ZIMSEC O Level Mathematics Paper 1 June 2014

Question 101

[1 marks]Approximations & Estimations

Express 2046,489 correct to the nearest ten.

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Question 102

[1 marks]Approximations & Estimations

Express 2046,489 correct to 2 decimal places.

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Question 103

[1 marks]Approximations & Estimations

Express 2046,489 correct to 2 significant figures.

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Question 201

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{3}{5} + \frac{1}{7}

, giving your answer as a common fraction in its lowest terms.

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Question 202

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{5}{8} \times \frac{32}{45}

, giving your answer as a common fraction in its lowest terms.

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Question 203

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{5}{24} \div \frac{1}{3}

, giving your answer as a common fraction in its lowest terms.

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Question 301

[1 marks]Fractions, Decimals & Percentages

Giving your answer as a decimal, find the exact value of

0,175 - 0,049

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Question 302

[1 marks]Fractions, Decimals & Percentages

Giving your answer as a decimal, find the exact value of

\sqrt{0,0144}

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Question 303

[1 marks]Fractions, Decimals & Percentages

Giving your answer as a decimal, find the exact value of

(0,06)^2

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Question 401

[2 marks]Algebraic Expressions

Expand

(2a - b)(1 + c)

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Question 402

[1 marks]Algebraic Fractions

Simplify

\dfrac{m^2 - mn}{n^2 - np} \div \dfrac{m}{(n - p)}

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Question 501

[1 marks]Sets

It is given that

\xi = \{30; 31; 32; 33; 34; 35; 36; 37; 38; 39\}

, A is the set of odd numbers and B is the set of prime numbers. List the elements of A.

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Question 502

[1 marks]Sets

It is given that

\xi = \{30; 31; 32; 33; 34; 35; 36; 37; 38; 39\}

, A is the set of odd numbers and B is the set of prime numbers. List the elements of

B^1

(the complement of B).

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Question 503

[1 marks]Sets

It is given that

\xi = \{30; 31; 32; 33; 34; 35; 36; 37; 38; 39\}

, A is the set of odd numbers and B is the set of prime numbers. Find

n(A \cap B^1)

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Question 601

[1 marks]Symmetry

State the special type of a triangle which has one line of symmetry.

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Question 602

[2 marks]Polygons, Symmetry & Circles

A polygon has

n

sides. Two of its exterior angles are

55^\circ

and

45^\circ

. The remaining

(n - 2)

exterior angles are each

20^\circ

. Calculate the value of

n

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Question 701

[1 marks]Time

Express 9 minutes after midnight as time on the 24 hour clock.

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Question 702

[2 marks]Fractions, Decimals & Percentages

In 1998 the population of a village was

2,8 \times 10^2

. In 2004, the population was

3,5 \times 10^2

. Calculate the percentage increase of the population from 1998 to 2004.

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Question 801

[3 marks]Simultaneous Equations

Solve the simultaneous equations

\frac{1}{3}x = y

and

2x + y = -7

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Question 901

[1 marks]Functional Notation

Given that

f(x) = (x - 1)(x + 6)

and that

f(0) = p

, find the value of

p

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Question 902

[2 marks]Change of Subject of Formula

yk = ax - bk

, make

k

the subject of the formula.

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Question 1001

[1 marks]Number Bases

Express

3^4 + 3^2 + 3

as a number in base 3.

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Question 1002

[1 marks]Number Bases

Evaluate

143_8 + 57_8

, giving your answer in base 8.

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Question 1003

[1 marks]Number Bases

Evaluate

4_5 - 2_3 + 1_2

, giving your answer in base 10.

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Question 1101

[1 marks]Circle Geometry

In the diagram, ABCD is a circle. Tangents at C and D meet at E and ED is produced to F such that

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

and

A\hat{B}C = 116^\circ

. Calculate

A\hat{D}C

Answer this when you sit the paper.

Question 1102

[1 marks]Circle Geometry

In the diagram, ABCD is a circle. Tangents at C and D meet at E and ED is produced to F such that

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

and

A\hat{B}C = 116^\circ

. Calculate

C\hat{D}E

Answer this when you sit the paper.

Question 1103

[1 marks]Circle Geometry

In the diagram, ABCD is a circle. Tangents at C and D meet at E and ED is produced to F such that

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

and

A\hat{B}C = 116^\circ

. Calculate

C\hat{E}D

Answer this when you sit the paper.

Question 1201

[1 marks]Inequalities

The cost of making a telephone call on Teneco is 25 cents per minute. Kuda has

p

cents and is able to make a call. Xolani has

q

cents which is insufficient to make a call. Write down an inequality in

p

, other than

p > 0

, that satisfies the given conditions.

