ZIMSEC O Level Mathematics Paper 1 June 2009

Question 101

[1 marks]Ordinary and Standard Form

Express 97,85 in standard form. [1]

Answer this when you sit the paper.

Question 102

[1 marks]Fractions, Decimals and Percentages

Giving your answer as a decimal, evaluate

15,915 + 24,09

. [1]

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Question 103

[1 marks]Fractions, Decimals and Percentages

Giving your answer as a decimal, evaluate

85,34 \div 17

. [1]

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Question 201

[1 marks]Approximations and Estimations

Estimate

4,63 \times 33,6

correct to 1 significant figure. [1]

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Question 202

[2 marks]Measures and Mensuration

The perimeter of a square is 36 cm. Find the area of the square. [2]

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Question 301

[1 marks]Inequalities

Solve the inequality

5y - 5 < 10

. [1]

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Question 302

[2 marks]Algebra

Giving your answer in ascending powers of

x

, expand

(x + 2)^2

. [2]

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Question 401

[1 marks]Fractions, Decimals and Percentages

Find the product of

\dfrac{4}{13}

and

3,25

. [1]

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Question 402

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

Factorise completely

18x^2 + 15x + 3

. [2]

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Question 501

[2 marks]Polygons

The diagram shows part of a regular polygon of interior angle

156^\circ

. Find the number of sides of the polygon. [2]

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Question 502

[1 marks]Polygons, Symmetry and Circles

State the number of lines of symmetry of a regular decagon. [1]

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Question 601

[1 marks]Number Bases

Giving your answer in base 9, evaluate

785_9 + 306_9

. [1]

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Question 602

[1 marks]Time

Express 20,45 hours in hours and minutes. [1]

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Question 603

[1 marks]Approximations and Estimations

Express 0,0256 to one significant figure. [1]

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Question 701

[1 marks]Time

Express 22 35 as time on the 12-hour clock. [1]

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Question 702

[2 marks]Speed, distance and time

Chipo takes 35 minutes to walk to school which is

3\frac{1}{2}

km away from her home. Calculate her average speed in km/h. [2]

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Question 801

[3 marks]Consumer Arithmetic

A man was awarded a 15% salary increase. If his previous salary was $5 240, calculate his new salary. [3]

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Question 901

[3 marks]Statistics

The mean age of a father and his 4 children is 18 years. The mean age of the four children is 12 years. Calculate the father's age. [3]

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Question 1001

[1 marks]Similarity and Congruency

Two similar cones have their curved surface areas in the ratio 4 : 9. Write down the ratio of the height of the smaller cone to the height of the larger cone. [1]

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Question 1002

[2 marks]Similarity and Congruency

Two similar cones have their curved surface areas in the ratio 4 : 9. Given that the volume of the smaller cone is 40 cm

^3

, calculate the volume of the larger cone. [2]

Answer this when you sit the paper.

Question 1101

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

Write down the next two numbers in the sequence

27;\ 9;\ 3;\ 1;\ \frac{1}{3};\ \_\_\_;\ \_\_\_;\ \dots

[2]

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Question 1102

[1 marks]Change of Units

Express

2,6\ \text{m}^2

in cm

^2

. [1]

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Question 1201

[1 marks]Circle Geometry

In the triangle XYZ in the diagram,

X\hat{Z}Y = 53^\circ

V\hat{W}Z = 75^\circ

X\hat{Y}V = 26^\circ

and XY is parallel to VW. Find

W\hat{V}Y

. [1]

Answer this when you sit the paper.

Question 1202

[1 marks]Circle Geometry

In the triangle XYZ in the diagram,

X\hat{Z}Y = 53^\circ

V\hat{W}Z = 75^\circ

X\hat{Y}V = 26^\circ

and XY is parallel to VW. Find

V\hat{Y}W

. [1]

Answer this when you sit the paper.

Question 1203

[1 marks]Circle Geometry

In the triangle XYZ in the diagram,

X\hat{Z}Y = 53^\circ

V\hat{W}Z = 75^\circ

X\hat{Y}V = 26^\circ

and XY is parallel to VW. Find

X\hat{V}Y

. [1]

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Question 1301

[2 marks]Matrices

Write down the 2 by 2 identity matrix for multiplication. [2]

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Question 1302

[2 marks]Matrices

It is given that

3\begin{pmatrix} p & 10 \\ 8 & 16 \end{pmatrix} - \begin{pmatrix} -4 & 14 \\ 0 & 4 \end{pmatrix} = 2\begin{pmatrix} -10 & 8 \\ 12 & q \end{pmatrix}

. Find the value of

p

and the value of

q

. [2]

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Question 1401

[1 marks]Laws of Indices

Evaluate

9^2 \times 9^0

. [1]

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Question 1402

[1 marks]Laws of Indices

Evaluate

8^{\frac{1}{3}}

. [1]

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Question 1403

[2 marks]Laws of Indices

Solve the equation

4^x = 32

. [2]

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Question 1501

[1 marks]Number

The array below represents a magic square, in which the sum of the numbers horizontally, vertically or diagonally is the magic number.

