some cxc math mc questions .pdf
TRANSCRIPT
CXC Math Past Paper Type Questions
Math CXC/CSEC Past Paper Type Question Practice
: MATHEMATICS
Paper: 1
Date: 2013
Multiple Choice
INSTRUCTIONS TO CANDIDATES
Each question has four options: A, B, C & D
Clearly indicate your answers
Calculators must not be used
Β©
Caribbean Correspondence School
1. πβπ ππ’ππππ 3.14063 π€πππ‘π‘ππ πππππππ‘ π‘π 3 πππππππ πππππ ππ A) 3.140 B) 3.141 C) 3.146 D) 3.150
2. (β3)2 + (β2)2 = A) β13 B) β10 C) 13 D) 25
3. In scientific notation, 170.04 is written as A) 0.17004 π₯ 103 B) 1.7004 π₯ 102 C) 17.004 π₯ 101 D) 1.7004 π₯ 10β2
4. 0.386 Γ 0.06 = A) 0.02316 B) 0.2316 C) 2.316 D) 23.16
5. πβππ‘ ππ’ππππ π€βππ πππππ π‘π 1 1
3 πππ£ππ 2 ?
A) 13
B) 23
C) 1 D) 3
6. πβπ πΈππ΄πΆπ π£πππ’π ππ 37.26Γ·1.8
1000 ππ
A) 0.207 B) 0.0207 C) 20.7000 D) 20700
7. The H.C.F. of 12, 15 and 60 is A) 3 B) 5 C) 12 D) 60
8. The number 301 can be written as A) 3 Γ 103 + 1 Γ 10 B) 3 Γ 102 + 1 Γ 10 C) 3 Γ 103 + 1 D) 3 Γ 102 + 1
9. πΌπ 3π ππ ππ πππ ππ’ππππ,π€βππβ ππ π‘βπ ππππππ€πππ ππ ππ ππ£ππ ππ’ππππ?
A) 3π β 1 B) 3π β 2 C) 3π + 2 D) 3π + 2π
10. 25 Γ 130 ππ π‘βπ π πππ ππ A) (25 Γ 100) + 30 B) (25 + 30) Γ 100 C) (25 Γ 30) + (25 Γ 100) D) (100 Γ 30) + (100 Γ 25)
11. πΌπ π ππππ π ππ 32 π π‘π’ππππ‘π , 17 π π‘π’ππ¦ ππ’π ππ πππ 20 π π‘π’ππ¦ π΄ππ‘.πβππ‘ ππ π‘βπ πΏπΈπ΄ππ ππ’ππππ ππ π π‘π’ππππ‘π π€βπ πππ π π‘π’ππ¦πππ π΅πππ» ππ’π ππ πππ π΄ππ‘?
A) 3 B) 5 C) 12 D) 15
12. πΌπ π = {π, π, π} π‘βππ π‘βπ ππ’ππππ ππ π π’ππ ππ‘π ππ π ππ A) 8 B) 6 C) 4 D) 3
13. πΌπ π {πΉπππ‘πππ ππ 6} πππ π {πΉπππ‘πππ ππ 4}, π‘βππ π‘βπ π βππππ ππππππ ππππππ πππ‘π A) { } B) {1,2} C) {4,6,8, . . . } D) {12,24,36, . . . . }
14. πΌπ ππ$6.00 ππ πππ’ππ£πππππ‘ π‘π ππ$1.00, π‘βππ ππ$15.00 ππ π. π.πππππππ ππ A) $0.25 B) $0.40 C) $2.50 D) $4.00
15. 3 ΒΌ % ππ $500 ππ A) $ 1.62 B) $15.52 C) $16.00 D) $16.25
16. πΌπ π π π€πππ‘π πππ π‘ π ππππ‘π , π‘βππ π‘βπ πππ π‘ ππ πππ π π€πππ‘ ππ A) π
π ππππ‘π
B) ππ ππππ‘π C) π
π ππππ‘π
D) (π β π ) ππππ‘π
17. π΄ π ππππ πππ ππ ππππ 5% ππ βππ π ππππ ππ ππππππ π πππ.π»ππ π ππππ πππ πππ π‘ ππππ‘β π€πππ $2020.π»ππ€ ππ’πβ ππππππ π πππ π€ππ βπ ππππ?
