ZIMSEC O Level Mathematics Paper 1 November 2008

Question 101

[1 marks]Fractions, Decimals & Percentages

Simplify

6{,}3 \times 1{,}1

, giving your answer as a decimal.

Answer this when you sit the paper.

Question 102

[1 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{2}{3} - \dfrac{3}{4}

, giving your answer as a common fraction.

Answer this when you sit the paper.

Question 103

[2 marks]Fractions, Decimals & Percentages

Find 5% of 130 metres.

Answer this when you sit the paper.

Question 201

[1 marks]Number Bases

Evaluate

54_6 + 305_6

, giving your answer in base 6.

Answer this when you sit the paper.

Question 202

[2 marks]Number Bases

Convert

10011_2

to a number in base 3.

Answer this when you sit the paper.

Question 301

[1 marks]Approximations and Estimations

Given that

94 \times 152 = 14\,288

, find the value of

N

95 \times 152 = 14\,288 + N

Answer this when you sit the paper.

Question 302

[1 marks]Approximations and Estimations

Given that

94 \times 152 = 14\,288

, write down the exact value of

0{,}094 \times 1\,520

Answer this when you sit the paper.

Question 303

[1 marks]Approximations and Estimations

Given that

94 \times 152 = 14\,288

, write down the exact value of

0{,}14\,288 \div 0{,}0094

Answer this when you sit the paper.

Question 401

[1 marks]Laws of Indices

Simplify

(0{,}2)^3 \times (0{,}2)^2

, giving your answer as a decimal.

Answer this when you sit the paper.

Question 402

[2 marks]Equations

Solve the equation

5x - 2(x + 3) = 9

Answer this when you sit the paper.

Question 501

[1 marks]Time

Write 0019 in 12-hour notation.

Answer this when you sit the paper.

Question 502

[2 marks]Ratios, Rates & Proportions

Tapiwa and Netsai share some money in the ratio 2: 5. Given that Tapiwa's share is $620 000, calculate Netsai's share.

Answer this when you sit the paper.

Question 601

[1 marks]Polygons, Symmetry and Circles

In the diagram, BCD is a straight line and AB is parallel to ED. Given that BC = AC,

A\hat{D}B = 20^\circ

and

A\hat{C}B = 50^\circ

, calculate

B\hat{A}C

Answer this when you sit the paper.

Question 602

[1 marks]Polygons, Symmetry and Circles

In the diagram, BCD is a straight line and AB is parallel to ED. Given that BC = AC,

A\hat{D}B = 20^\circ

and

A\hat{C}B = 50^\circ

, calculate

D\hat{A}C

Answer this when you sit the paper.

Question 603

[1 marks]Polygons, Symmetry and Circles

In the diagram, BCD is a straight line and AB is parallel to ED. Given that BC = AC,

A\hat{D}B = 20^\circ

and

A\hat{C}B = 50^\circ

, calculate

A\hat{D}E

Answer this when you sit the paper.

Question 701

[1 marks]Ordinary and Standard Form

Given that

m = 4 \times 10^{6}

and

n = 2{,}4 \times 10^{-3}

, calculate

mn

, giving your answer in standard form.

Answer this when you sit the paper.

Question 702

[2 marks]Ordinary and Standard Form

Given that

m = 4 \times 10^{6}

and

n = 2{,}4 \times 10^{-3}

, calculate

\dfrac{n}{m}

, giving your answer in standard form.

Answer this when you sit the paper.

Question 801

[1 marks]Circle Geometry

WXYZ is a cyclic quadrilateral. The diagonals XZ and YW intersect at P and YX is produced to S.

Y\hat{W}X = 70^\circ

X\hat{Y}P = 25^\circ

and

Y\hat{P}Z = 43^\circ

. Calculate

X\hat{Z}Y

Answer this when you sit the paper.

Question 802

[1 marks]Circle Geometry

WXYZ is a cyclic quadrilateral. The diagonals XZ and YW intersect at P and YX is produced to S.

Y\hat{W}X = 70^\circ

X\hat{Y}P = 25^\circ

and

Y\hat{P}Z = 43^\circ

. Calculate

Y\hat{X}Z

Answer this when you sit the paper.

Question 803

[1 marks]Circle Geometry

WXYZ is a cyclic quadrilateral. The diagonals XZ and YW intersect at P and YX is produced to S.

