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Examinations Council of Zambia — past paper

ECZ 2013 O-Level Paper 1 — Mathematics

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

G12 Titan
1.
Evaluate 34-2.
  1. A169
  2. B916
  3. C-169
  4. D43
2.
The diagram shows three sets A, B and C inside the universal set E. Use set notation to describe the shaded region.
Diagram for question 2
  1. AC n (A u B)
  2. BC n (A u B)'
  3. CC u (A n B)'
  4. DC' n (A u B)
3.
Find the equation of the line joining the point A(0, 7) to the point B(7, 0).
  1. Ay = x + 7
  2. Bx + y = 7
  3. Cy = x - 7
  4. Dx - y = 7
4.
For the sequence 2, 5, 8, 11, ... find the sixth term.
  1. A14
  2. B20
  3. C16
  4. D17
5.
For the sequence 2, 5, 8, 11, ... find an expression for the nth term.
  1. A3n - 1
  2. B3n + 1
  3. Cn + 3
  4. D2n + 1
6.
How many subsets has the set A = {1}?
  1. A1
  2. B3
  3. C2
  4. D4
7.
In the diagram, C is due East of A and due North of B. Angle BAC is 50°. Find the bearing of A from B.
Diagram for question 7
  1. A040°
  2. B220°
  3. C140°
  4. D320°
8.
Given that vector AB = 1-3 and B is the point (4, 5), find the coordinates of A.
  1. A(5, 2)
  2. B(3, 2)
  3. C(5, 8)
  4. D(3, 8)
9.
Factorise completely 3ap - 8bq - 4aq + 6bp.
  1. A(a + 2b)(3p - 4q)
  2. B(a - 2b)(3p + 4q)
  3. C(a + 2b)(3p + 4q)
  4. D(3a + 2b)(p - 4q)
10.
A function h is defined as h(x) = (12)x - 5. Find h(-4).
  1. A-3
  2. B-7
  3. C7
  4. D-2
11.
A function h is defined as h(x) = (12)x - 5. Find the value of x for which h(x) = 3.
  1. A4
  2. B8
  3. C16
  4. D-4
12.
A function h is defined as h(x) = (12)x - 5. Find h-1(x).
  1. Ax2 + 5
  2. B2x - 10
  3. C2x + 10
  4. Dx + 52
13.
The diagram shows a cylinder of height 9 cm and diameter 7 cm. Calculate the curved surface area of the cylinder. Take π to be 227.
Diagram for question 13
  1. A99 cm2
  2. B198 cm2
  3. C346.5 cm2
  4. D396 cm2
14.
Solve the equation (x - 1)(x + 1) = 8.
  1. Ax = 3
  2. Bx = 3 or x = -3
  3. Cx = 9 or x = -9
  4. Dx = √7 or x = -√7
15.
In the diagram, triangle A is mapped onto triangle B by a single transformation. Describe fully the transformation.
Diagram for question 15
  1. ARotation of 90° clockwise about (2, 2)
  2. BReflection in the line y = -x
  3. CReflection in the line y = x
  4. DRotation of 90° anticlockwise about (2, 2)
16.
Bonzo is a town on (53 S, 65 W) and Munyefu is another town on (53 S, 19 E). A football match is scheduled to kick off at 15 30 hours local time at Bonzo. What will be the kick off time at Munyefu?
  1. A09 54 hours
  2. B20 06 hours
  3. C21 30 hours
  4. D21 06 hours
17.
A circle centre O passes through the points A, B, C and D. Angle AOC = 110° and AO is parallel to BC. Find angle OCA.
Diagram for question 17
  1. A35°
  2. B55°
  3. C70°
  4. D110°
18.
A circle centre O passes through the points A, B, C and D. Angle AOC = 110° and AO is parallel to BC. Find angle ACB.
Diagram for question 18
  1. A55°
  2. B35°
  3. C70°
  4. D145°
19.
A circle centre O passes through the points A, B, C and D. Angle AOC = 110° and AO is parallel to BC. Find angle ABC.
