconds. The car starts from rest and accelerates uniformly until it attains a velocity of 20 m/s in 4 seconds. It then retards uniformly to 8 m/s in 2 seconds. The car then moves at this velocity for a further 6 seconds and finally retards uniformly until it comes to rest 2 seconds later. Calculate the acceleration of the car during the first 4 seconds.

Answer this when you sit the paper.

Question 2702

[2 marks]Kinematics

The diagram shows the velocity-time graph of a car during a period of 14 seconds (0-4s: 0 to 20 m/s; 4-6s: 20 to 8 m/s; 6-12s: constant 8 m/s; 12-14s: 8 to 0 m/s). Calculate the velocity of the car at the end of the 13th second.

Answer this when you sit the paper.

Question 2703

[2 marks]Kinematics

The diagram shows the velocity-time graph of a car during a period of 14 seconds (0-4s: 0 to 20 m/s; 4-6s: 20 to 8 m/s; 6-12s: constant 8 m/s; 12-14s: 8 to 0 m/s). Calculate the distance travelled by the car during the last 7 seconds.

Answer this when you sit the paper.

Question 2801

[1 marks]Co-ordinate Geometry

Two points,

A(5,2)

and

B(-3,8)

, lie on a straight line

l

and

C(-2,4)

lies on another straight line

m

. Find the gradient of

l

Answer this when you sit the paper.

Question 2802

[1 marks]Co-ordinate Geometry

Two points,

A(5,2)

and

B(-3,8)

, lie on a straight line

l

. Find

\vec{AB}

as a column vector.

Answer this when you sit the paper.

Question 2803

[2 marks]Co-ordinate Geometry

Two points,

A(5,2)

and

B(-3,8)

, lie on a straight line

l

. Find the length of the line

AB

Answer this when you sit the paper.

Question 2804

[2 marks]Co-ordinate Geometry

Two points,

A(5,2)

and

B(-3,8)

, lie on a straight line

l

(gradient

-\frac{3}{4}

) and

C(-2,4)

lies on another straight line

m

. Given that

m

is parallel to

l

, find the equation of

m

in its simplest form.

Answer this when you sit the paper.

Mathematics Paper 1 June 2000

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 702

Question 703

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 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2101

Question 2102

Question 2103

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2404

Question 2501

Question 2502

Question 2602

Question 2603

Question 2701

Question 2702

Question 2703

Question 2801

Question 2802

Question 2803

Question 2804

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