Name:
ACHIMOTA SCHOOL Index Number:
MOCK
MATHEMATICS (CORE) 1
SHS 2 – December, 2022
Duration: 1½ HOURS.
Do not open this booklet until you are told to do so. While you are waiting, read
and observe the following instructions carefully. Write your name and index
number in ink in the spaces provided above.
This booklet consists of one paper. Answer this booklet on your shading sheet.
This paper will last for 1½ Hours after which the objective sheet will be collected.
(𝑝−𝑟)2 −𝑟 2
1. Simply the expression 2𝑝2 −4𝑝𝑟
1 1 2
A. 2 B. 𝑝−2𝑟 C. 𝑝−2𝑟 D. 𝑝 − 2𝑟
2. The relation 𝑦 = 𝑥 2 + 2𝑥 + 𝑘 passes through the point (2, 0). Find the value of k.
A. -8 B. -4 C. 4 D. 8
3. Redeemer is n years old. Her brother’s age is 5 years more than half of her age. How old is
𝑛 5 𝑛 𝑛 𝑛
her brother? A. 2 + 2 B. 2 + 5 C. 2 − 5 D. 5 − 2
4.
m n
From the diagram which of the following statement is true?
A. m + n + p = 180o B. m + n = 180o
C. m = p + n D. n = m + p
5. If cos 𝜃 = 𝑥 and sin 60⁰ = 𝑥 + 0.5, 𝑤ℎ𝑒𝑟𝑒 0⁰ ≤ 𝜃 ≤ 90⁰ . Find the value of 𝜃, to the
nearest degree. A. 66o B. 67o C. 68o D. 69o
Use the following information to answer Questions 6 to 8.
A pie chart was drawn to represent the monthly expenditure of a school budget for the period
January to June 2020. The angles for the six sectors of the pie chart are; 50o , 54o , 73o , xo ,
59o and 70o . The total amount spent for that period was Ghc511,200.00.
6. Calculate the amount spent in January
A. Ghc7100.00 B. Ghc76.680.00 C. Ghc99,400.00 D. 103,660.00
7. What was the highest amount spent during this period?
A. Ghc7100.00 B. Ghc83,780.00 C. Ghc99,400.00 D. 103,660.00
8. What was the average amount spent by the school from January to June?
A. Ghc42,600.00 B. Ghc82,500.00 C. Ghc85,200.00 D. 102,240.00
9. Calculate the perimeter, in cm of a sector of a circle of radius 8 cm and angle 45°
subtended at the centre.
A. 2𝜋 𝑐𝑚 B. 8 + 2𝜋 𝑐𝑚 C. 18 + 2𝜋 𝑐𝑚 D. 16 + 2𝜋 𝑐𝑚
10. Find the equation of the line parallel to 2𝑦 = 3(𝑥 − 2) and passes through the point (2, 3)
A. 3𝑦 = − 2𝑥 B. 2𝑦 = 3𝑥 C. 3𝑦 = 2𝑥 − 6 D. 2𝑦 = 3𝑥 – 6
11. At what values of x on the graph is 𝑥 2 − 7𝑥 + 6 = 0 ?
A. x =-2 and -3 B. x = -6 and -1 C. x = 1 and 6 D. x = 2 and 3
12. If log 2 = 0.3010 log 2𝑦 = 1.8060 and , find correct to the nearest whole number, the value of y.
A. 7 B. 6 C. 5 D. 4
13. If the mean of the numbers 5, 8, 𝑥, 12, (𝑥 + 5) and 10 is 10. Find the value of 𝑥.
A. 6 B. 10 C. 8 D. 60
14. Which of the following lines are parallel?
I. 5𝑦 + 3𝑥 + 1 = 0 II. 3𝑦 + 5𝑥 + 1 = 0 III. 6𝑥 − 7 + 10𝑦 = 0
A. I and III only B. I and II only
C. I, II, III D. II and III only
15. The statement 5 + 𝑝q = 5 + 𝑞p illustrates that
A. addition is associative B. multiplication is associative
C. addition is commutative D. multiplication is commutative.
16. Given that 𝜇 = {1, 2, 3, … ,10} 𝑃 = {𝑥: 𝑥 𝑖s prime} and 𝑄 = {𝑦: 𝑦 is odd} , find 𝑃′ ∩ 𝑄 .
(A) {3,5,7} (B) {4,,6,8,10} (C) {2} (D) {1,9}
17. Which of the following is used to determine the mode of a grouped data?
A. Bar Chart B. Frequency Polygon
C. Ogive D. Histogram
The marks obtained by students in class exercise were 2, 6, 4, 3, 3, 4, 5, and 7.
Use this information to answer questions 17 and 18.
18. Find the semi-interquartile range of the data 2, 6, 4, 3, 3, 4, 5, 7
A. 1 B. 2 C. 3 D. 4
19. Calculate the variance to 2 decimal places
A. 2.42 B. 2.43 C. 2.44 D. 2.45
20. Evaluate 10012 – 1
A. 1002 B. 10020 C. 100200 D. 1002000
21. A cyclist covers 900m in 5 minutes. What is his average speed in kmh-1.
A. 10.8 B. 75.0 C. 108.0 D. 180.0
The diagram below shows a sector of a circle of radius 14 cm. The angle of the sector is 270o
The sector is folded to form a cone.
2700
Use this information to answer questions 22 and 23.
22. Find the radius of the cone
A. 73.5 cm B. 28 cm 14 cm D. 10.5 cm
23. Calculate the surface area of the cone.
A. 462 cm2 B. 616 cm2 C. 1232 cm2 D. 3234 cm2 .
24. Determine the least value of y such that 7 + y = 3(mod8).
A. 3 B. 4 C. 5 D.6
25. Given that log 2 3 = 𝑚2 and log 3 2 = 𝑛2 .
Express log 2 81 − log 3 512 in terms of 𝑚 and 𝑛.
