Save as PDF or print — the answers and worked solutions live online, where your work gets marked free.
Back to the paper

Examinations Council of Zambia — past paper

ECZ 2020 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Use set notation to describe the shaded region in the diagram below
Diagram for question 1
  1. AQ∩R
  2. BP∩Q∩R
  3. C(Q∩R)∩P′
  4. D(Q∪R)∩P′
2.
Simplify 2a + (b - a) - 2b.
  1. Aa - b
  2. Ba - 3b
  3. C3a - b
  4. Da + b
3.
Evaluate 64125-13.
  1. A45
  2. B54
  3. C-1.25
  4. D12564
4.
Given that the lines 3y = x + 6 and y = kx + 12 are perpendicular, find the value of k.
  1. A13
  2. B-3
  3. C-0.333333333
  4. D3
5.
Factorise completely 6ax - 4ay - 3bx + 2by.
  1. A(3a - 2b)(2x - y)
  2. B(2a - b)(3x + 2y)
  3. C(2a - b)(3x - 2y)
  4. D(2a + b)(3x - 2y)
6.
Given that A is the point (-2, 1) and B is the point (1, 5), find |AB|.
  1. A7 units
  2. B5 units
  3. C25 units
  4. D3 units
7.
Given that A = 2310, B = -10x2 and C = 76-10, find (a) CT,
  1. A70-16
  2. B-1706
  3. C7-160
  4. D76-10
8.
Given that A = 2310, B = -10x2 and C = 76-10, find (b) x for which AB = C.
  1. A1
  2. B7
  3. C3
  4. D-3
9.
Given that the 11th term of an arithmetic progression is 43 and that the first term is 3, find the (a) common difference,
  1. A3
  2. B4.3
  3. C4
  4. D40
10.
Given that the 11th term of an arithmetic progression is 43 and that the first term is 3, find the (b) 4th term.
  1. A19
  2. B12
  3. C15
  4. D16
11.
A plane flying at a speed of 900 knots takes 5 hours to fly from town A to town B. Calculate the distance between the two towns.
  1. A4 500 knots
  2. B4 500 nautical miles
  3. C180 nautical miles
  4. D900 nautical miles
12.
Point Q on longitude 85°E lies on the equator and is due east of P. The time difference between P and Q is 5 hours. Calculate the longitude on which P lies.
  1. A10°W
  2. B85°W
  3. C10°E
  4. D160°E
13.
The probability of a girl not wearing a neck tie is 0.55. What is the probability that the same girl will wear a neck tie?
  1. A0.55
  2. B1.55
  3. C0.275
  4. D0.45
14.
Given that 8x - 1 = 16, find the value of x.
  1. A3
  2. B43
  3. C7
  4. D73
15.
Given that S = {x: 1 < x ≤ 15, x is a prime number}, list the elements of set S.
  1. A{3, 5, 7, 11, 13}
  2. B{1, 2, 3, 5, 7, 11, 13}
  3. C{2, 3, 5, 7, 11, 13}
  4. D{2, 3, 5, 7, 9, 11, 13}
16.
The diagram below shows a right square pyramid ABCDE of base 6cm and EF = 5cm. Calculate the total surface area of the triangular faces of the pyramid.
Diagram for question 16
  1. A60 cm2
  2. B90 cm2
  3. C120 cm2
  4. D30 cm2
17.
A function f is defined by f(x) = 2x - 5. Find f-1(x).
  1. Ax + 52
  2. Bx - 52
  3. C2x + 5
  4. D2x + 52
18.
A function f is defined by f(x) = 2x - 5. Find ff-1(2).
  1. A2
  2. B-3
  3. C9
  4. D72
19.
A function f is defined by f(x) = 2x - 5. Find the value of x for which ff(x) = x.
  1. A0
  2. B53
  3. C15
  4. D5
20.
The diagram below shows two figures P and Q on the XOY plane. Describe fully the single transformation that maps P onto Q.
Diagram for question 20
  1. ATranslation by 0-4
  2. BReflection in the x-axis
  3. CReflection in the line y = 2
  4. DRotation 180° about (3, 2)
21.
Given that y = 2x3 - 4x2, find dydx.
  1. A6x2 + 8x
  2. B2x2 + 8x3
  3. C6x2 - 8x3
  4. D6x2 + 8x3
22.
The diagram below shows three points O, A and B in which OB = AB. Given that the bearing of A from O is 030° and angle ABO = 40°, calculate the bearing of (a) B from A.
Diagram for question 22
  1. A140°
  2. B100°
  3. C320°
  4. D220°
23.
The diagram below shows three points O, A and B in which OB = AB. Given that the bearing of A from O is 030° and angle ABO = 40°, calculate the bearing of (b) O from B.
Diagram for question 23
  1. A280°
  2. B100°
  3. C140°
  4. D320°
24.
The values of x and y are given to 1 decimal place as x = 4.2 and y = 7.3. Find the maximum value of x + y.
  1. A11.7
  2. B3.1
  3. C11.5
  4. D11.6
25.
The values of x and y are given to 1 decimal place as x = 4.2 and y = 7.3. Find the minimum value of x - y.
  1. A3.2
  2. B-3.1
  3. C-2.9
  4. D-3.2
26.