A) $11.00 B) $20.00 C) $101.00 D) $110.00
18. π»ππ€ ππ’πβ ππππ π ππ’π π‘ππππ πππ¦ πππ ππ πππ‘ππππ ππππππ ππ‘ $50.00 ππ π ππππ π‘ππ₯ ππ 6% ππ c
harged? A) $56.00 B) $53.00 C) $47.00 D) $44.00
19. π΄ π‘ππππ ππ π πππ ππ βπππ ππ’ππβππ π.πβπ π πππ πππππ ππππ ππ π‘π ππ π πππππ ππ‘ ππ $306 πππ π ππ₯ mo
nthly instalments of $60 each. How much does a customer pay for the table? A) $360 B) $366 C) $666 D) $966
20. A loan of $8000 was repaid in 2 years in monthly payments of $400.00. The interest on the loan,
as a percentage, was A) 5% B) 8% C) 16% D) 20%
21. A man pays 60 cents for every 200 π3 of gas used, plus a fixed charge of $13.75. How much
does he pay when he uses 55000π3 of gas? A) $178.75 B) $175.25 C) $165.00 D) $151.25
22. πβπ ππππππ π‘πππ ππ π‘βπ ππ₯ππππ π πππ ππ (π₯ + 3)(π₯ β 1) ππ A) 2 B) 3 C) 2π₯ D) 4π₯
23. 5(π₯ + π¦) β 3(π₯ β π¦) = A) 2π₯ B) 2π₯ + 2π¦ C) 2π₯ + 8π¦ D) 8π₯ + 8π¦
24. 4π₯
7π¦ + 3π₯
5π¦ πππ¦ ππ π€πππ‘π‘ππ ππ
A) 41π₯
35π¦
B) 41π₯
2
35π¦
C) 41π₯π¦
35π¦
D) 20π₯ + 21π¦
35π¦
25. Iπ π β π = π/π β 1, π‘βππ 7 β 28 = A) 3
4
B) ΒΌ C) 3 D) 4
26. πΊππ£ππ 2π₯ + 3 β₯ 9, π‘βπ πππππ ππ π£πππ’ππ ππ π₯ ππ A) π₯ > 6 B) π₯ β₯ 6 C) π₯ > 3 D) π₯ β₯ 3
27. Iπ π₯ = β2,π¦ = 3, π‘ = 2, π‘βππ οΏ½π₯π¦οΏ½π‘
=
A) β49
B) 49
C) 4
3
D) 9
4
28. When 6 is added to a number and the sum is divided by three, the result is four. This statement written in mathematical symbols is
A) 6+π₯
3= 4
B) 63
+ π₯ = 4
C) (6+π₯)3
= 43
D) 6 + π₯3
= 4
29. The values of π₯ and π¦ which satisfy the equations π₯ + 2π¦ = 27 πππ 2π₯ β π¦ = 19 are respectively
A) 15 and 10 B) 10 and 15 C) 7 and 13 D) 13 and 7
30. The volume of a cube of edge 10cm is A) 30ππ3 B) 100ππ3 C) 300ππ3 D) 1000ππ3
31. 2500 millimetres expressed in metres is A) 0.25 B) 2.5 C) 25 D) 250
32. A boy leaves home at 09:15 hours and arrives at school at 10:05 hours. If he travels non- stop at
an average speed of 6 ππββ1, what is the distance, in km, of his home from school? A) 2km B) 5km C) 6km D) 9km
33. The distance around the edge of a circular pond is 88m. The radius, in metres, is A) 176π B) 88π C) 88
π
D) 88
2π
34. A man leaves home at 22:15 hrs and reaches his destination in the same time zone at 04:00 hrs on the following day. How many hours did the journey take?
