ZIMSEC O Level Mathematics Paper 1 June 2013

Question 101

[1 marks]Directed numbers

Subtract

-2

from 2.

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Question 102

[2 marks]Fractions, Decimals and Percentages

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

\frac{8}{15} \div \frac{2}{3}

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Question 201

[1 marks]Fractions, Decimals and Percentages

Express

3\frac{4}{5}

as a decimal number.

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Question 202

[2 marks]Fractions, Decimals and Percentages

Find the exact value of

\frac{0,83 + 8,368}{0,42}

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Question 301

[1 marks]Ordinary and Standard Form

Find

n

such that

0,0075 = 7,5 \times 10^{n}

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Question 302

[2 marks]Points, Lines and Angles

In the diagram ACE and BCD are straight lines intersecting at C.

C\hat{E}D = 90^\circ

C\hat{D}E = 60^\circ

and

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

. Calculate

A\hat{B}C

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Question 401

[1 marks]Number

Write down the square of 4.

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Question 402

[2 marks]Laws of Indices

Evaluate

125^{\frac{1}{3}} \times \sqrt{144}

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Question 501

[1 marks]Change of Units

Express

3\ \text{m}^2

\text{cm}^2

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Question 502

[2 marks]Change of Units

Express

32,5\ \text{m/s}

in km/h.

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Question 601

[1 marks]Quadrilaterals

In the diagram, ABCD is a quadrilateral in which AB is parallel to DC, AB = 12 cm, CD = 18 cm, BX = 7 cm and

B\hat{X}C = 90^\circ

. State the special name given to the quadrilateral ABCD.

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Question 602

[2 marks]Measures and Mensuration

In the diagram, ABCD is a quadrilateral in which AB is parallel to DC, AB = 12 cm, CD = 18 cm, BX = 7 cm and

B\hat{X}C = 90^\circ

. Calculate the area of the quadrilateral.

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Question 701

[3 marks]Algebraic Fractions

Simplify

\frac{x^2 + 7x + 6}{x^2 - 36}

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Question 801

[1 marks]Circle Geometry

In the diagram P, Q, R and S are points on the circumference of a circle and arcs QR and RS are equal. TP is a tangent to the circle at P,

T\hat{P}S = 70^\circ

and

R\hat{P}S = 30^\circ

. Calculate

Q\hat{P}R

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Question 802

[1 marks]Circle Geometry

In the diagram P, Q, R and S are points on the circumference of a circle and arcs QR and RS are equal. TP is a tangent to the circle at P,

T\hat{P}S = 70^\circ

and

R\hat{P}S = 30^\circ

. Calculate

P\hat{R}S

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Question 803

[1 marks]Circle Geometry

In the diagram P, Q, R and S are points on the circumference of a circle and arcs QR and RS are equal. TP is a tangent to the circle at P,

T\hat{P}S = 70^\circ

and

R\hat{P}S = 30^\circ

. Calculate

P\hat{Q}R

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Question 901

[1 marks]Variation

E varies directly as the square of

V

. Express E in terms of

V

and a constant

m

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Question 902

[2 marks]Variation

E varies directly as the square of

V

, so that

E = mV^2

. Given that

E = 3

when

V = 2

, find

m

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Question 1001

[1 marks]Laws of Indices

Evaluate

(-3)^0

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Question 1002

[2 marks]Laws of Indices

Evaluate

\left(\frac{16}{81}\right)^{-\frac{3}{4}}

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Question 1101

[1 marks]Trigonometry

In the diagram GHJ is a straight line,

H\hat{J}K = 90^\circ

, JK = 5 cm and HK = 10 cm. Find

\sin G\hat{H}K

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Question 1102

[2 marks]Pythagoras

In the diagram GHJ is a straight line,

H\hat{J}K = 90^\circ

, JK = 5 cm and HK = 10 cm. Calculate HJ leaving your answer in surd form.