It is given that y varies inversely as the square of x. The table below shows some values of x and corresponding values of y. x2b6y94a Find the value of k, the constant of variation.
  1. A4.5
  2. B72
  3. C36
  4. D18
27.
It is given that y varies inversely as the square of x. The table below shows some values of x and corresponding values of y. x2b6y94a Find the value of a.
  1. A1
  2. B9
  3. C6
  4. D36
28.
It is given that y varies inversely as the square of x. The table below shows some values of x and corresponding values of y. x2b6y94a Find the values of b.
  1. Ab = 3 or b = -3
  2. Bb = 9 or b = -9
  3. Cb = 3
  4. Db = 6 or b = -6
29.
In the diagram below, A, B, C, and D lie on the circumference of the circle, centre O. Given that ∠BAD = 47° and ∠DBC = 28°, calculate (a) ∠BOD.
Diagram for question 29
  1. A94°
  2. B86°
  3. C47°
  4. D133°
30.
In the diagram below, A, B, C, and D lie on the circumference of the circle, centre O. Given that ∠BAD = 47° and ∠DBC = 28°, calculate (b) ∠OBD.
Diagram for question 30
  1. A43°
  2. B47°
  3. C86°
  4. D68°
31.
In the diagram below, A, B, C, and D lie on the circumference of the circle, centre O. Given that ∠BAD = 47° and ∠DBC = 28°, calculate (c) ∠BDC.
Diagram for question 31
  1. A28°
  2. B19°
  3. C133°
  4. D47°
32.
The diagram below shows a right angled triangle PQR. Given that PQ = 15 cm and cos x° = 23, calculate the length of QR.
Diagram for question 32
  1. A22.5 cm
  2. B10 cm
  3. C7.5 cm
  4. D5 cm
33.
A straight line L has equation 3y = 5x - 6. Find the y co-ordinate of the point where L cuts the y-axis.
  1. A-6
  2. B-2
  3. C53
  4. D2
34.
Rectangle ABCD and DAEF are geometrically similar. Given that AB = 10 cm and AD = 4 cm, calculate the area of rectangle DAEF.
Diagram for question 34
  1. A4 cm2
  2. B16 cm2
  3. C6.4 cm2
  4. D8 cm2
35.
Mrs Kalomba bought 120 shares at a nominal value of K40.00 each which she later sold at K42.50 each. Find her profit.
  1. AK300.00
  2. BK5 100.00
  3. CK4 800.00
  4. DK30.00
36.
On the diagram in the answer space, shade three more triangles to make a pattern with rotational symmetry of order 3.
Diagram for question 36
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
37.
Simple interest is given by the formula I = PTR100. Complete the flow chart in the answer space below for calculating simple interest.
Diagram for question 37
  1. AInput I; P = I*100TR
  2. BInput P, T and R; I = P*T*R100
  3. CInput P and R; I = P*R100
  4. DInput P, T and R; I = P+T+R100
38.
In the diagram below, point A is (1, 1), B is (0, 7), C is (14, 0), D is (7, 0) and E is (7, 1). Write down the four inequalities that define the unshaded region R.
Diagram for question 38
  1. Ay ≥ 1; x > 7; y < x; x + 2y ≤ 14
  2. By ≥ 1; x < 7; y < x; x + 2y ≤ 14
  3. Cy ≤ 1; x < 7; y < x; x + 2y ≤ 14
  4. Dy ≥ 1; x < 7; y > x; x + 2y ≤ 14
39.
Solve the equation x2 - 7x = 8.
  1. Ax = 8 or x = 1
  2. Bx = 7 or x = -1
  3. Cx = 4 or x = -2
  4. Dx = 8 or x = -1
40.
The diagram below is the graph of y = -4x - 122 + 9. Find the (i) x coordinates of A and B.
Diagram for question 40
  1. AA = -1 and B = 1
  2. BA = -2 and B = 1
  3. CA = -1 and B = 2
  4. DA = 1 and B = -2
41.
The diagram below is the graph of y = -4x - 122 + 9. Find the (ii) coordinates of C.
Diagram for question 41
  1. A(0, -8)
  2. B(12, 9)
  3. C(0, 9)
  4. D(0, 8)
42.
A sprinter runs a race of 200m. Her total time for running the race is 25 seconds ending at U m/s. Below is a sketch of the motion of the sprinter. Calculate the (a) acceleration in the first 4 seconds.
Diagram for question 42
  1. A9 m/s2
  2. B2.25 m/s2
  3. C4 m/s2
  4. D36 m/s2
43.
A sprinter runs a race of 200m. Her total time for running the race is 25 seconds ending at U m/s. Below is a sketch of the motion of the sprinter. Calculate the (b) distance covered in the first 20 seconds.
Diagram for question 43
  1. A200 m
  2. B180 m
  3. C144 m
  4. D162 m
44.
A sprinter runs a race of 200m. Her total time for running the race is 25 seconds ending at U m/s. Below is a sketch of the motion of the sprinter. Calculate the (c) value of U.
Diagram for question 44
  1. A4.2 m/s
  2. B6.2 m/s
  3. C9 m/s
  4. D7.6 m/s