ZIMSEC O Level Mathematics Paper 1 June 2007

Question 101

[1 marks]Fractions, Decimals & Percentages

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

\frac{5}{8} - \frac{3}{5}

Answer this when you sit the paper.

Question 102

[1 marks]Fractions, Decimals & Percentages

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

\frac{6}{7} \div 2\frac{1}{7}

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Question 103

[1 marks]Fractions, Decimals & Percentages

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

\frac{3}{4} + \frac{1}{4} \times \frac{2}{3}

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Question 201

[1 marks]Fractions, Decimals & Percentages

Express 0,016 as a common fraction in its lowest terms.

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Question 202

[1 marks]Approximations & Estimations

Express 0,016 correct to 1 significant figure.

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Question 203

[1 marks]Ordinary & Standard Form

Express 0,016 in standard form.

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Question 301

[1 marks]Laws of Indices

Evaluate

0,05^2

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Question 302

[1 marks]Laws of Indices

Evaluate

\sqrt[3]{0,027}

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Question 303

[1 marks]Laws of Indices

Evaluate

4^{-1}

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Question 401

[1 marks]Measures & Mensuration

A window is in the shape of a semi-circle of radius 70 cm. Write down the length of the diameter, in centimetres.

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Question 402

[2 marks]Measures & Mensuration

A window is in the shape of a semi-circle of radius 70 cm. Calculate the perimeter of the window, in centimetres. Use

\pi = \frac{22}{7}

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Question 501

[1 marks]Number Bases

Express

4 \times 8^3 + 3 \times 8^2 + 5 \times 8

as a number in base 8.

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Question 502

[2 marks]Number Bases

Evaluate

431_5 - 244_5

, giving the answer in base 10.

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Question 601

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

Factorize completely

2\pi rh + 2\pi r^2

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Question 602

[2 marks]Algebraic Fractions

Express

\frac{4}{x + 5} - \frac{3}{x}

as a single fraction in its simplest form.

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Question 701

[3 marks]Simultaneous Equations

Solve the simultaneous equations

2x + 3y = 13

and

x + 2y = 8

Answer this when you sit the paper.

Question 801

[1 marks]Variation

M varies directly as the square of

d

and inversely as

q

. Write down an expression for M in terms of

d

q

and a constant

k

Answer this when you sit the paper.

Question 802

[2 marks]Variation

M varies directly as the square of

d

and inversely as

q

, so that

M = \frac{kd^2}{q}

. Find

k

, given that

M = 6

when

d = 4

and

q = 8

Answer this when you sit the paper.

Question 901

[1 marks]Sets

Given that

n(\xi) = 20

n(X) = 15

and

n(Y) = 8

, find

n(Y')

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Question 902

[1 marks]Sets

Given that

n(\xi) = 20

n(X) = 15

and

n(Y) = 8

, find the largest possible value of

n(X \cap Y)

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Question 903

[1 marks]Sets

Given that

n(\xi) = 20

n(X) = 15

and

n(Y) = 8

, find the smallest possible value of

n(X \cup Y)

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Question 1001

[2 marks]Co-ordinate Geometry

The straight line

l

cuts the

x

-axis at

(6; 0)

and the

y

-axis at

(0; -4)

. Find the equation of the line

l

Answer this when you sit the paper.

Question 1002

[1 marks]Co-ordinate Geometry

The straight line

l

cuts the

x

-axis at

(6; 0)

and the

y

-axis at

(0; -4)

. Find the equation of the line

m

, parallel to line

l

and passing through the origin.

Answer this when you sit the paper.

Question 1101

[1 marks]Points, Lines & Angles

In the diagram the straight line

l

cuts across two parallel lines AB and CD. Write down the special name given to line

l

with respect to the parallel lines.

Answer this when you sit the paper.

Question 1102

[1 marks]Points, Lines & Angles

In the diagram the straight line

l

cuts across two parallel lines AB and CD. Write down an equation in its simplest form, connecting

m

and

p

Answer this when you sit the paper.

