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Examinations Council of Zambia — past paper

ECZ 2020 O-Level Paper 1 — Mathematics

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

G12 Titan
1.
Simplify 2(x + 3) - 3x(x - 2).
  1. A-3x2 + 8x + 6
  2. B-3x2 - 4x + 6
  3. C3x2 + 8x + 6
  4. D-3x2 + 2x + 6
2.
Evaluate (∛27)2.
  1. A6
  2. B9
  3. C27
  4. D729
3.
Factorise completely 16x2 - 100.
  1. A4(x - 5)(x + 5)
  2. B(4x - 10)(4x + 10)
  3. C4(2x - 5)(2x + 5)
  4. D(2x - 5)(2x + 5)
4.
The points A and B are (-5, 15) and (3w, w) respectively. Given that the midpoint of the straight line joining A and B is (5, 10), find the value of w.
  1. A103
  2. B-5
  3. C253
  4. D5
5.
The vector RS = -43. Given that R is a point (-2, 1), find the coordinates of point S.
  1. A(-6, 4)
  2. B(2, -2)
  3. C(-6, -2)
  4. D(6, 4)
6.
On the Venn diagram in the answer space below, shade the set A' ∩ (B ∪ C).
Diagram for question 6
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
7.
Given that M = -3-1420-2 and N = -21, find (a) MT.
  1. A-3-1420-2
  2. B-340-12-2
  3. C-340-122
  4. D04-3-22-1
8.
Given that M = -3-1420-2 and N = -21, find (b) MN as a single matrix.
  1. A7-10-2
  2. B5-62
  3. C5-6-2
  4. DMN is not possible
9.
For the sequence 7, 11, 15, 19, ..., find the 9th term.
  1. A43
  2. B35
  3. C47
  4. D39
10.
For the sequence 7, 11, 15, 19, ..., find the sum of the first 16 terms.
  1. A592
  2. B616
  3. C1184
  4. D296
11.
The probability of Masamushi failing an examination is 310. What is the probability that she will pass that particular examination?
  1. A310
  2. B710
  3. C1310
  4. D1
12.
A plan of a play boat is drawn to a scale of 1 : 20. If the actual area of the base of the boat is 0.64 m2, calculate its area on the map in square centimetres.
  1. A12.8 cm2
  2. B6.4 cm2
  3. C16 cm2
  4. D32 cm2
13.
Given that E = {3, 6, 9, 12, 15, 18}, A = {6, 9, 12} and B = {3, 6, 18}, list A ∩ B'.
  1. A{6}
  2. B{9, 12, 15}
  3. C{3, 18}
  4. D{9, 12}
14.
Solve the equation 3x + 3 = 275.
  1. A12
  2. B2
  3. C18
  4. D5
15.
The diagram below shows two towns A and B on the equator. A is on longitude 35°W and B is on longitude 40°E. Find the time at A when it is 18 00 hours at B.
Diagram for question 15
  1. A23 00 hours
  2. B13 00 hours
  3. C11 00 hours
  4. D13 20 hours
16.
The diagram below shows two towns A and B on the equator. A is on longitude 35°W and B is on longitude 40°E. A plane flying from A to B takes 5 hours. Find its speed.
Diagram for question 16
  1. A750 knots
  2. B4500 knots
  3. C900 knots
  4. D180 knots
17.
The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. Find f-1(x).
  1. Ax - 23
  2. B13x - 2
  3. C3x + 2
  4. Dx + 23
18.
The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. Find gf(x).
  1. A12x - 7
  2. B12x + 1
  3. C12x - 8
  4. D7x - 1
19.
The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. Find gf(-2).
  1. A31
  2. B-31
  3. C-17
  4. D17
20.
Chiyalwa estimated the length of a string as 15 cm. The true length of the string was 14.6 cm. Find the absolute error in Chiyalwa's estimate.
  1. A0.6 cm
  2. B29.6 cm
  3. C0.4 cm
  4. D0.04 cm
21.
Chiyalwa estimated the length of a string as 15 cm. The true length of the string was 14.6 cm. Find the relative error in Chiyalwa's estimate.
  1. A275
  2. B0.4
  3. C173
  4. D273
22.
A point A(2, 4) is mapped onto A'(-3, 5) by a translation T. Find the translation T.
  1. A-51
  2. B5-1
  3. C-19
  4. D-59
23.
Integrate y = x-3 - 3x4 + 5.
  1. A-3x-4 - 12x3
  2. B-12x2 - 3x55 + 5x + c
  3. C12x2 - 3x55 + 5x + c
  4. D-12x2 - 3x5 + 5x + c
24.
In the diagram below, the bearing of C from A is 160°. Angle ACB is 30° and AB = AC. Find (a) angle BAC.
Diagram for question 24
  1. A60°
  2. B30°
  3. C120°
  4. D150°
25.
In the diagram below, the bearing of C from A is 160°. Angle ACB is 30° and AB = AC. Find (b) the bearing of A from C.
Diagram for question 25
  1. A210°
  2. B020°
  3. C160°
  4. D340°
26.
The diagram below shows triangle ABC in which angle ABC = 90°. BC is produced to D. Given that tan(angle BAC) = 43, find the value of cos(angle ACD).
Diagram for question 26
  1. A-45
  2. B45
  3. C-35
  4. D35
27.