Diagram for question 19
  1. A55°
  2. B110°
  3. C125°
  4. D145°
20.
Kaponya got a simple interest of K375.00 from a bank after investing a sum of money for 18 months. Find the amount of money he invested, if the bank interest rate was 10% per annum.
  1. AK3 750.00
  2. BK250.00
  3. CK625.00
  4. DK2 500.00
21.
Given that y varies directly as x and inversely as 2m - 1, and that y = 5 when x = 7 and m = 4, calculate the constant of variation, k.
  1. A5
  2. B35
  3. C7
  4. D1
22.
y varies directly as x and inversely as 2m - 1, with constant k = 5 (so y = 5x2m - 1). Find the value of y when x = 2 and m = 3.
  1. A10
  2. B2
  3. C5
  4. D0.5
23.
y varies directly as x and inversely as 2m - 1, with constant k = 5 (so y = 5x2m - 1). Find the value of m when y = 2 and x = 4.
  1. A10
  2. B11
  3. C5.5
  4. D5
24.
A 10 m ladder rests against a vertical wall with its foot 6 m from the wall. How far up the wall does the ladder reach?
  1. A4 m
  2. B6 m
  3. C11.7 m
  4. D8 m
25.
Simplify 2x - 9 + 3x2 - 2 - 4x.
  1. A3x2 - 2x - 11
  2. B3x2 + 2x - 11
  3. C3x2 - 6x - 11
  4. D3x2 - 2x - 7
26.
In the diagram, R is the unshaded region. Which three inequalities describe the region R?
Diagram for question 26
  1. Ax ≥ 0, y ≤ -x, y ≥ x + 8
  2. Bx ≤ 0, y ≥ -x, y ≤ x + 8
  3. Cx ≤ 0, y ≤ -x, y ≥ x + 8
  4. Dx ≥ 0, y ≥ -x, y ≤ x + 8
27.
Two containers are geometrically similar. The ratio of their base areas is 9 : 16. If the volume of the smaller container is 135 m3, what would be the volume of the larger container?
  1. A240 m3
  2. B180 m3
  3. C320 m3
  4. D427 m3
28.
In the diagram, ABC is a straight line, BC = 8 cm, BD = 10 cm and sin(ABD) = 35. Find the area of triangle BCD.
Diagram for question 28
  1. A40 cm2
  2. B32 cm2
  3. C48 cm2
  4. D24 cm2
29.
The diagram shows a 4 by 4 grid with two squares already shaded. Which two further squares must be shaded so that the figure has two lines of symmetry?
Diagram for question 29
  1. ARow 1 column 4, and row 3 column 2
  2. BRow 1 column 1, and row 3 column 3
  3. CRow 2 column 2, and row 4 column 4
  4. DRow 1 column 2, and row 3 column 4
30.
Two towns Katulya and Twasika are 50 km apart. Kachova started off from Twasika for Katulya at the same time as Namutekenya from Katulya to Twasika, as shown in the distance-time graph. How far was Kachova from arriving at Katulya when Namutekenya reached Twasika?
Diagram for question 30
  1. A40 km
  2. B10 km
  3. C30 km
  4. D50 km
31.
Using the distance-time graph, how long had Namutekenya been in Twasika before Kachova restarted his trip after a short rest?
Diagram for question 31
  1. A2 hours
  2. B30 minutes
  3. C1 hour 30 minutes
  4. D1 hour
32.
Using the distance-time graph, calculate the difference between the average speeds of Kachova and Namutekenya.
Diagram for question 32
  1. A30 km/h
  2. B60 km/h
  3. C45 km/h
  4. D40 km/h
33.
A road between two villages A and B is 1.2 km long. It is represented by 3 cm on the map. Calculate the scale of the map, in the form 1 : n.
  1. A1 : 400
  2. B1 : 4000
  3. C1 : 40 000
  4. D1 : 120 000