A) 5 B) 5 3
4
C) 6 D) 6 1
4
35. AOB is a sector of a circle such that angle π΄ππ΅ = 60Β° and OB is r units long. The area of AOB
is A) 1
3ππ
B) 1
6ππ
C) 1
3ππ2
D) 1
6ππ2
36. The area of a triangle is 30 ππ2 πππ ππ‘π πππ π ππ 10ππ2. What is the perpendicular height, in cm,
of the triangle? A) 6 B) 12 C) 13 D) 17
37. The median of the numbers: 1, 1, 5, 5, 6, 7, 7, 7, 8 is A) 5.4 B) 6 C) 6.5 D) 7
38. Six hundred students write an examination. The probability of a randomly selected student failing
the examination is 15
How many students are expected to pass A) 120 B) 480 C) 500 D) 600
39. The lengths of 30 cabbage leaves were measured, to the nearest cm, and the information grouped as shown in the table below. Length of Leaf (cm
10 β 14 15 -19 20 β 24 25 β 29
Frequency 3 8 12 7
The limits of the class intervals are
A) 3, 8, 12, 7 B) 5, 5, 5, 5 C) 9.5, 14.5, 19.5, 24.5, 29.5 D) 10, 14, 15, 19, 20, 24, 29
40. Each of the letters of the word, β CHANCEβ is written on a slip of paper similar in size and
shape. The slips of paper are then placed in a bag and thoroughly shaken. What is the probability of drawing a letter C?
A) 16
B) 1
5
C) 1
3
D) 2
3
41. Which of the following represents the equation of a straight line? A) π¦ = 2π₯ + 3 B) π¦ = 4
π₯
C) π¦ = π₯2 β 4 D) π¦ = π₯2 + 2π₯ β 5
42. What percentage of 340 is 425? A) 80% B) 85% C) 125% D) 152%
43. Ann and Betty shared a sum of money in the ratio 2 : 3 respectively. Ann received $120
What was Bettyβs share? A) $ 72 B) $ 80 C) $ 180 D) $ 300
44. 11.1 Γ· 0.01 ππ πππ’ππ π‘π A) 110 B) 111 C) 1100 D) 1110
45. If 60% of a number is 90, what is the number? A) 30 B) 54 C) 150 D) 180
46. β οΏ½12οΏ½3 is the same as
A) β18
B) β16
C) 18
D) 16
47. What is the LEAST number of plums that can be shared equally among 6, 9, or 12 children? A) 27 B) 36 C) 54 D) 72
48. Which of the following sets is equivalent to {a, b, c, d} A) {4} B) {a, b, c} C) {p, q, r, s } D) {1, 2, 3, 4, 5 }
49. Which of the following sets defined by {π₯ β π:β2 β€ π₯ β€ 4} ? A) {1, 2, 3, 4 } B) {0, 1, 2, 3, 4 } C) {-1, 0, 1, 2, 3 } D) {-2, -1, 0, 1, 2, 3, 4}