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Question 1201

[1 marks]Matrices

Given that

M = \begin{pmatrix} 5 & 5 \\ 3 & x \end{pmatrix}

, find the determinant of M in terms of

x

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Question 1202

[1 marks]Vectors

Given that

N = \begin{pmatrix} 3 \\ 4 \end{pmatrix}

, find the modulus of the vector N.

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Question 1203

[1 marks]Matrices

Given that

M = \begin{pmatrix} 5 & 5 \\ 3 & x \end{pmatrix}

and

N = \begin{pmatrix} 3 \\ 4 \end{pmatrix}

, find the value of

x

given that

\det M = |N|

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Question 1301

[1 marks]Co-ordinate Geometry

Write down the gradient of the line whose equation is

3x + 2y = 18

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Question 1302

[2 marks]Co-ordinate Geometry

Find the equation of the straight line which is parallel to the line

3x + 2y = 18

and passes through

(-2; 3)

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Question 1401

[2 marks]Vectors

Given that

h\begin{pmatrix} 3 \\ 5 \end{pmatrix} + k\begin{pmatrix} 2 \\ -1 \end{pmatrix} = \begin{pmatrix} 14 \\ 6 \end{pmatrix}

, find the scalar

h

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Question 1402

[2 marks]Vectors

Given that

h\begin{pmatrix} 3 \\ 5 \end{pmatrix} + k\begin{pmatrix} 2 \\ -1 \end{pmatrix} = \begin{pmatrix} 14 \\ 6 \end{pmatrix}

, find the scalar

k

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Question 1501

[2 marks]Logarithms

Given that

\log_{10} 3 = 0,4771

and

\log_{10} 5 = 0,6991

, find

\log_{10} 1\frac{2}{3}

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Question 1502

[2 marks]Logarithms

Given that

\log_{10} 3 = 0,4771

and

\log_{10} 5 = 0,6991

, find

\log_{10} 30

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Question 1601

[2 marks]Measures and Mensuration

In the diagram, OAB is a sector of a circle of radius 7 cm and

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

. Use

\pi = \frac{22}{7}

. Calculate the length of the arc AB, in centimetres.

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Question 1602

[2 marks]Measures and Mensuration

In the diagram, OAB is a sector of a circle of radius 7 cm and

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

. Use

\pi = \frac{22}{7}

. Calculate the area of the sector AOB, in square centimetres.

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Question 1701

[2 marks]Symmetry

Given the capital letters M, N, Z, E and H, write down the letters with line symmetry.

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Question 1702

[2 marks]Symmetry

Given the capital letters M, N, Z, E and H, write down the letters with rotational symmetry of order two.

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Question 1801

[1 marks]Number Bases

Write down the greatest possible digit of a number in base 8.

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Question 1802

[2 marks]Number Bases

Convert

111_5

to a number in base 2.

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Question 1803

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

Find the Lowest Common Multiple, (LCM), of 18 and 24.

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Question 1901

[1 marks]Travel Graphs

A car starts from rest and accelerates uniformly to a speed of 100 km/h in 10 minutes. It maintains that speed for 3 minutes and then accelerates uniformly for a further 11 minutes until it reaches a speed of 120 km/h. Calculate the acceleration of the car during the first 10 minutes, in km/h per minute.

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Question 1902

[2 marks]Travel Graphs

A car starts from rest and accelerates uniformly to a speed of 100 km/h in 10 minutes. It maintains that speed for 3 minutes and then accelerates uniformly for a further 11 minutes until it reaches a speed of 120 km/h. Calculate the distance covered at a constant speed of 100 km/h, in kilometres.

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Question 1903

[2 marks]Travel Graphs

33\frac{1}{2}

km, calculate the average speed of the car in km/h.

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Question 2001

[2 marks]Measures and Mensuration

AB is a line segment which is 8 cm long. Point Q is such that the area of

\triangle ABQ = 12

^2

. Calculate the perpendicular height of the

\triangle ABQ

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Question 2101

[1 marks]Consumer Arithmetic

A trader bought a tonne of goods worth \$2 500. Calculate the cost price per kilogram, in dollars.