Y\hat{W}X = 70^\circ

X\hat{Y}P = 25^\circ

and

Y\hat{P}Z = 43^\circ

. Calculate

S\hat{X}W

Answer this when you sit the paper.

Question 901

[1 marks]Trigonometry, Bearing & Distances

The bearing of town B from town A is

141^\circ

. Find the bearing of town A from town B.

Answer this when you sit the paper.

Question 902

[2 marks]Polygons

The interior angle of a regular polygon is

162^\circ

. Find the number of sides of the polygon.

Answer this when you sit the paper.

Question 1001

[1 marks]Circle Geometry

In the diagram, the shaded sector AOB is

\dfrac{7}{15}

of the circle centre O. Calculate

A\hat{O}B

Answer this when you sit the paper.

Question 1002

[2 marks]Measures and Mensuration

Calculate the radius of a circle whose area is

154\ \text{cm}^2

. [Take

\pi

to be

\dfrac{22}{7}

]

Answer this when you sit the paper.

Question 1101

[1 marks]Algebraic Expressions

Taurai is

x

years old. Zvikomborero, her brother, is 9 years older than her. Their father is 3 times as old as Taurai. Their mother is twice as old as Zvikomborero. Write down and simplify, in terms of

x

, an expression for the total age of the four members of the family.

Answer this when you sit the paper.

Question 1102

[2 marks]Equations

Taurai is

x

years old. Zvikomborero, her brother, is 9 years older than her. Their father is 3 times as old as Taurai. Their mother is twice as old as Zvikomborero. Given that the sum of the ages of the four members is 139 years, find the value of

x

Answer this when you sit the paper.

Question 1201

[2 marks]Scales & Simple Map Problems

The scale of a map is 1: 1 000 000. Find the length, in cm, of a line on the map which represents a road 160 km long.

Answer this when you sit the paper.

Question 1202

[2 marks]Scales & Simple Map Problems

The scale of a map is 1: 1 000 000. Find the actual area of a piece of land which is represented by

2{,}64\ \text{cm}^2

on the map, giving your answer in

\text{km}^2

Answer this when you sit the paper.

Question 1301

[1 marks]Functional Notation

f(x) = x^2 - 7x + 5

, find

f(-1)

Answer this when you sit the paper.

Question 1302

[2 marks]Quadratic Equations

f(x) = x^2 - 7x + 5

, find the values of

x

for which

f(x) = -7

Answer this when you sit the paper.

Question 1401

[1 marks]Probability

A bag contains red, blue and green counters all of which are identical except for colour. A counter is picked at random from the bag, its colour is noted and then it is replaced. The probability that it is red is 0,2 and the probability that it is blue is 0,5. Calculate the probability that the counter picked is either blue or green.

Answer this when you sit the paper.

Question 1402

[2 marks]Probability

A bag contains red, blue and green counters. The probability that a counter picked at random is red is 0,2 and the probability that it is blue is 0,5. Two counters are picked at random one after the other, with replacement. Calculate the probability that one is red and the other is blue.

Answer this when you sit the paper.

Question 1501

[1 marks]Factorisation, H.C.F and L.C.M

Factorise

x^2 - y^2

Answer this when you sit the paper.

Question 1502

[1 marks]Simultaneous Equations

Given that

x - y = 4

and

x^2 - y^2 = 20

, find the value of

x

Answer this when you sit the paper.

Question 1503

[3 marks]Simultaneous Equations

Given that

x - y = 4

and

x^2 - y^2 = 20

, find the value of

y

Answer this when you sit the paper.

Question 1601

[2 marks]Measures and Mensuration

The diagram shows an isosceles triangle ABC with AB = AC, BC = 24 cm and AD perpendicular to BC. Given that the area of the triangle is

108\ \text{cm}^2

, find AD.

Answer this when you sit the paper.

Question 1602

[2 marks]Measures and Mensuration

The diagram shows an isosceles triangle ABC with AB = AC, BC = 24 cm and AD perpendicular to BC. Given that the area of the triangle is

108\ \text{cm}^2

, find AC.

Answer this when you sit the paper.

Question 1701

[2 marks]Measures and Mensuration

The diagram shows a cross-section of a swimming pool which is 25 m long, 1 m deep at the shallow end and 2 m deep at the deep end. Calculate the area of the cross-section in

\text{m}^2

Answer this when you sit the paper.