50. 3 1
4% of $ 500 is
A) $1.62 B) $15.52 C) $16.00 D) $16.25
51. During a sale, a shop allows 20% discount off the marked price of clothing. What will a
customer pay for a dress with a marked price of $30 A) $10 B) $20 C) $24 D) $30
52. A man bought a calf for $200 and sold it for $250. What was his gain as a percentage of the cost price?
A) 5% B) 15% C) 20% D) 25%
53. How much does a customer pay for an article marked at $50.00 before taxes, if a sales tax of 6%
is charge ? A) $56.00 B) $53.00 C) $47.00 D) $44.00
54. At the end of any year a car worth 5% less than what it was worth at the beginning of the year. If
a car was bought for $10000 in January 2009, its value in December 2009 was A) $9000 B) $9025 C) $9500 D) $9995
55. If the simple interest on $800 for 3 years is $54, what is the rate of interest per annum? A) 4
9%
B) 2 14
% C) 5% D) 44%
56. A man pays 60 cents for every 200π3 of gas used, plus a fixed charge of $13.25. How much
does he pay when he uses 55000π3 of gas? A) $178.25 B) $175.25 C) $165.00 D) $151.25
57. If $7000 is borrowed at the rate of 5% per annum for 3 years, the simple interest is A) $ 105 B) $ 210 C) $ 370 D) $ 1050
58. 45π₯
+ 25π₯
= A) 6
25π₯
B) 8
25π₯
C) 6
10π₯
D) 6
5π₯
59. (π₯ β 2)(3π₯ + 4) = A) π₯2 β 6π₯ β 8 B) 3π₯2 β 2π₯ β 8 C) 3π₯2 + 10π₯ + 8 D) 3π₯2 β 10π₯ + 8
60. If 5π₯ β 26 = π₯ + 50, then the value of π₯ ππ A) -12 B) 16 C) 6 D) 19
61. 3π₯2 Γ 2π₯3 = A) 6π₯5 B) 6π₯6 C) 5π₯6 D) 72π₯5
62. π = π2
2βπ.π€βππ π = 3, π‘βπ π£πππ’π ππ π ππ
A) 9 B) 9
5
C) β65
D) β6
63. John has π₯ marbles and Max has twice as many. Max gives John 5 of his marbles. How many marbles does Max now have?
A) π₯ + 5 B) π₯ β 5 C) 2π₯ + 5 D) 2π₯ β 5
64. ππ 3 + 2π₯
= 1, π‘βππ π‘βπ π£πππ’π ππ π₯ ππ A) -1 B) 1
5
C) 1 D) 5
65. How many kilograms are there in one tonne A) 10 B) 100 C) 1000 D) 10000
66. The area of a rectangle is 53.6ππ2. If the length is multiplied by four and the width is halved, the
area would then be A) 26.8ππ2 B) 53.6ππ2 C) 107.2ππ2 D) 214.4ππ2
Item 39 refers to the table below showing the frequency of scores obtained by students in a test.
Score 2 3 5 6 8 11
Students 8 4 6 3 12 2
67. The modal score is A) 8 B) 9 C) 10 D) 12
68. The perimeter of a square is 48cm. What is the area in ππ2 A) 36 B) 72 C) 108 D) 144
69. The mean of the following numbers is 15
14, 10, 18, c, 21, 15, 14 The value of c is
A) 13 B) 14 C) 20 D) 91
70. A bag contains 2 red, 4 yellow and 6 blue balls. The probability of drawing a blue ball from the bag at random is
A) 16
B) 1
3
C) 1
2
D) 6
11
71. If π(π₯) = 2π₯2 β 1, π‘βππ π(β3) = A) 32 B) -19 C) 17 D) 35
72. What is the gradient of the straight line 2π¦ + 3π₯ = β8? A) -3 B) β3
2
C) 23
D) 3
73. Which of the following sets is represented by the relation π: π₯ β π₯2 + 3 ? A) {(0, 3),(1, 4),(2, 7),(3, 12)} B) {(0, 3),(1, 5),(2, 7),(3, 9)} C) {(0, 3),(1, 4),(2, 5),(3, 16)} D) {(0, 3),(1, 1),(2, 4),(3, 9)}
74. Written in scientific notation, 0.045 Γ 10β3 A) 4.5 Γ 10β6 B) 4.5 Γ 10β5 C) 4.5 Γ 10β4 D) 4.5 Γ 10β1
75. What percentage of 30 is 6? A) 5% B) 18% C) 20% D) 150%
76. What is the value of the digit 2 in the number 48.621? A) 2
100
B) 210
C) 2 D) 200
77. The simple interest on $400 at 5% per annum for 2 years is A) $ 400Γ5Γ2
100
B) $ 400Γ5
2Γ100
C) $(400Γ2)
5Γ100
D) $ 400Γ100
2Γ5
78. During a sale, a shop allows 20% discount off the marked price of clothing. What will a customer
pay for a dress with a marked price of $30? A) $10 B) $20 C) $24 D) $30
79. In the Venn diagram, n(P) = 5, n(Q) =9 and π(π βͺ π) = 10. what is π(π β© π)? A) 4 B) 6 C) 14 D) 24
80. Tom bought a pen for $60 and sold it to gain 20% on his cost price. How much money
did he gain? A) $12 B) $40 C) $72 D) $80
81. Susan bought a calculator for $120. She had to pay a sales tax of 10% on the price. How much
change would she receive from $140? A) $8.00 B) $12.00 C) $28.00 D) $32.00
82. Marry invested $200 for 3 years at 5% per annum. John invested %300 at the same rate. If they
both received the same amount of money in interest, for how many years did John invest his money?