A. 4𝑚2 + 9𝑛2 B. 9𝑛2 − 4𝑚2 C. (2𝑚 + 3𝑛)(2𝑚 − 3𝑛) D. (4𝑚 − 9𝑛)2
1
26. Given that 82−3𝑛 = 2𝑛+2 , find the value of 𝑛.
4 2
A.− 5 B. -1 C. 1 D. 5
2𝑥−1
27. State the domain of the function 𝑓(𝑥) = .
√3𝑥−9
1
A. {𝑥: 𝑥 ∈ 𝑅, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑥 = 2 } B. {𝑥: 𝑥 ∈ 𝑅, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑥 = 3 }
C. {𝑥: 𝑥 ∈ 𝑅, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑥 < 3 } D. {𝑥: 𝑥 ∈ 𝑅, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑥 ≤ 3 }
28. The graph of 𝑦 = 2𝑝𝑥 2 − 𝑝2 𝑥 − 14 passes through the point (3, 10). Find the values of p.
A. 2 and -4 B. -2 and 4 C. 2 and 4 D. -2 and -4
From the diagram below
400
(13𝑥 − 20)⁰
29. Find the value of x. A. 100 B. 200 C. 1100 D. 1300
30. the image of the point u (-2, 3) under a translation by a vector T is (-5, 5). Find the
image of the point v (3, 7) under a translation by the vector T.
A. (-2, 12) B. (0, 5) C. (0, 9) D. (6, 5)
31. Express the true bearing of 230o as a compass bearing.
A. S50oE B. S54oE C. N54oE D. S36oW
32. Solve the equation 81𝑦 = 3𝑦−5 × 3√3.
−7 −3 −5
A. B. C. D. -1
6 2 7
33. Given that 𝐴𝐵 ⃗⃗⃗⃗⃗ = (−4). Find the magnitude of 𝐵𝐶
⃗⃗⃗⃗⃗ = (3) and 𝐶𝐴 ⃗⃗⃗⃗⃗ .
2 −1
A. √58 B. √2 C. √17 D. √13
34.
P Q
𝑥
𝑦
R S
In the diagram PQ⫽RS. Given that 𝑥 ∶ 𝑦 = 2 ∶ 7. Find the value of y.
A. 40o B. 140o C. 51.4o D. 128.6o
1
35. Given that the gradient of the line joining the points 𝑃(7, 𝑢 + 4) and 𝑄(𝑢, 14) is 2.
−43 43
calculate the value of 𝑢. A. B. C. 9 D. -9
3 3
36. If the mean of 2, 4, x, 5 and 8 is 6, what is the sum of 5, 8, x, 2, 12 and 4?
A. 11 B. 31 C. 42 D. 30
37. A man will be (𝑥 + 10) years old in 8 years time. If 2 years ago he was 63 years, find the
value of 𝑥. A. 67 B. 57 C. 55 D. 63
38. If events 𝐴 and 𝐵 are such that (𝐴) + (𝐵) = 𝑃(𝐴 ∪ 𝐵), then 𝐴 and 𝐵 are
A. Mutually exclusive B. Independent events
C. Dependent events D. Simple events
39. P is a point 2m above the ground and 15m away from a tower. The angle of elevation of
the tower from P is 65°. Calculate the height of the tower, correct to 2 decimal
places. A. 8.33m B. 15.59m C. 15.17m D. 34.17m
40. Given that cos(2𝑥 + 15°) = sin(𝑥 − 30°), where 0⁰ ≤ 𝑥 ≤ 90⁰. Find the value of x.
A. 35⁰ B. 15⁰ C. 105⁰ D. 120⁰
41. How many terms of the arithmetic progression (A.P) 3, 7, 11, 15, … must be added
together to produce a total of 300?
A. 14 B. 12 C. 10 D. 8
42. If F(n) denotes the set of factors of natural number, including n but excluding 1, find a
number p such that F(12) ∩ F(18) = F(p).
A. 2 B. 3 C. 6 D. 18
43. If 𝑝 ∶ 𝑞 = 𝑟 ∶ 𝑠, then (𝑝 + 𝑞) ∶ (𝑟 + 𝑠) is equal to
A. 𝑝𝑠 ∶ 𝑞𝑟 B. 𝑝𝑞 − 𝑟𝑠 C. 𝑞 ∶ 𝑠 D. (𝑟 ∶ 𝑠) − (𝑝 ∶ 𝑞)
44. If 3124 + 52x = 96 find the value of x.
A. 5 B. 6 C. 7 D. 8
1
45. The sum of two numbers is 15. One of the number is 1 2 times the other. Find the bigger
number. A. 6 B. 9 C. 10 D. 12
46. Redeemer and Racheal entered into a business partnership and agreed to share the profit
in the ratio 4:5 respectively . If Redeemer received GH₵5,000.00 less than Racheal, how
much profit did they make?
A. GH₵30,000.00 B. GH₵40,000.00 C. GH₵35,000.00 D. GH₵45,000.00
47. Solve for the equation 3log(2 + 𝑥) = log 27
A. 7 B. 22 C. 1 D. 25
48. Two points A and B are on bearing 140o and 050o respectively from a point O.
If |𝑂𝐴| = 7𝑚 and |𝑂𝐵| = 4𝑚. Find the bearing of A from B.
A. 350o B. 170o C. 080o D. 060o
49. Find the product of 11012 and 1112
A. 11010112 B. 10111012 C. 1110012 D. 10110112
50. Find the image of the point A(2 , 3) under a reflection in the line x = 4.
A. (2, 7) B. (8, 3) C. (3, 6) D. (6, 3)
End of Paper
Mathematics Department
