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Examinations Council of Zambia — past paper

ECZ 2021 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Using set notation, describe the shaded region.
Diagram for question 1
  1. A(A∪B)∩C′
  2. B(A∩B)∩C′
  3. CA∪B
  4. DC∩(A∪B)
2.
Given that A = {x: x<6, x is a natural number}, list set A.
  1. A{0,1,2,3,4,5}
  2. B{2,3,4,5}
  3. C{1,2,3,4,5}
  4. D{1,2,3,4,5,6}
3.
Simplify 2ab − ab2 − 7ab + a2b + 5ab2.
  1. Aa2b − 6ab2 − 5ab
  2. Ba2b + 4ab2 + 5ab
  3. Ca2b + 4ab2 − 5ab
  4. D5a2b2 − 5ab
4.
Evaluate 912 + 1.
  1. A5.5
  2. B4
  3. C4.5
  4. D82
5.
Solve the equation x2 − 2x = 0.
  1. Ax = 0 or x = 2
  2. Bx = 2 only
  3. Cx = 0 or x = −2
  4. Dx = ±√2
6.
Factorise completely 2x2 − x − 6.
  1. A(2x − 3)(x + 2)
  2. B(2x + 3)(x − 2)
  3. C(x − 3)(2x + 2)
  4. D(2x + 1)(x − 6)
7.
At the end of the financial year, a public limited company declared a dividend. An investor with 1 500 shares in the company received K750.00. What was the dividend per share?
  1. AK0.05
  2. BK2.00
  3. CK0.50
  4. DK5.00
8.
Given that 9, 15, 21, 27 ... is an Arithmetic Progression, find the twelfth term.
  1. A69
  2. B75
  3. C81
  4. D72
9.
Given that 9, 15, 21, 27 ... is an Arithmetic Progression, find the formula for the nth term.
  1. A6n + 9
  2. B6n − 3
  3. C6n + 3
  4. D9n + 6
10.
Given that A = 1−35210, find the transpose of A.
  1. A12−3150
  2. B1−35210
  3. C211−305
  4. D5−31012
11.
Given that P = 2−134 and Q = −23, find PQ.
  1. A−16
  2. B−76
  3. C7−6
  4. D−7−6
12.
A letter is chosen at random from the letters of the word HELLO. What is the probability that it is the letter L?
  1. A25
  2. B15
  3. C12
  4. D35
13.
Solve the equation 125x = 125.
  1. A23
  2. B−23
  3. C−32
  4. D−15
14.
The diagram shows a sector XOY. The arc XY subtends an angle of θ at the centre O and the radius of the sector is 6cm. Given that the area of the sector is 33cm2, find the value of θ. [π = 227]
Diagram for question 14
  1. A210°
  2. B60°
  3. C95°
  4. D105°
15.
The diagram below shows the positions of towns A, B and C on the earth's surface. NACS is the prime meridian. A ship takes 26 hours to travel from B to C, a distance of 1 560 nautical miles. Find the speed of the ship in knots.
Diagram for question 15
  1. A26 knots
  2. B60 knots
  3. C600 knots
  4. D40 560 knots
16.
The diagram shows towns A, B and C on the earth's surface, where NACS is the prime meridian, A is on longitude 0° and B is on longitude 30°W. If the local time at A is 10 30 hours, find the local time at B.
Diagram for question 16
  1. A12 30 hours
  2. B06 30 hours
  3. C08 30 hours
  4. D10 30 hours
17.
The mass (m) of a bag of maize is 62kg to the nearest kilogram. Complete the statement ___ ≤ m < ___.
  1. A61.5 ≤ m < 62.5
  2. B61 ≤ m < 63
  3. C62 ≤ m < 63
  4. D61.5 < m ≤ 62.5
18.
A woman estimates the weight of her dog to be 13.15kg. The actual weight of the dog is 10kg. Find the percentage error.
  1. A24%
  2. B31.5%
  3. C3.15%
  4. D315%
19.
In the diagram, A, B, C and D are points on the circumference of a circle, centre O. Angle DAB = 36°, BC = CD and EBF is a tangent to the circle at B. Find angle BOD.
Diagram for question 19
  1. A72°
  2. B36°
  3. C144°
  4. D18°
20.
In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. Angle DAB = 36°, BC = CD and EBF is a tangent to the circle at B. Find angle BCD.
Diagram for question 20
  1. A36°
  2. B72°
  3. C144°
  4. D108°
21.
In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. Angle DAB = 36°, BC = CD and EBF is a tangent to the circle at B. Find angle CBF.
Diagram for question 21
  1. A144°
  2. B72°
  3. C36°
  4. D18°
22.
The diagram shows two lines l and n that are perpendicular to each other. The equation of the line n is 3x + 2y = 6. The line l passes through the point (5, 4). Find the equation of line l.
Diagram for question 22
  1. A3y = 2x + 2
  2. B2y = 3x − 7
  3. C3y = −2x + 22
  4. Dy = 2x − 6
23.
The diagram shows triangle ABC in which AB = 5cm and AC = 13cm. Angle ABC = 90° and BC is produced to D. Find the value of cos ACD.
Diagram for question 23
  1. A1213
  2. B−1213
  3. C−513
  4. D512
24.
Given that z varies as x and inversely as the square of y, and that z = 3 when x = 8 and y = 4, find the value of k, the constant of variation.
