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Examinations Council of Zambia — past paper

ECZ 2011 O-Level Paper 1 — Mathematics

35 questions · downloaded from g12titan.com, where this paper is marked free online

G12 Titan
1.
Evaluate 6423.
  1. A16
  2. B8
  3. C32
  4. D12
2.
The diagram shows three sets A, B and C in the universal set E. Which description matches the region A' n (B u C)?
Diagram for question 2
  1. AEverything that lies in A, B or C
  2. BThe part of A that lies outside both B and C
  3. CThe parts of B and C that lie outside A
  4. DOnly the region common to all three sets
3.
Given that x = -4 and y = -12, find the value of xy - x2.
  1. A-18
  2. B-14
  3. C14
  4. D18
4.
The ratio of the surface areas of two similar bottles is 4 : 9. What is the ratio of their volumes?
  1. A2 : 3
  2. B4 : 9
  3. C16 : 81
  4. D8 : 27
5.
Write the next number in the sequence 2, -8, 32, -128, ...
  1. A512
  2. B-512
  3. C256
  4. D-256
6.
Write the nth term of the sequence 5, 7, 9, 11, ...
  1. An + 4
  2. B2n + 3
  3. C2n + 5
  4. D3n + 2
7.
A function f is defined as f(x) = 35x + 1, x is not -15. Find f(1).
  1. A3
  2. B13
  3. C12
  4. D2
8.
A function f is defined as f(x) = 35x + 1. Find x if f(x) = 6.
  1. A110
  2. B-12
  3. C12
  4. D-110
9.
The figure shows triangle ABC in which AC = 5 cm and angle A is a right angle. Given that sin B = 0.5, cos B = 0.9 and tan B = 0.6, calculate the length of BC.
Diagram for question 9
  1. A10 cm
  2. B2.5 cm
  3. C5.6 cm
  4. D8.3 cm
10.
Solve the equation (y + 7)2 = 9.
  1. Ay = 2 or y = -16
  2. By = -4 or y = -10
  3. Cy = -4 only
  4. Dy = 3 or y = -3
11.
The position vectors of A and B are 01 and 35 respectively. Find AB.
  1. A36
  2. B-3-4
  3. C34
  4. D03
12.
Find the gradient of the line x + 2y = 4.
  1. A2
  2. B-2
  3. C12
  4. D-12
13.
A set has 6 proper subsets. How many elements does it have?
  1. A3
  2. B2
  3. C6
  4. D4
14.
In the diagram, C is due south of A, AB = BC and the bearing of B from A is 110°. Find the bearing of C from B.
Diagram for question 14
  1. A290°
  2. B250°
  3. C070°
  4. D200°
15.
An aeroplane flew from point A(60 S, 30 W) to point B(60 S, 60 E). Taking π = 227, R = 6370 km and cos 60 = 0.50, find the distance covered in kilometres.
  1. A10 010 km
  2. B20 020 km
  3. C5 005 km
  4. D2 502.5 km
16.
In the diagram, ABC is a straight line and BS is parallel to UT. Angle SBV = 64° and BS bisects angle ABV. Find angle ABS.
Diagram for question 16
  1. A32°
  2. B116°
  3. C128°
  4. D64°
17.
Using the same diagram, find angle BUT.
Diagram for question 17
  1. A116°
  2. B64°
  3. C128°
  4. D32°
18.
Using the same diagram, find angle SBC.
Diagram for question 18
  1. A64°
  2. B116°
  3. C128°
  4. D96°
19.
A transformation is represented by the matrix 20-31. A point J is mapped onto the point Y(6, 16) by this matrix. Find the coordinates of J.
  1. A(12, 34)
  2. B(3, 7)
  3. C(3, 25)
  4. D(6, 16)
20.
Factorise completely x2y + 2x2 - 9y - 18.
  1. A(x2 - 9)(y + 2)
  2. B(x - 3)(x + 3)(y + 2)
  3. C(x - 3)2(y + 2)
  4. D(x2 + 9)(y - 2)
21.
In the diagram, ABCDEF is a regular hexagon and HEFG is part of a regular pentagon. Calculate angle DEH.
Diagram for question 21
  1. A132°
  2. B108°
  3. C120°
  4. D152°
22.
Express as a single matrix 4-3 2-1.
  1. A8-6-43
  2. B83
  3. C11
  4. D8-4-63
23.
Given that x varies as y and inversely as z2, and that x = 12 when y = 3 and z = 2, find the equation connecting x, y and z.
  1. Ax = 4yz2
  2. Bx = 16yz2
  3. Cx = 16yz2
  4. Dx = y16z2
24.
x varies directly as y and inversely as z2, with constant k = 16 (so x = 16yz2). Find the value of x when y = 3 and z = 4.
  1. A12
  2. B6
  3. C1.5
  4. D3
25.
x varies directly as y and inversely as z2, with constant k = 16 (so x = 16yz2). Find the values of z when x = 4 and y = 25.
  1. Az = 10 or z = -10
  2. Bz = 10 only
  3. Cz = 5 or z = -5
  4. Dz = 100
26.
Six pupils obtained the following marks in a Mathematics Contest: 23, 24, 39, 40, 26, 37. Find the probability that a pupil selected at random obtained more than 27 marks.
  1. A13
  2. B12
  3. C23
  4. D16
27.
What is the angle of rotational symmetry of a regular pentagon?
  1. A108°
  2. B60°
  3. C72°
  4. D120°
28.
A vegetable garden is an irregular pentagon ABCDE with AB = BC = CD = AD, AE = 12 m, DE = 5 m and angles ABC, BCD and DEA all 90°. Find AD.
Diagram for question 28
  1. A17 m
  2. B7 m
  3. C11 m
  4. D13 m
29.
Using the same garden, calculate the perimeter of the garden.
Diagram for question 29
  1. A56 m
  2. B69 m
  3. C43 m
  4. D52 m
30.
In the diagram, R is the unshaded region. Which three inequalities describe R?
Diagram for question 30
  1. Ax ≥ 3, y ≤ x + 2, y ≥ -x + 2
  2. Bx ≤ 3, y ≤ x + 2, y ≥ -x + 2
  3. Cx ≤ 3, y ≥ x + 2, y ≤ -x + 2
  4. Dx ≤ 3, y ≤ x + 2, y ≤ -x + 2
31.
Find the maximum value of 2x + y within the region R.
Diagram for question 31
  1. A8
  2. B5
  3. C11
  4. D2
32.
The speed-time graph shows a lorry which starts from rest and increases speed at a constant rate for 6 seconds, reaching V1 m/s. If the lorry travelled 120 m in the first 6 seconds, calculate the value of V1.
Diagram for question 32
  1. A30
  2. B20
  3. C60
  4. D40
33.
Given that the acceleration of the lorry between 10 and 16 seconds is 2 m/s2, find the value of V2.
Diagram for question 33
  1. A52
  2. B12
  3. C64
  4. D44
34.
Calculate the total distance covered by the lorry.
Diagram for question 34
  1. A540 m
  2. B660 m
  3. C720 m
  4. D600 m
35.
A map is drawn to a scale of 1 : 200 000. The actual area of a town is 60 km2. Calculate, in cm2, the area of the town on the map.
  1. A30 cm2
  2. B15 cm2
  3. C120 cm2
  4. D7.5 cm2