Answer this when you sit the paper.

Question 1202

[1 marks]Inequalities

The cost of making a telephone call on Teneco is 25 cents per minute. Kuda has

p

cents and is able to make a call. Xolani has

q

cents which is insufficient to make a call. Write down an inequality in

q

, other than

q > 0

, that satisfies the given conditions.

Answer this when you sit the paper.

Question 1203

[1 marks]Inequalities

The cost of making a telephone call on Teneco is 25 cents per minute. Kuda has

p

cents and is able to make a call. Xolani has

q

cents which is insufficient to make a call. Write down an inequality relating

p

and

q

that satisfies the given conditions.

Answer this when you sit the paper.

Question 1301

[1 marks]Co-ordinate Geometry

AB is a line whose equation is

6y = 7x + 48

. Find the gradient of line AB.

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Question 1302

[2 marks]Co-ordinate Geometry

AB is a line whose equation is

6y = 7x + 48

. Find the equation of the line parallel to AB which passes through the point

(3; 1)

, giving your equation in the form

ay + bx + c = 0

Answer this when you sit the paper.

Question 1401

[1 marks]Ratios, Rates & Proportions

Given that

4m = 7n

, find the ratio

m : n

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Question 1402

[2 marks]Consumer Arithmetic

A holiday trip to South Africa cost R333. If the exchange rate was US$1 to R8, calculate the cost of the trip in US$, giving your answer to the nearest cent.

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Question 1501

[3 marks]Factorisation

Factorise completely

3x^3y - 12xy^3

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Question 1601

[3 marks]Quadratic Equations

Solve the equation

\left(y + \frac{1}{4}\right)^2 = \frac{9}{16}

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Question 1701

[2 marks]Laws of Indices

Simplify

\left(32x^{10}\right)^{\frac{1}{5}}

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Question 1702

[2 marks]Laws of Indices

Given that

\dfrac{2^{-2} \times 2^c}{2^4} = 2^3

, find the value of

c

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Question 1801

[2 marks]Matrices

It is given that

\mathbf{P} = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}

and

\mathbf{Q} = 2\mathbf{P} - \mathbf{I}

where

\mathbf{I}

is the identity matrix. Find

\mathbf{P}^{-1}

Answer this when you sit the paper.

Question 1802

[2 marks]Matrices

It is given that

\mathbf{P} = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}

and

\mathbf{Q} = 2\mathbf{P} - \mathbf{I}

where

\mathbf{I}

is the identity matrix. Find

\mathbf{Q}

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Question 1901

[1 marks]Vectors

In the diagram, OABCDE is a hexagon drawn on a grid, with O at the origin, A at

(-2; 1)

, B at

(0; 4)

, C at

(2; 5)

, D at

(3; 3)

and E at

(2; 1)

. Express

\overrightarrow{OE}

as a column vector.

Answer this when you sit the paper.

Question 1902

[1 marks]Vectors

In the diagram, OABCDE is a hexagon drawn on a grid, with O at the origin, A at

(-2; 1)

, B at

(0; 4)

, C at

(2; 5)

, D at

(3; 3)

and E at

(2; 1)

. Express

\overrightarrow{OA} + \overrightarrow{AD}

as a column vector.

Answer this when you sit the paper.

Question 1903

[2 marks]Vectors

In the diagram, OABCDE is a hexagon drawn on a grid, with O at the origin, A at

(-2; 1)

, B at

(0; 4)

, C at

(2; 5)

, D at

(3; 3)

and E at

(2; 1)

. Describe fully the single transformation which maps side BC onto side OE.

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Question 2001

[1 marks]Scales & Simple Map Problems

All lengths on a map are

\frac{1}{500}

of their actual lengths. Calculate the actual length of a line represented on the map by a line 7,3 cm.

Answer this when you sit the paper.

Question 2002

[3 marks]Scales & Simple Map Problems

All lengths on a map are

\frac{1}{500}

of their actual lengths. Calculate the area on the map which represents an actual area of 525

\text{m}^2

, giving your answer in

\text{cm}^2

Answer this when you sit the paper.

Question 2101

[2 marks]Logarithms

Evaluate

\dfrac{\log_5 64}{\log_5 4}

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Question 2102

[2 marks]Logarithms

Evaluate

1 + \log_3 9

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Question 2201

[1 marks]Constructions and Loci

AB is a line segment 7 cm long.

P_1

and

P_2

are the two points which are 3 cm from B and 2 cm from line AB, on the same side of AB. Find the distance

P_1P_2

, in centimetres.

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Question 2301

[2 marks]Trigonometry, Bearing & Distances

P and Q are points on level ground. The bearing of P from Q is

237^\circ

. Find the bearing of Q from P.