  1. A1.5
  2. B24
  3. C6
  4. D23
25.
Given that z varies as x and inversely as the square of y, with constant of variation k = 6, find the value of z when x = 18 and y = 3.
  1. A4
  2. B12
  3. C36
  4. D108
26.
Given that z varies as x and inversely as the square of y, with constant of variation k = 6, find the values of y when x = 30 and z = 5.
  1. Ay = ±6
  2. By = 6 only
  3. Cy = ±36
  4. Dy = ±√5
27.
Find ∫(10x4 − 4x + 3x2) dx.
  1. A2x5 − 2x2 − 3x + c
  2. B2x5 − 2x2 + 3x + c
  3. C40x3 − 4 − 6x3 + c
  4. D2x5 − 4x2 − 3x + c
28.
The diagram in the answer space shows an incomplete flowchart to calculate the area (A) of a rectangle with length (l) and breadth (b). Which pair of statements correctly fills the two blank symbols, in order?
Diagram for question 28
  1. AEnter l, b then A = l × b
  2. BA = l × b then Enter l, b
  3. CEnter A then l = A ÷ b
  4. DEnter l, b then A = 2(l + b)
29.
Triangle ABC is mapped onto triangle A₁B₁C₁ by a translation represented by T = 3−3. Which diagram shows triangle A₁B₁C₁ correctly drawn?
Diagram for question 29
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
30.
In the diagram, A, B and C are points on level ground. The bearing of B from A is 032°, angle ACB = 100° and AC = BC. Find the bearing of A from C.
Diagram for question 30
  1. A072°
  2. B212°
  3. C252°
  4. D288°
31.
In the diagram, A, B and C are points on level ground. The bearing of B from A is 032°, angle ACB = 100° and AC = BC. Find the bearing of C from B.
Diagram for question 31
  1. A172°
  2. B212°
  3. C152°
  4. D188°
32.
The functions f and g are defined by f(x) = x − 34 and g(x) = 2x + 1. Find f-1(x).
  1. A4x + 3
  2. Bx + 34
  3. C4x − 3
  4. D4x − 3
33.
The functions f and g are defined by f(x) = x − 34 and g(x) = 2x + 1. Find fg(x).
  1. Ax − 14
  2. Bx − 12
  3. Cx + 22
  4. D2x − 54
34.
The functions f and g are defined by f(x) = x − 34 and g(x) = 2x + 1. Find fg(−3).
  1. A−2
  2. B2
  3. C−1
  4. D−52
35.
The points P and Q have coordinates (2, 6) and (−3, −6) respectively. Find the distance between P and Q.
  1. A13
  2. B√13
  3. C17
  4. D5
36.
The areas of the faces of cubes A and B are 9cm2 and 25cm2 respectively. Find the ratio of their volumes.
  1. A9:25
  2. B3:5
  3. C27:125
  4. D81:625
37.
Write the four inequalities that define the unshaded region R on the diagram.
Diagram for question 37
  1. Ax ≥ 1, x ≤ 5, y ≤ 4, 2x + 3y > 10
  2. Bx > 1, x < 5, y < 4, 2x + 3y ≥ 10
  3. Cx ≥ 1, x ≤ 5, y ≥ 4, 2x + 3y < 10
  4. Dx ≤ 1, x ≥ 5, y ≤ 4, 2x + 3y > 10
38.
The components of the vectors OA and OB are 23 and 42 respectively. Write BA as a column vector.
  1. A2−1
  2. B−21
  3. C65
  4. D−2−1
39.
The diagram shows a sketch of the graph of y = 5 − 4x − x2, cutting the x-axis at A and B. Find the coordinates of the points A and B.
Diagram for question 39
  1. AA(−5, 0), B(1, 0)
  2. BA(−1, 0), B(5, 0)
  3. CA(−5, 0), B(−1, 0)
  4. DA(0, −5), B(0, 1)
40.
The diagram shows a sketch of the graph of y = 5 − 4x − x2. Find the maximum value of y.
Diagram for question 40
  1. A5
  2. B−2
  3. C9
  4. D21
41.
The diagram is a speed-time graph of a moving car. The car decelerates uniformly from a speed of 24m/s to a speed of Vms in 3 seconds. Find the speed V, if the deceleration in the first 3 seconds was 2m/s2.
Diagram for question 41
  1. A18 m/s
  2. B6 m/s
  3. C22 m/s
  4. D12 m/s
42.
From the speed-time graph, the car decelerates from 24m/s to 18m/s in the first 3 seconds and then travels at 18m/s until the 13th second. Calculate the distance covered in the first 13 seconds.
Diagram for question 42
  1. A234 m
  2. B243 m
  3. C180 m
  4. D252 m
43.
From the speed-time graph, the car travels at 18m/s until the 13th second and then decelerates at 3m/s2 until it comes to rest after t seconds. Find the value of t.
Diagram for question 43
  1. A6 s
  2. B16 s
  3. C19 s
  4. D22 s
44.
Describe fully the symmetry of the diagram below, given that OA and OB are two identical arms of a windmill and angle AOB = 90°.
Diagram for question 44
  1. ARotational symmetry of order 4 about O
  2. BRotational symmetry of order 2 about O
  3. COne line of symmetry, along the bisector of angle AOB
  4. DTwo lines of symmetry, along OA and OB