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Examinations Council of Zambia — past paper

ECZ 2019 GCE Paper 1 — Mathematics

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

G12 Titan
1.
The Venn diagram below shows three sets A,B and C . Use set notation to describe the shaded region.
Diagram for question 1
  1. A(A∪B)∩C
  2. B(A∪B)′∩C
  3. C(A∪B)′∪C
  4. DA∩B∩C
2.
Given that E={0,1,2,3,4,5,6,7,8,9},A={2,3,6,8} and B={3,6,7,9}, list (A∩B)'.
  1. A{3,6}
  2. B{2,3,6,7,8,9}
  3. C{2,7,8,9}
  4. D{0,1,2,4,5,7,8,9}
3.
Simplify 4 − 2(b − a) − 1.
  1. A2a − 2b + 3
  2. B2a + 2b + 3
  3. C−2a − 2b + 3
  4. D2a − 2b − 5
4.
Evaluate (⁴√81)3.
  1. A12
  2. B27
  3. C9
  4. D81
5.
Factorise completely 32x2 − 50.
  1. A2(16x2 − 25)
  2. B(8x − 10)(4x + 5)
  3. C2(4x − 5)2
  4. D2(4x − 5)(4x + 5)
6.
Find the gradient of a line which passes through (−5, 3) and (−4, 1).
  1. A2
  2. B−½
  3. C−2
  4. D½
7.
The vector PQ = -32. Given that the point P is (1, 4), find the coordinates of the point Q.
  1. A(4, 2)
  2. B(−2, 6)
  3. C(2, −6)
  4. D(−4, −2)
8.
Given that S = 10-4-211, find ST.
  1. A[1 −2; 0 1; −4 1]
  2. B[−4 0 1; 1 1 −2]
  3. C[1 0 −4; −2 1 1]
  4. D[−2 1 1; 1 0 −4]
9.
Given that R = 2-113 and S = 10-4-211, find RS.
  1. A[2 0 4; −2 3 3]
  2. B[4 1 −9; −5 3 −1]
  3. C[0 −1 −9; 7 3 −1]
  4. D[4 −1 −9; −5 3 −1]
10.
For the sequence −10, −7, −4, −1, …, find the 17th term.
  1. A41
  2. B−58
  3. C38
  4. D44
11.
For the sequence −10, −7, −4, −1, …, find the sum of the first 20 terms.
  1. A370
  2. B740
  3. C570
  4. D185
12.
There are 4 blue and 5 white marbles in a bag. What is the probability of randomly picking a white marble?
  1. A49
  2. B15
  3. C59
  4. D45
13.
Solve the equation 2x2 + 5x − 3 = 0.
  1. Ax = 2 or x = −3
  2. Bx = −½ or x = 3
  3. Cx = 1 or x = −32
  4. Dx = ½ or x = −3
14.
The diagram shows a prism with a base that is a regular hexagon. How many planes of symmetry does it have?
Diagram for question 14
  1. A6
  2. B12
  3. C8
  4. D7
15.
The diagram below shows point A(60°N, 30°W), B(30°S, 30°W) and C(30°S, 75°E) on the surface of the Earth. If the local time at B is 15 00, what is the local time at C?
Diagram for question 15
  1. A08 00
  2. B22 00
  3. C18 30
  4. D12 00
16.
The points A(60°N, 30°W) and B(30°S, 30°W) lie on the same meridian. It takes a plane 6 hours to fly from A to B. What is its speed in knots?
Diagram for question 16
  1. A540 knots
  2. B900 knots
  3. C150 knots
  4. D5 400 knots
17.
Evaluate 30 × 33 + 31.
  1. A27
  2. B12
  3. C84
  4. D30
18.
The diagram shows a sector of a circle with centre O and radius 4.2 cm. Angle AOB = θ. Given that the area of the sector AOB is 9.24 cm2, find the value of θ. [π = 227]
Diagram for question 18
  1. A30°
  2. B120°
  3. C60°
  4. D45°
19.
The mass, m, of a block of wood is 876.4 g, correct to 1 decimal place. Complete the statement: … ≤ m ≤ …
  1. A876.35 ≤ m ≤ 876.45
  2. B876.3 ≤ m ≤ 876.5
  3. C875.9 ≤ m ≤ 876.9
  4. D876.0 ≤ m ≤ 876.8
20.
The length of a piece of wire is 15.2 cm, correct to 1 decimal place. What is the relative error of the length of the piece of wire?
  1. A1152
  2. B11520
  3. C1304
  4. D176
21.
The diagram below shows Mr Moenda's trip. He travels on a bearing of 141° from A to B. He then decides to continue with his trip from B on a bearing of 255° to C. The angle BCA = 35°. Find the bearing of A from B.
Diagram for question 21
  1. A141°
  2. B321°
  3. C219°
  4. D039°
22.
The diagram below shows Mr Moenda's trip. He travels on a bearing of 141° from A to B. He then decides to continue with his trip from B on a bearing of 255° to C. The angle BCA = 35°. Find the bearing of A from C.
Diagram for question 22
  1. A010°
  2. B075°
  3. C110°
  4. D040°
23.
The functions f and g are defined as f(x) = 2x + 1 and g(x) = 3x − 52. Find f-1(x).
  1. Ax + 12
  2. B2x − 1
  3. Cx − 12
  4. D12x + 1
24.
The functions f and g are defined as f(x) = 2x + 1 and g(x) = 3x − 52. Find fg(x).
  1. A3x − 4
  2. B6x − 52
  3. C3x − 5
  4. D3x − 32
25.
The functions f and g are defined as f(x) = 2x + 1 and g(x) = 3x − 52. Find fg(4).
  1. A12
  2. B7
  3. C16
  4. D8
26.
In the diagram below, A, B, C, D and E are points on the circumference of the circle with centre O. DE = AD, AĈB = 20° and AÔE = 80°. Find AD̂E.
Diagram for question 26
  1. A80°
  2. B40°