Calculate the radius of a semicircle whose area is 77 cm2. [Take π to be 227.]
  1. A3.5 cm
  2. B7 cm
  3. C14 cm
  4. D49 cm
28.
In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR and TS are parallel. Angle TQR = 70° and angle TRP = 20°. Find (a) angle RTQ.
Diagram for question 28
  1. A70°
  2. B55°
  3. C40°
  4. D20°
29.
In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR and TS are parallel. Angle TQR = 70° and angle TRP = 20°. Find (b) angle RST.
Diagram for question 29
  1. A70°
  2. B40°
  3. C90°
  4. D110°
30.
In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR and TS are parallel. Angle TQR = 70° and angle TRP = 20°. Find (c) angle TRS.
Diagram for question 30
  1. A50°
  2. B20°
  3. C70°
  4. D40°
31.
A woman has 500 company shares with a nominal value of K70.00 each, which she bought at K30.00 each. How much did she pay for the shares?
  1. AK35 000.00
  2. BK15 000.00
  3. CK20 000.00
  4. DK150.00
32.
P is the point (3, 1) and Q is another point such that the gradient of the line PQ is -12. Write down the equation of PQ.
  1. A2y = x + 5
  2. By = -2x + 5
  3. C2y = -x + 5
  4. D2y = -x - 5
33.
An incomplete pseudocode for a program that calculates the curved surface area S of a cone with radius r and slant height l is: StartEnter ...... / S = ...... / Output SStop. Which correctly completes the two blanks?
  1. AEnter r, h ; S = π*r2*h
  2. BEnter r, l ; S = 2*π*r*l
  3. CEnter S ; r = Sπ*l
  4. DEnter r, l ; S = π*r*l
34.
The diagram below is a right triangular pyramid ABCD with AB = BC = CA. What is the order of rotational symmetry of the pyramid about OD?
Diagram for question 34
  1. A3
  2. B1
  3. C2
  4. D6
35.
It is given that y varies directly as the cube root of x and inversely as the square of z, and y = 2 when x = 8 and z = 4. Find k, the constant of variation.
  1. A2
  2. B16
  3. C8
  4. D116
36.
It is given that y varies directly as the cube root of x and inversely as the square of z, and y = 2 when x = 8 and z = 4. Find the equation connecting x, y and z.
  1. Ay = ∛x16z2
  2. By = (16z2) / ∛x
  3. Cy = 16∛xz2
  4. Dy = 16x3z2
37.
It is given that y varies directly as the cube root of x and inversely as the square of z, and y = 2 when x = 8 and z = 4. Find the values of z when y = 12 and x = 27.
  1. Az = 2 only
  2. Bz = ±4
  3. Cz = ±16
  4. Dz = ±2
38.
Write three inequalities that define the unshaded region R.
Diagram for question 38
  1. Ax < 3, x + y ≥ 3, x + 2y ≤ 6
  2. Bx > 3, x + y ≥ 3, x + 2y ≤ 6
  3. Cx < 3, x + y ≤ 3, x + 2y ≥ 6
  4. Dx < 3, x + y ≥ 3, x + 2y ≥ 6
39.
Solve the equation 5x2 = x.
  1. Ax = 15 only
  2. Bx = 0 or x = 15
  3. Cx = 0 or x = 5
  4. Dx = ±15
40.
The diagram below shows the sketch of the graph of y = -x2 + 2x + 3 cutting the x-axis at A and B. Find the (i) coordinates of A.
Diagram for question 40
  1. A(3, 0)
  2. B(0, 3)
  3. C(-1, 0)
  4. D(1, 0)
41.
The diagram below shows the sketch of the graph of y = -x2 + 2x + 3 cutting the x-axis at A and B. Find the (ii) maximum value of the graph.
Diagram for question 41
  1. A1
  2. B3
  3. C-1
  4. D4
42.
The diagram below is a graph of a moving object which decelerates uniformly at 8 m/s2 from a speed of 52 m/s to v m/s in 6 seconds. It then moves at a constant speed for 10 seconds and finally decelerates uniformly to come to rest in 4 seconds. Calculate the (a) speed v.
Diagram for question 42
  1. A4 m/s
  2. B48 m/s
  3. C44 m/s
  4. D8 m/s
43.
The diagram below is a graph of a moving object which decelerates uniformly at 8 m/s2 from a speed of 52 m/s to v m/s in 6 seconds. It then moves at a constant speed for 10 seconds and finally decelerates uniformly to come to rest in 4 seconds. Calculate the (b) total distance travelled for the whole journey.
Diagram for question 43
  1. A876 m
  2. B216 m
  3. C200 m
  4. D312 m
44.
The diagram below is a graph of a moving object which decelerates uniformly at 8 m/s2 from a speed of 52 m/s to v m/s in 6 seconds. It then moves at a constant speed for 10 seconds and finally decelerates uniformly to come to rest in 4 seconds. Calculate the (c) average speed for the whole journey.
Diagram for question 44
  1. A43.8 m/s
  2. B18 m/s
  3. C10.8 m/s
  4. D12 m/s