$\begin{array}{|c|c|c|c|} \hline 13 & 8 & 12 & 1 \\ \hline 3 & 10 & 6 & 15 \\ \hline 2 & A & 7 & 14 \\ \hline 16 & 5 & 9 & 4 \\ \hline \end{array}$

Write down the magic number. [1]

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Question 1502

[1 marks]Number

The array below represents a magic square, in which the sum of the numbers horizontally, vertically or diagonally is the magic number.

$\begin{array}{|c|c|c|c|} \hline 13 & 8 & 12 & 1 \\ \hline 3 & 10 & 6 & 15 \\ \hline 2 & A & 7 & 14 \\ \hline 16 & 5 & 9 & 4 \\ \hline \end{array}$

Write down the value of A. [1]

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Question 1503

[2 marks]Probability

A number is chosen at random from the magic square below, in which A = 11.

$\begin{array}{|c|c|c|c|} \hline 13 & 8 & 12 & 1 \\ \hline 3 & 10 & 6 & 15 \\ \hline 2 & A & 7 & 14 \\ \hline 16 & 5 & 9 & 4 \\ \hline \end{array}$

Write down the probability that it is a perfect cube. [2]

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Question 1601

[2 marks]Fractions, Decimals and Percentages

The figure in the diagram is made up of squares of equal size. Find the percentage of the figure which is shaded. [2]

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Question 1602

[1 marks]Logarithms

Given that

\log M = -5

and

\log N = 2

, find the value of

\log MN

. [1]

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Question 1603

[1 marks]Logarithms

Given that

\log M = -5

and

\log N = 2

, find the value of

\log M^{-\frac{1}{2}}

. [1]

Answer this when you sit the paper.

Question 1701

[2 marks]Measures and Mensuration

A plot whose area is 60 000 m

^2

is divided into residential stands each of area 950 m

^2

. Find the number of stands obtained. [2]

Answer this when you sit the paper.

Question 1702

[2 marks]Measures and Mensuration

A plot whose area is 60 000 m

^2

is divided into residential stands each of area 950 m

^2

. Find the area of the plot left over. [2]

Answer this when you sit the paper.

Question 1801

[2 marks]Trigonometry, Bearing & Distances

Find the angle through which one turns from

027^\circ

to S

82^\circ

W in an anticlockwise direction. [2]

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Question 1802

[2 marks]Change of Units

A lorry is loaded with 608 boxes each of mass 42 kg. Calculate the mass of the load in tonnes correct to two decimal places. [2]

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Question 1901

[1 marks]Similarity and Congruency

\triangle

KLM is such that KL = MK = 8 cm and

L\hat{K}M = 40^\circ

. Its line of symmetry is drawn from K to meet LM at T. Write down two triangles which are congruent. [1]

Answer this when you sit the paper.

Question 2001

[1 marks]Travel Graphs

The diagram shows the velocity-time graph of a body which accelerates uniformly from rest to 16 m/s in 8 seconds, travels at constant velocity for a further 8 seconds and finally retards uniformly to rest in 4 seconds. Calculate the acceleration during the first 8 seconds. [1]

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Question 2002

[1 marks]Travel Graphs

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Question 2003

[2 marks]Travel Graphs

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Question 2101

[2 marks]Sets

Given that

\xi = \{x : x

is an integer and

30 \le x \le 85\}

and

P = \{x : x

is a multiple of

9\}

, list the members of P. [2]

Answer this when you sit the paper.

Question 2102

[1 marks]Sets

Given that

\xi = \{x : x

is an integer and

30 \le x \le 85\}

P = \{x : x

is a multiple of

9\}

and

Q = \{x : x

is a perfect square

\}

, list the members of

P \cap Q

. [1]

Answer this when you sit the paper.

Question 2103

[1 marks]Sets

Given that

\xi = \{x : x

is an integer and

30 \le x \le 85\}

, find

n(\xi)

. [1]

Answer this when you sit the paper.

Question 2104

[1 marks]Sets

Given that

\xi = \{x : x

is an integer and

30 \le x \le 85\}

Q = \{x : x

is a perfect square

\}

and

R = \{35; 45; 55; 65; 75; 85\}

, find

n(Q \cap R)

. [1]

Answer this when you sit the paper.