  3. C20°
  4. D60°
27.
In the diagram below, A, B, C, D and E are points on the circumference of the circle with centre O. DE = AD, AĈB = 20° and AÔE = 80°. Find DÂE.
Diagram for question 27
  1. A40°
  2. B55°
  3. C70°
  4. D35°
28.
In the diagram below, A, B, C, D and E are points on the circumference of the circle with centre O. DE = AD, AĈB = 20° and AÔE = 80°. Find BÂD.
Diagram for question 28
  1. A50°
  2. B70°
  3. C90°
  4. D30°
29.
A point R(−3, 1) is mapped onto a point S(2, −1) by a translation T. Express T as a column vector.
  1. A[−5; 2]
  2. B[5; −2]
  3. C[−1; 0]
  4. D[2; −1]
30.
An incomplete program in pseudocode reads: Start; Enter ……; m = ……; Output m; Stop. The program calculates the mean (m) of 10 numbers whose sum is S. Which statements correctly fill the two blanks?
Diagram for question 30
  1. AEnter m; m = S × 10
  2. BEnter S; m = 10S
  3. CEnter S; m = S10
  4. DEnter 10; m = S + 10
31.
Given that y varies directly as x and inversely as the square of z, and that y = 10 when x = 32 and z = 4, find the value of k, the constant of variation.
  1. A5
  2. B10
  3. C2
  4. D8
32.
y varies directly as x and inversely as the square of z, with constant k = 5 (so y = 5xz2). Find y when x = 20 and z = 5.
  1. A20
  2. B4
  3. C100
  4. D2
33.
y varies directly as x and inversely as the square of z, with constant k = 5 (so y = 5xz2). Find z when x = 9 and y = 5.
  1. Az = 3 only
  2. Bz = 9 or −9
  3. Cz = 3 or −3
  4. Dz = ±√5
34.
A company's working capital consists of 450 10% preference shares of K50.00 each and 700 ordinary shares of K10.00 each. After 6 months, the company declared a dividend of K5 750.00. How much dividend will be paid to each ordinary shareholder?
  1. AK8.20
  2. BK2 250.00
  3. CK5.00
  4. DK3.50
35.
The ratio of the volumes of two similar solids is 64 : 27. The surface area of the smaller solid is 180 cm2. What is the surface area of the bigger solid?
  1. A405 cm2
  2. B240 cm2
  3. C426⅔ cm2
  4. D320 cm2
36.
The diagram shows triangle KLM in which KL = 16 cm, angle KLM = 150° and its area is 32 cm2. Calculate the length of LM.
Diagram for question 36
  1. A4 cm
  2. B8 cm
  3. C16 cm
  4. D2 cm
37.
The equation of line A is 3x + 2y = 10. Line B is parallel to line A and passes through the point (4, 6). Find the equation of the line B.
  1. Ay = −³⁄₂x + 12
  2. By = ³⁄₂x + 12
  3. Cy = −³⁄₂x + 5
  4. Dy = −²⁄₃x + 12
38.
The diagram shows an unshaded region R bounded by four lines: the dashed horizontal line y = 6; the vertical line x = 2; the line through (0, 0) and (−2, 2); and the line through (−2, 0) and (0, 4). Write four inequalities that define R.
Diagram for question 38
  1. Ay < 6, x ≤ 2, y > −x, y ≤ 2x + 4
  2. By < 6, x ≤ 2, y > −x, y ≥ 2x + 4
  3. Cy ≤ 6, x < 2, y ≥ −x, y ≤ 2x + 4
  4. Dy > 6, x ≥ 2, y < −x, y ≥ 2x + 4
39.
Find the integral of 3x32 − 5x + 1x2 with respect to x.
  1. A⅜x4 − 5x2 − 1x + c
  2. B⅜x⁴ − ⁵⁄₂x² + 1x + c
  3. C9x22 − 5 − 2x3 + c
  4. D⅜x⁴ − ⁵⁄₂x² − 1x + c
40.
A function y = (1 + x)(x − 2). Which description matches the sketch of its graph?
Diagram for question 40
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
41.
A function y = (1 + x)(x − 2). Find the minimum value of y.
Diagram for question 41
  1. A−2
  2. B−94
  3. C−12
  4. D−3
42.
The diagram below shows a speed time graph of an object. It starts from rest and accelerates uniformly for 2 seconds until it reaches a speed of 10 m/s. It moves at this constant speed for 6 seconds then accelerates until it reaches a speed of V m/s after 5 seconds. Finally, it retards for the next 8 seconds until it comes to a halt. Calculate the acceleration during the first 2 seconds.
Diagram for question 42
  1. A10 m/s2
  2. B2 m/s2
  3. C5 m/s2
  4. D20 m/s2
43.
In the same journey (rest → 10 m/s in 2 s; constant for 6 s; accelerating from 8 s to 13 s up to V m/s; then retarding to rest over the last 8 seconds), find the value of V if the retardation in the last 8 seconds is 3 m/s2.
Diagram for question 43
  1. A30 m/s
  2. B18 m/s
  3. C11 m/s
  4. D24 m/s
44.
In the same journey (rest → 10 m/s in 2 s; constant 10 m/s for 6 s; speeding up to 24 m/s between 8 s and 13 s; then retarding to rest at 21 s), calculate the average speed for the whole journey.
Diagram for question 44
  1. A14.5 m/s
  2. B≈ 12 m/s
  3. C24 m/s
  4. D10 m/s