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Question 2302

[3 marks]Measures & Mensuration

The diagram shows two semi circles APM and AQB, where M is the midpoint of AB and AM = MB = 3,5 cm. The shaded region is the part of semi circle AQB that lies outside semi circle APM. Taking

\pi

to be

\frac{22}{7}

, calculate the perimeter of the shaded region, in centimetres.

Answer this when you sit the paper.

Question 2401

[2 marks]Probability

The ages of pupils in a class of 30 are: age 11, 3 pupils; age 12, 10 pupils; age 13, 8 pupils; age 14, 6 pupils; age 15, 3 pupils. Two pupils are chosen at random from the class. Find the probability that one is aged 11 years and the other is aged 14.

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Question 2402

[3 marks]Statistics

The ages of pupils in a class of 30 are: age 11, 3 pupils; age 12, 10 pupils; age 13, 8 pupils; age 14, 6 pupils; age 15, 3 pupils. Calculate the mean age of the pupils.

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Question 2501

[1 marks]Similarity & Congruency

In the diagram, PQ is parallel to RS. PS and QR intersect at X. It is given that PX = 2 cm, SX = 3 cm, QX =

(y + 2)

cm and RX =

(2y - 1)

cm. Name the triangle which is similar to triangle PQX.

Answer this when you sit the paper.

Question 2502

[3 marks]Similarity & Congruency

In the diagram, PQ is parallel to RS. PS and QR intersect at X. It is given that PX = 2 cm, SX = 3 cm, QX =

(y + 2)

cm and RX =

(2y - 1)

cm. Find the value of

y

Answer this when you sit the paper.

Question 2503

[1 marks]Similarity & Congruency

In the diagram, PQ is parallel to RS. PS and QR intersect at X. It is given that PX = 2 cm, SX = 3 cm, QX =

(y + 2)

cm and RX =

(2y - 1)

cm. Given that

y = 8

, write down the length of QR, in centimetres.

Answer this when you sit the paper.

Question 2601

[1 marks]Travel Graphs

The velocity-time graph shows an object which accelerated uniformly for 10 seconds. During this time the velocity, V m/s, at time t seconds from the start, was given by

V = 6 + 2t

. It then decelerated uniformly to rest in a further 12 seconds. Calculate the velocity of the object when

t = 0

Answer this when you sit the paper.

Question 2602

[2 marks]Travel Graphs

The velocity-time graph shows an object which accelerated uniformly for 10 seconds. During this time the velocity, V m/s, at time t seconds from the start, was given by

V = 6 + 2t

. It then decelerated uniformly to rest in a further 12 seconds. Calculate the deceleration of the object.

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Question 2603

[2 marks]Travel Graphs

The velocity-time graph shows an object which accelerated uniformly for 10 seconds. During this time the velocity, V m/s, at time t seconds from the start, was given by

V = 6 + 2t

. It then decelerated uniformly to rest in a further 12 seconds. Calculate the distance covered by the object in the 22 seconds.

Answer this when you sit the paper.

Question 2604

[1 marks]Travel Graphs

The velocity-time graph shows an object which accelerated uniformly for 10 seconds. During this time the velocity, V m/s, at time t seconds from the start, was given by

V = 6 + 2t

. It then decelerated uniformly to rest in a further 12 seconds. Calculate the average speed of the object for the whole journey.

Answer this when you sit the paper.

Question 2701

[4 marks]Trigonometry, Bearing & Distances

In the diagram, ABC is a triangle in which AB =

x

cm, AC =

2x

cm, BC = 14 cm and

B\hat{A}C = 120^\circ

. [

\sin 60^\circ = 0,87

;

\cos 60^\circ = 0,5

;

\tan 60^\circ = 1,73

] Calculate the value of

x

, leaving your answer in surd form.

Answer this when you sit the paper.

Question 2702

[2 marks]Trigonometry, Bearing & Distances

In the diagram, ABC is a triangle in which AB =

x

cm, AC =

2x

cm, BC = 14 cm and

B\hat{A}C = 120^\circ

. [

\sin 60^\circ = 0,87

;

\cos 60^\circ = 0,5

;

\tan 60^\circ = 1,73

] Calculate the area of triangle ABC, in

\text{cm}^2

Answer this when you sit the paper.

Mathematics Paper 1 June 2014

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 503

Question 601

Question 602

Question 701

Question 702

Question 801

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1101

Question 1102

Question 1103

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1401

Question 1402

Question 1501

Question 1601

Question 1701

Question 1702

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2101

Question 2102

Question 2201

Question 2301

Question 2302

Question 2401

Question 2402

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

Question 2603

Question 2604

Question 2701

Question 2702

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