Question 2201

[2 marks]Algebraic Fractions

Express

\dfrac{3}{b+1} - \dfrac{2}{b-2}

as a single fraction in its simplest form. [2]

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Question 2202

[3 marks]Linear Equations

Solve the equation

\dfrac{2-x}{15} = \dfrac{2}{3} + \dfrac{x}{5}

. [3]

Answer this when you sit the paper.

Question 2301

[1 marks]Circle Geometry

In the diagram, ABC is a semi-circle, OA, OB and OC are radii, AC = 14 cm and

B\hat{A}O = 27^\circ

. Find

B\hat{O}C

. [1]

Answer this when you sit the paper.

Question 2302

[4 marks]Measures and Mensuration

In the diagram, ABC is a semi-circle, OA, OB and OC are radii, AC = 14 cm and $B\hat{A}O = 27^\circ$ , so that $B\hat{O}C = 54^\circ$ . Taking $\pi$ to be $\frac{22}{7}$ and using as much of the information below as is necessary, calculate the shaded area, which is the region between the chord BC and the arc BC. [4]

$\begin{array}{lll} \sin 27^\circ = 0,45 & \cos 27^\circ = 0,89 & \tan 27^\circ = 0,51 \\ \sin 54^\circ = 0,80 & \cos 54^\circ = 0,59 & \tan 54^\circ = 1,4 \end{array}$

Answer this when you sit the paper.

Question 2401

[2 marks]Variation

It is given that

y^2 \propto x

and that

y = 15

when

x = 25

. Find

x

when

y = 12

. [2]

Answer this when you sit the paper.

Question 2402

[3 marks]Variation

It is given that

y^2 \propto x

and that

y = 15

when

x = 25

. Find

y

when

x = 4

. [3]

Answer this when you sit the paper.

Question 2501

[2 marks]Quadratic Equations

The straight line

y = 2x

intersects with the curve

y = x^2 - 3

at two points, and the resulting equation reduces to

x^2 - 2x - 3 = 0

. Solve the equation

x^2 - 2x - 3 = 0

. [2]

Answer this when you sit the paper.

Question 2502

[2 marks]Co-ordinate Geometry

The straight line

y = 2x

intersects with the curve

y = x^2 - 3

at the two points whose

x

values satisfy

x^2 - 2x - 3 = 0

, that is

x = 3

and

x = -1

. Find the coordinates of the two points of intersection. [2]

Answer this when you sit the paper.

Question 2601

[1 marks]Trigonometry, Bearing & Distances

In the diagram, ADC is a straight line, AB = 6 cm, BC = 8 cm, $D\hat{B}C = 90^\circ$ and $A\hat{C}B = A\hat{B}D = 23^\circ$ . Using as much of the information below as is necessary, calculate BD. [1]

$\begin{array}{lll} \sin 23^\circ = 0,39 & \cos 23^\circ = 0,92 & \tan 23^\circ = 0,42 \\ \sin 67^\circ = 0,92 & \cos 67^\circ = 0,39 & \tan 67^\circ = 2.36 \end{array}$

Answer this when you sit the paper.

Question 2602

[2 marks]Trigonometry, Bearing & Distances

In the diagram, ADC is a straight line, AB = 6 cm, BC = 8 cm, $D\hat{B}C = 90^\circ$ and $A\hat{C}B = A\hat{B}D = 23^\circ$ . Using as much of the information below as is necessary, calculate the area of $\triangle$ ABC. [2]

$\begin{array}{lll} \sin 23^\circ = 0,39 & \cos 23^\circ = 0,92 & \tan 23^\circ = 0,42 \\ \sin 67^\circ = 0,92 & \cos 67^\circ = 0,39 & \tan 67^\circ = 2.36 \end{array}$

Answer this when you sit the paper.

Question 2603

[3 marks]Trigonometry, Bearing & Distances

$\begin{array}{lll} \sin 23^\circ = 0,39 & \cos 23^\circ = 0,92 & \tan 23^\circ = 0,42 \\ \sin 67^\circ = 0,92 & \cos 67^\circ = 0,39 & \tan 67^\circ = 2.36 \end{array}$

Answer this when you sit the paper.

Mathematics Paper 1 June 2009

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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 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 702

Question 801

Question 901

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1401

Question 1402

Question 1403

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1801

Question 1802

Question 1901

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2104

Question 2201

Question 2202

Question 2301

Question 2302

Question 2401

Question 2402

Question 2501

Question 2502

Question 2601

Question 2602

Question 2603

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The answers, and why they are the answers

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