Question 1702

[2 marks]Measures and Mensuration

A swimming pool is 25 m long, 1 m deep at the shallow end and 2 m deep at the deep end, so that its cross-section is a trapezium of area

37{,}5\ \text{m}^2

. Given that the swimming pool is 10 m wide, calculate the volume of the pool in

\text{m}^3

Answer this when you sit the paper.

Question 1801

[2 marks]Logarithms

Given that

\log_5 2 = 0{,}431

and

\log_5 3 = 0{,}683

, find the value of

\log_5 1\tfrac{1}{2}

Answer this when you sit the paper.

Question 1802

[2 marks]Logarithms

Given that

\log_5 2 = 0{,}431

and

\log_5 3 = 0{,}683

, find the value of

\log_5 \sqrt{3}

Answer this when you sit the paper.

Question 1901

[1 marks]Vector Geometry

It is given that

\overrightarrow{AB} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}

and

\overrightarrow{BC} = \begin{pmatrix} -8 \\ 6 \end{pmatrix}

. Find

\overrightarrow{AC}

, writing it as a column vector.

Answer this when you sit the paper.

Question 1902

[1 marks]Vector Geometry

It is given that

\overrightarrow{BC} = \begin{pmatrix} -8 \\ 6 \end{pmatrix}

. Find

\overrightarrow{CX}

, given that

2\overrightarrow{CX} = \overrightarrow{BC}

, writing it as a column vector.

Answer this when you sit the paper.

Question 1903

[2 marks]Vector Geometry

P is the point

(-3;\ 2)

and

\overrightarrow{PQ} = \begin{pmatrix} 3 \\ -5 \end{pmatrix}

. Find the coordinates of point Q.

Answer this when you sit the paper.

Question 2001

[1 marks]Sets

The Venn diagram shows the universal set

\xi

, set X and set Y. The letters

u

v

w

and

z

represent the numbers of elements in each subset, where

u

is in X only,

v

is in both X and Y,

w

is in Y only and

z

is in neither. It is given that

n(\xi) = 150

n(X) = 55

and

n(Y) = 32

. Find the smallest possible value of

z

Answer this when you sit the paper.

Question 2002

[1 marks]Sets

The Venn diagram shows the universal set

\xi

, set X and set Y, where

v

is the number of elements in both X and Y. It is given that

n(\xi) = 150

n(X) = 55

and

n(Y) = 32

. Find the largest possible value of

v

Answer this when you sit the paper.

Question 2003

[1 marks]Sets

The Venn diagram shows the universal set

\xi

, set X and set Y. The letters

u

v

w

and

z

represent the numbers of elements in each subset, where

u

is in X only,

v

is in both X and Y,

w

is in Y only and

z

is in neither. It is given that

n(\xi) = 150

n(X) = 55

and

n(Y) = 32

. Find the value of

w

u = 45

Answer this when you sit the paper.

Question 2101

[2 marks]Consumer Arithmetic

During a sale, a shop reduced all its prices by 20%. Calculate the original price of an article which was sold during the sale for $440 000.

Answer this when you sit the paper.

Question 2102

[2 marks]Consumer Arithmetic

On a particular day, a bank bought British pounds at a rate of 1 British pound to 35 000 Zimbabwean dollars and sold British pounds at a rate of $40 000 per pound. Calculate the amount, in British pounds, bought for $10 500 000.

Answer this when you sit the paper.

Question 2103

[1 marks]Consumer Arithmetic

On a particular day, a bank sold British pounds at a rate of $40 000 per pound. Calculate the amount, in Zimbabwean dollars, received for selling 112 British pounds.

Answer this when you sit the paper.

Question 2201

[2 marks]Travel Graphs

The diagram shows a velocity-time graph for a particular journey. The velocity rises steadily from 0 m/s at 0 s to 20 m/s at 30 s, stays at 20 m/s until 50 s and then falls steadily to 0 m/s at 60 s. Calculate the distance travelled in the first 30 seconds.

Answer this when you sit the paper.

Question 2202

[1 marks]Travel Graphs

Answer this when you sit the paper.

Question 2203

[2 marks]Travel Graphs

Answer this when you sit the paper.

Question 2301

[1 marks]Variation

x

is partly constant and partly varies as

y

. Express

x

in terms of

y

and constants

h

and

k

Answer this when you sit the paper.