Question 1103

[1 marks]Points, Lines & Angles

In the diagram the straight line

l

cuts across two parallel lines AB and CD. Write down an equation in its simplest form, connecting

n

and

p

Answer this when you sit the paper.

Question 1104

[1 marks]Points, Lines & Angles

In the diagram the straight line

l

cuts across two parallel lines AB and CD. Write down an equation in its simplest form, connecting

n

and

q

Answer this when you sit the paper.

Question 1201

[1 marks]Statistics

The table shows some scores and their corresponding frequencies.

Score ( $x$ ): 5, 15, 25, 35, 45
Frequency ( $y$ ): 5, 10, 8, 5, 2

Find the mode.

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Question 1202

[1 marks]Statistics

The table shows some scores and their corresponding frequencies.

Score ( $x$ ): 5, 15, 25, 35, 45
Frequency ( $y$ ): 5, 10, 8, 5, 2

Find the median.

Answer this when you sit the paper.

Question 1203

[2 marks]Statistics

The table shows some scores and their corresponding frequencies.

Score ( $x$ ): 5, 15, 25, 35, 45
Frequency ( $y$ ): 5, 10, 8, 5, 2

Find the mean.

Answer this when you sit the paper.

Question 1301

[1 marks]Geometrical Transformation

In the diagram, triangle T has vertices

(0; 1)

(2; 3)

and

(3; 1)

, and triangle

\text{T}_1

has vertices

(8; 4)

(10; 6)

and

(11; 4)

. Write down the column vector which translates triangle T onto triangle

\text{T}_1

Answer this when you sit the paper.

Question 1302

[3 marks]Geometrical Transformation

In the diagram, triangle T has vertices

(0; 1)

(2; 3)

and

(3; 1)

, and triangle

\text{T}_2

has vertices

(0; 1)

(2; -1)

and

(3; -5)

. Which single transformation maps triangle T onto triangle

\text{T}_2

AA shear with the $x$ -axis invariant and factor $-2$ .
BA stretch with the $y$ -axis invariant and factor $-2$ .
CA shear with the $y$ -axis invariant and factor $-2$ .
DA rotation through $90^\circ$ clockwise about the origin.

Question 1401

[2 marks]Functional Notation

Given that

f(x) = x^2 - 9

, find

f(7)

Answer this when you sit the paper.

Question 1402

[2 marks]Functional Notation

Given that

f(x) = x^2 - 9

, find the values of

x

for which

f(x) = 16

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Question 1501

[2 marks]Matrices

Given that

\mathbf{M} = \begin{pmatrix} 1 & -1 \\ -1 & 3 \end{pmatrix}

, find

\mathbf{M}^2

Answer this when you sit the paper.

Question 1502

[2 marks]Matrices

Given that

\mathbf{N} = \begin{pmatrix} 1 & -2 \\ x & 6 \end{pmatrix}

, find

x

, given that

\mathbf{N}

has no inverse.

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Question 1601

[2 marks]Substitution

The formula connecting

v

u

a

and

t

v = u + at

. Find

v

when

u = 50

a = -9,8

and

t = 3

Answer this when you sit the paper.

Question 1602

[2 marks]Change of Subject of Formula

The formula connecting

v

u

a

and

t

v = u + at

. Make

t

the subject of the formula.

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Question 1701

[2 marks]Polygons

ABCDE is a regular pentagon. Calculate the size of each interior angle of the pentagon, in degrees.

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Question 1702

[2 marks]Polygons

ABCDE is a regular pentagon. The sides AE and CD are produced to meet at X. Calculate the size of

E\hat{X}D

, in degrees.

Answer this when you sit the paper.

Question 1801

[2 marks]Consumer Arithmetic

The price of petrol was increased from \$2 700 per litre by 20%. The following year the new price was increased by a further 25%. Calculate the price per litre of petrol after the second increase, in dollars.

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Question 1802

[2 marks]Consumer Arithmetic

The price of petrol was increased from \$2 700 per litre by 20%. The following year the new price was increased by a further 25%, taking it to \$4 050 per litre. Calculate the overall percentage by which the original price was increased.

Answer this when you sit the paper.

