ZIMSEC O Level Mathematics Paper 1 June 2017

Question 101

[1 marks]Approximations & Estimations

Express

68,975

to the nearest ten.

Answer this when you sit the paper.

Question 102

[1 marks]Approximations & Estimations

Express

68,975

to the nearest tenth.

Answer this when you sit the paper.

Question 103

[1 marks]Approximations & Estimations

Express

68,975

to one significant figure.

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Question 201

[1 marks]Fractions, Decimals & Percentages

Find the exact value of

0,04 \times 0,3

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Question 202

[1 marks]Fractions, Decimals & Percentages

Find the exact value of

1,44 \div 0,09

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Question 203

[1 marks]Fractions, Decimals & Percentages

Find the exact value of

0,89 - 1,72

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Question 301

[1 marks]Laws of Indices

Evaluate

2^{1,6} \times 2^{0,4}

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Question 302

[2 marks]Laws of Indices

Evaluate

\left(\frac{12}{27}\right)^{-\frac{1}{2}}

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Question 401

[3 marks]Quadratic Equations

Solve the equation

x(x - 3) - x + 3 = 0

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Question 501

[1 marks]Time

Express 6 minutes to 8 at night as a time in 24-hour notation.

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Question 502

[2 marks]Time

Express

43,35

hours in hours and minutes.

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Question 601

[1 marks]Logarithms

Evaluate

\log_4 \frac{1}{4}

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Question 602

[2 marks]Logarithms

Evaluate

3\log 5 + 3\log 2 - 1

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Question 701

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

Write down the next two terms of the pattern

16; 8; 4; 2; \ldots; \ldots

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Question 702

[2 marks]Consumer Arithmetic

By selling an item for $529, a retailer makes a profit of 15%, on the cost price. Calculate the cost price.

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Question 801

[2 marks]Inequalities

Solve the inequality

3x + 7 < 2x + 9

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Question 901

[3 marks]Algebraic Fractions

Express

\frac{3a}{2a - b} + \frac{3b}{2b - 4a}

as a single fraction in its simplest form.

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Question 1001

[3 marks]Simultaneous Equations

Solve the simultaneous equations

x + \frac{1}{2}y = 1

and

3x - 4y = 14

Answer this when you sit the paper.

Question 1101

[1 marks]Fractions, Decimals & Percentages

Find

12\frac{1}{2}\%

64,8

kg.

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Question 1102

[2 marks]Matrices

The determinant of a matrix

\begin{pmatrix} a - 1 & 9 \\ 6 & 3 \end{pmatrix}

is 9. Find the value of

a

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Question 1201

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

Factorise completely

9 - 36x^2

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Question 1202

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

Factorise completely

a - bx + ax - b

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Question 1301

[1 marks]Polygons, Symmetry & Circles

State the order of rotational symmetry of a regular pentagon.

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Question 1302

[3 marks]Polygons, Symmetry & Circles

Three angles of a pentagon are

110^\circ

80^\circ

and

140^\circ

. The remaining two angles are such that one is twice the other. Find the size of each of the remaining two angles.

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Question 1401

[2 marks]Ordinary & Standard Form

It is given that

p = 3,6 \times 10^4

and

q = 9 \times 10^{-4}

. Find, giving the answer in standard form,

pq

Answer this when you sit the paper.

Question 1402

[2 marks]Ordinary & Standard Form

It is given that

p = 3,6 \times 10^4

and

q = 9 \times 10^{-4}

. Find, giving the answer in standard form,

\frac{p}{q}

Answer this when you sit the paper.

Question 1501

[2 marks]Change of Subject of Formula

It is given that

p = \pi w^2\left(r - \frac{w}{2}\right)

. Make

r

the subject of the formula.

Answer this when you sit the paper.

Question 1502

[2 marks]Change of Subject of Formula

It is given that

p = \pi w^2\left(r - \frac{w}{2}\right)

. Find

r

in terms of

\pi

when

w = 6

and

p = 72

Answer this when you sit the paper.

Question 1601

[2 marks]Fractions, Decimals & Percentages

Evaluate

\left(1\frac{1}{5} \div 3\frac{1}{5}\right) \times 2\frac{2}{3}

Answer this when you sit the paper.

Question 1602

[2 marks]Rational, Irrational Numbers & Surds

Simplify

2\sqrt{75} + 3\sqrt{75} - \sqrt{48}

, giving the answer in the form

a\sqrt{b}

, where

a

and

b

are integers.

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Question 1701

[2 marks]Measures & Mensuration

A solid cone has base radius of 7 cm and a perpendicular height of 24 cm. Find the slant height.

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Question 1702

[2 marks]Measures & Mensuration

A solid cone has base radius of 7 cm and a perpendicular height of 24 cm. Find the volume of the cone. (Volume of cone

= \frac{1}{3}\pi r^2 h

.) Take

\pi

to be

\frac{22}{7}

Answer this when you sit the paper.

Question 1801

[1 marks]Travel Graphs

The diagram shows the speed-time graph of a car which travelled 705 metres in 60 seconds. Calculate the acceleration during the first 10 seconds.

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Question 1802

[3 marks]Travel Graphs

The diagram shows the speed-time graph of a car which travelled 705 metres in 60 seconds. Find the time

T

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Question 1901

[1 marks]Circle Geometry

In the diagram, points A, B, C, D and E are on the circumference of a circle centre O. FAG is a tangent to the circle at A.

B\hat{A}G = 30^\circ

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

and

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

. Calculate

A\hat{E}C

Answer this when you sit the paper.

Question 1902

[1 marks]Circle Geometry

In the diagram, points A, B, C, D and E are on the circumference of a circle centre O. FAG is a tangent to the circle at A.