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Question 2102

[2 marks]Consumer Arithmetic

A trader bought a tonne of goods worth \$2 500. The goods were later sold at \$2,10 per kilogram. Calculate the percentage loss.

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Question 2103

[2 marks]Substitution

Find the value of

n^4 - 4n

n = 3

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Question 2201

[1 marks]Sets

Given that

\xi = \{x : 1 \le x \le 15,\ x \text{ is an integer}\}

A = \{x : x \text{ is a multiple of } 4\}

B = \{x : x \text{ is a perfect square}\}

and

C = \{x : x \text{ is a multiple of } 2\}

, write down the relationship between sets A and C in set notation.

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Question 2202

[1 marks]Sets

Given that

\xi = \{x : 1 \le x \le 15,\ x \text{ is an integer}\}

A = \{x : x \text{ is a multiple of } 4\}

B = \{x : x \text{ is a perfect square}\}

and

C = \{x : x \text{ is a multiple of } 2\}

, find

n(A \cap B \cap C)

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Question 2301

[1 marks]Probability

A teacher gave ball-point pens as prizes to pupils who passed his test. He had 2 boxes of pens. Box A had 6 blue, 4 green and 3 red pens while Box B had 6 blue and 4 green pens. Ben was asked to pick a pen from Box A and Laiza from Box B. Find the probability that Ben picked a blue pen.

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Question 2302

[2 marks]Probability

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Question 2303

[3 marks]Probability

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Question 2401

[2 marks]Inequalities

n

is an integer, calculate the greatest possible value of

n

which satisfies the inequality

3n - 25 < 2

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Question 2402

[1 marks]Equations

In the diagram AB = BC =

x

cm, AC =

\sqrt{128}

cm and

A\hat{B}C = 90^\circ

. Form an equation in

x

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Question 2403

[3 marks]Quadratic Equations

In the diagram AB = BC =

x

cm, AC =

\sqrt{128}

cm and

A\hat{B}C = 90^\circ

. Find the value of

x

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Question 2501

[1 marks]Statistics

A class of 40 pupils from different families were asked how many pets they kept. The results are shown in the table.

$\begin{array}{|l|c|c|c|c|} \hline \text{number of pets per family} & 1 & 2 & 3 & 4 \\ \hline \text{number of families} & 3 & 7 & 17 & 13 \\ \hline \end{array}$

State the mode.

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Question 2502

[2 marks]Statistics

A class of 40 pupils from different families were asked how many pets they kept. The results are shown in the table.

$\begin{array}{|l|c|c|c|c|} \hline \text{number of pets per family} & 1 & 2 & 3 & 4 \\ \hline \text{number of families} & 3 & 7 & 17 & 13 \\ \hline \end{array}$

Calculate the mean number of pets per family.

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Question 2503

[2 marks]Statistics

A class of 40 pupils from different families were asked how many pets they kept. The results are shown in the table.

$\begin{array}{|l|c|c|c|c|} \hline \text{number of pets per family} & 1 & 2 & 3 & 4 \\ \hline \text{number of families} & 3 & 7 & 17 & 13 \\ \hline \end{array}$

If the results in the table were shown on a pie chart, calculate the angle representing the number of pupils who kept two pets.

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Question 2504

[3 marks]Statistics

A class of 40 pupils from different families were asked how many pets they kept. The results are shown in the table.

$\begin{array}{|l|c|c|c|c|} \hline \text{number of pets per family} & 1 & 2 & 3 & 4 \\ \hline \text{number of families} & 3 & 7 & 17 & 13 \\ \hline \end{array}$

Express the number of pupils who kept three pets as a percentage of the class.

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Mathematics Paper 1 June 2013

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The questions

Question 101

Question 102

Question 201

Question 202

Question 301

Question 302

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 801

Question 802

Question 803

Question 901

Question 902

Question 1001

Question 1002

Question 1101

Question 1102

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 1803

Question 1901

Question 1902

Question 1903

Question 2001

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2504

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