Question 1901

[1 marks]Inequalities & Linear Programming

The lines

x = 8

and

x + y = 12

are drawn on the same grid. Write down the coordinates of the point where they meet.

Answer this when you sit the paper.

Question 2001

[2 marks]Probability

A cash tin has a simple combination lock with two dials. The first dial has the numbers 3, 5, 7 and 9 on it and the second dial has the numbers 4, 6 and 8. How many different combinations are possible?

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Question 2002

[1 marks]Probability

Answer this when you sit the paper.

Question 2003

[1 marks]Probability

A cash tin has a simple combination lock with two dials. The first dial has the numbers 3, 5, 7 and 9 on it and the second dial has the numbers 4, 6 and 8. Only one combination will open the tin, and the sum of the digits of the correct combination is 13. If one combination with digits adding up to 13 is tried, find the probability that is will open the tin.

Answer this when you sit the paper.

Question 2101

[1 marks]Trigonometry, Bearing & Distances

Villages A and C are equidistant from village B. The bearing of B from A is

050^\circ

and the bearing of C from B is

130^\circ

. Write down the three-figure bearing of C from A.

Answer this when you sit the paper.

Question 2102

[1 marks]Trigonometry, Bearing & Distances

Villages A and C are equidistant from village B. The bearing of B from A is

050^\circ

and the bearing of C from B is

130^\circ

. Write down the special name of triangle ABC.

Answer this when you sit the paper.

Question 2201

[1 marks]Laws of Indices

Find the value of

k

when

\left(\sqrt{x}\right)^k = x

Answer this when you sit the paper.

Question 2202

[2 marks]Laws of Indices

Evaluate

9^{\frac{1}{2}} \times 9^{-\frac{3}{2}}

Answer this when you sit the paper.

Question 2203

[2 marks]Quadratic Equations

Solve the equation

2y^2 + 3y - 5 = 0

Answer this when you sit the paper.

Question 2301

[1 marks]Vectors

X, Y and Z are three points on a Cartesian plane whose position vectors are

\mathbf{x} = \binom{-3}{-6}

\mathbf{y} = \binom{-5}{12}

and

\mathbf{z} = \binom{11}{4}

respectively. Find

\mathbf{y} + \mathbf{x}

as a column vector.

Answer this when you sit the paper.

Question 2302

[2 marks]Vectors

Y is a point on a Cartesian plane whose position vector is

\mathbf{y} = \binom{-5}{12}

. Find

|\mathbf{y}|

Answer this when you sit the paper.

Question 2303

[2 marks]Vectors

X and Z are points on a Cartesian plane whose position vectors are

\mathbf{x} = \binom{-3}{-6}

and

\mathbf{z} = \binom{11}{4}

. Find

\overrightarrow{\text{XZ}}

as a column vector.

Answer this when you sit the paper.

Question 2401

[3 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is equilateral with AB = 40 cm and a height of

h

cm, and DCB is a straight line. Given that

\sqrt{3} = 1,73

, find the value of

h

as a decimal.

Answer this when you sit the paper.

Question 2402

[1 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is equilateral and DCB is a straight line. Given that

\sqrt{3} = 1,73

, write down as a decimal the value of

\sin A\hat{C}D

Answer this when you sit the paper.

Question 2403

[1 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is equilateral and DCB is a straight line. Write down as a decimal the value of

\cos A\hat{C}D

Answer this when you sit the paper.

Question 2601

[2 marks]Logarithms

Given that

\log 2 = 0,30

and

\log 9 = 0,95

, find

\log 3

Answer this when you sit the paper.

Question 2602

[2 marks]Logarithms

Given that

\log 2 = 0,30

and

\log 9 = 0,95

, find

\log 18

Answer this when you sit the paper.

Question 2603

[2 marks]Logarithms

Given that

\log 2 = 0,30

and

\log 9 = 0,95

, find

\log 4,5

Answer this when you sit the paper.

Mathematics Paper 1 June 2007

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 303

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 801

Question 802

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1101

Question 1102

Question 1103

Question 1104

Question 1201

Question 1202

Question 1203

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 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2601

Question 2602

Question 2603

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