A) 1 12
B) 2 C) 3 D) 10
83. A company employs 12 gardeners at $26 per day, and 8 clerks at $17 per day. What is the mean daily wage, in dollar, of the 20 employees?
A) $20.00 B) $21.50 C) $22.40 D) $31.50
84. If the simple interest on $800 for 3 years is $54, what is rate of interest per annum? A) 4
9%
B) 2 14
% C) 5% D) 44%
85. Given that π β π = 2π β 3π then 2 β (β3) = A) -7 B) -5 C) 3 D) 13
86. If 20π β 16 = 12(3 β π), π‘βππ π = A) 5
8
B) 21
16
C) 13
8
D) 5
2
87. 2(π2π)3 = A) 2π5π3 B) 2π6π3 C) 6π2π D) 8π6π3
88. For all of π πππ π, 3π(π + 2π)β π(2π β 3π) = A) 3π2 β ππ + 3π2 B) 3π2 + 4ππ + 3π2 C) 3π2 + 4ππ β 3π2 D) 3π2 + 8ππ β 3π2
89. Which of the following represent the statement βthe Difference of two square numbers is
positiveβ? A) π₯2 β π¦2 > 0 B) 2π₯ β 2π¦ > 0 C) (π¦ β π₯)2 > 0 D) 2(π¦ β π₯) > 0
90. On leaving Trinidad, the time on a pilots watch was 23:00hrs. When he arrived at his destination, in the same time zone, on the following day his watch showed 03:00hrs. How many hours did the flight take?
A) 4 B) 30 C) 26 D) 52
91. The circumference of a circle is 132cm. Given that π = 22
7 , the radius of the circle in centimetres
, is A) 42 B) 21 C) β42 D) β21
92. The marks obtain by ten students in a test mark out of 25 were: 14, 22, 15, 19, 19, 16, 24, 13, 20, 19 The range of marks was A) 11 B) 13 C) 18 D) 19
93. If the mean of the four numbers 4, 8,π₯,πππ 12 is 10 then π₯ ππ A) 4 B) 10 C) 12 D) 16
94. If π(π₯) = π₯2 β π₯ β 1 , π‘βππ π(β5) = A) -31 B) 24 C) 29 D) 31
95. The range of π: π₯ β π₯3 for the domain {-2, -1, 0, 1, 2} is A) {0, 1, 8} B) {-2, -1, 0, 1, 2} C) {-6, -3, 0, 3, 6} D) {-8, -1, 0, 1, 8}
96. A boat was travelling on a bearing of 270Β°. In what direction was it travelling ? A) West B) East C) North D) South
97. The image of a point P(-2, 3) under a translation οΏ½34οΏ½ is
A) (-6, 12) B) (-5, -1) C) (5, 1) D) (1, 7)
A boy stands 12 metres from the foot of the building and observes the angle of elevation of the top of the building.
98. The height of the building is approximately A) 12π‘ππ40Β° B) 1.6 + 12π ππ40Β° C) 1.6 + 12πππ 40Β° D) 1.6 + 12π‘ππ40Β°