Question 2302

[1 marks]Variation

x

is partly constant and partly varies as

y

, so that

x = h + ky

. Given that

x = 1

when

y = 8

and that

x = 3

when

y = 12

, calculate the value of

h

Answer this when you sit the paper.

Question 2303

[1 marks]Variation

x

is partly constant and partly varies as

y

, so that

x = h + ky

. Given that

x = 1

when

y = 8

and that

x = 3

when

y = 12

, calculate the value of

k

Answer this when you sit the paper.

Question 2304

[2 marks]Variation

x

is partly constant and partly varies as

y

, so that

x = h + ky

with

h = -3

and

k = \tfrac{1}{2}

. Find the value of

x

when

y = 30

Answer this when you sit the paper.

Question 2401

[1 marks]Statistics

The table shows the test results of a class of pupils. The test was marked out of 10.

Mark: 0 1 2 3 4 5 6 7 8 9 10
No of pupils who scored this mark: 0 1 3 7 9 5 2 2 1 2 0

Find the number of pupil, in the class.

Answer this when you sit the paper.

Question 2402

[1 marks]Statistics

The table shows the test results of a class of pupils. The test was marked out of 10.

Mark: 0 1 2 3 4 5 6 7 8 9 10
No of pupils who scored this mark: 0 1 3 7 9 5 2 2 1 2 0

Find the modal mark.

Answer this when you sit the paper.

Question 2403

[1 marks]Statistics

The table shows the test results of a class of pupils. The test was marked out of 10.

Mark: 0 1 2 3 4 5 6 7 8 9 10
No of pupils who scored this mark: 0 1 3 7 9 5 2 2 1 2 0

Find the range of marks scored by the pupils.

Answer this when you sit the paper.

Question 2404

[2 marks]Statistics

The table shows the test results of a class of pupils. The test was marked out of 10.

Mark: 0 1 2 3 4 5 6 7 8 9 10
No of pupils who scored this mark: 0 1 3 7 9 5 2 2 1 2 0

Calculate the percentage of pupils who scored less than 5 marks.

Answer this when you sit the paper.

Question 2501

[2 marks]Functional Graphs

The diagram shows the graph of the function

y = x^2 - 2x - 1

. Use the graph to find the roots of the equation

x^2 - 2x - 1 = 0

Answer this when you sit the paper.

Question 2502

[1 marks]Functional Graphs

The diagram shows the graph of the function

y = x^2 - 2x - 1

. Use the graph to find the minimum value of

x^2 - 2x - 1

Answer this when you sit the paper.

Question 2503

[1 marks]Functional Graphs

The diagram shows the graph of the function

y = x^2 - 2x - 1

. Use the graph to find the equation of the line of symmetry.

Answer this when you sit the paper.

Question 2504

[2 marks]Functional Graphs

The diagram shows the graph of the function

y = x^2 - 2x - 1

. Use the graph to find the area enclosed by the curve, the

x

-axis, the

y

-axis and the line

x = 2

, giving your answer in square units.

Answer this when you sit the paper.

Question 2601

[2 marks]Quadratic Equations

Solve the equation

(2x - 3)^2 = 9

Answer this when you sit the paper.

Question 2602

[2 marks]Co-ordinate Geometry

The line

3y + 5x = 15

cuts the

x

-axis at A and the

y

-axis at B. Write down the coordinates of A and the coordinates of B.

Answer this when you sit the paper.

Question 2603

[2 marks]Co-ordinate Geometry

In the diagram, line

m

passes through the points

(-4;\ 0)

and

(0; 4)

. Find the equation of line

m

Answer this when you sit the paper.

Question 2604

[2 marks]Inequalities and Linear Programming

In the diagram, line

m

has equation

y = x + 4

and the line

3y + 5x = 15

cuts the

x

-axis at A and the

y

-axis at B. The unshaded region R lies above the

x

-axis and below both lines. Write down two inequalities, other than

y \geq 0

, which define the region R.

Answer this when you sit the paper.

Mathematics Paper 1 November 2008

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 302

Question 303

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 702

Question 801

Question 802

Question 803

Question 901

Question 902

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 1503

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2303

Question 2304

Question 2401

Question 2402

Question 2403

Question 2404

Question 2501

Question 2502

Question 2503

Question 2504

Question 2601

Question 2602

Question 2603

Question 2604

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