B\hat{A}G = 30^\circ

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

and

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

. Calculate

A\hat{B}C

Answer this when you sit the paper.

Question 1903

[1 marks]Circle Geometry

In the diagram, points A, B, C, D and E are on the circumference of a circle centre O. FAG is a tangent to the circle at A.

B\hat{A}G = 30^\circ

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

and

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

. Calculate

E\hat{A}F

Answer this when you sit the paper.

Question 1904

[1 marks]Circle Geometry

In the diagram, points A, B, C, D and E are on the circumference of a circle centre O. FAG is a tangent to the circle at A.

B\hat{A}G = 30^\circ

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

and

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

. Calculate

A\hat{C}E

Answer this when you sit the paper.

Question 2001

[1 marks]Trigonometry, Bearing & Distances

Three schools A, B and C are situated such that B is 9 km from A on a bearing of

060^\circ

and C is 8 km due east of B. Find the three-figure bearing of A from B.

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Question 2002

[3 marks]Trigonometry, Bearing & Distances

Three schools A, B and C are situated such that B is 9 km from A on a bearing of

060^\circ

and C is 8 km due east of B. Calculate the distance from A to C, leaving the answer in surd form. [Use as much of the information given below as is necessary.] (

\sin 30^\circ = 0,50

;

\cos 30^\circ = 0,87

;

\tan 30^\circ = 0,58

)

Answer this when you sit the paper.

Question 2102

[2 marks]Sets

It is given that the universal set,

\xi

, is a class of 46 pupils. B is the set of pupils who study Biology, C is the set of pupils who study Chemistry, 23 pupils study Biology, 32 pupils study Chemistry,

x

pupils study both Biology and Chemistry, 5 pupils study neither Biology nor Chemistry. Find

x

, the number of pupils who study both Biology and Chemistry.

Answer this when you sit the paper.

Question 2202

[2 marks]Probability

A bag contains 6 green (G) buttons and 3 white (W) buttons which are identical except for colour. Two buttons are picked at random from the bag one at a time without replacement. Find the probability of picking at least one white button.

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Question 2301

[2 marks]Measures & Mensuration

A farmer has a plot which measures 150 m by 140 m. The farmer wants to use chemicals to destroy weeds in the plot. For every 100

\text{m}^2

, 5 litres of chemicals are used. Calculate the quantity of the chemicals in litres, needed to destroy the weeds in the whole plot.

Answer this when you sit the paper.

Question 2302

[2 marks]Consumer Arithmetic

A farmer has a plot which measures 150 m by 140 m. The farmer wants to use chemicals to destroy weeds in the plot. For every 100

\text{m}^2

, 5 litres of chemicals are used. Five litres of the chemicals cost $8. Find the cost of the chemicals needed to destroy the weeds in the whole plot.

Answer this when you sit the paper.

Question 2401

[1 marks]Co-ordinate Geometry

In the diagram, the line

5y = 2x + 15

intersects with the

x

-axis at C and the

y

-axis at B. The line is also parallel to line

l

, which passes through the point

(0; -2)

. Find the coordinates of B.

Answer this when you sit the paper.

Question 2402

[1 marks]Co-ordinate Geometry

In the diagram, the line

5y = 2x + 15

intersects with the

x

-axis at C and the

y

-axis at B. The line is also parallel to line

l

, which passes through the point

(0; -2)

. Find the gradient of line

l

Answer this when you sit the paper.

Question 2403

[2 marks]Co-ordinate Geometry

In the diagram, the line

5y = 2x + 15

intersects with the

x

-axis at C and the

y

-axis at B. The line is also parallel to line

l

, which passes through the point

(0; -2)

. Write down the equation of line

l

in the form

y = mx + c

Answer this when you sit the paper.

Question 2501

[2 marks]Geometrical Transformation

In the diagram, triangles A, B and C are congruent. Describe fully the single transformation which maps triangle A onto triangle B.

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Question 2502

[3 marks]Geometrical Transformation

In the diagram, triangles A, B and C are congruent. Describe fully the single transformation which maps triangle B onto triangle C.

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Question 2601

[2 marks]Vector Geometry

It is given that O is the origin,

\overrightarrow{OX} = 2\mathbf{a} + 3\mathbf{b}

and

\overrightarrow{OY} = 3\mathbf{a} - 4\mathbf{b}

. Find

\overrightarrow{XY}

Answer this when you sit the paper.

Question 2602

[3 marks]Vector Geometry

It is given that O is the origin,

\overrightarrow{OX} = 2\mathbf{a} + 3\mathbf{b}

and

\overrightarrow{OY} = 3\mathbf{a} - 4\mathbf{b}

. Given also that

\overrightarrow{OX} = (1 - h)\mathbf{a} + k\mathbf{b}

, find the value of

h

and the value of

k

Answer this when you sit the paper.

Question 2701

[2 marks]Similarity & Congruency

In the diagram, ABC is a triangle in which DE is parallel to AC.

AD = 4

cm,

BD = 6

cm and

DE = 3

cm. Find AC.

Answer this when you sit the paper.

Question 2702

[3 marks]Similarity & Congruency

In the diagram, ABC is a triangle in which DE is parallel to AC.

AD = 4

cm,

BD = 6

cm and

DE = 3

cm. Find the area of ADEC, if the area of triangle BED is

3,6

\text{cm}^2

Answer this when you sit the paper.

Mathematics Paper 1 June 2017

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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 601

Question 602

Question 701

Question 702

Question 801

Question 901

Question 1001

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 1904

Question 2001

Question 2002

Question 2102

Question 2202

Question 2301

Question 2302

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2601

Question 2602

Question 2701

Question 2702

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