3. 1) (a) Determine the EXACT value of
3 2
1
4 5
2 1
3 1
5 4 (3 marks)
1.75
(b) 1.7 2 giving your answer correct to 2 significant figures. (3 marks)
15
(c) 4.25 0.25 0.0225 giving your answer correct to 2 decimal places. (3 marks)
2.07
(d) 5.2 2 (3 marks)
0. 6
TOTAL 12 MARKS
2) (a) A sum of money is to be shared between Chris and Rhianna in the ratio 3:5.
Chris received $120. How much money was shared altogether? (3 marks)
(b) The cash price of a television set is $1200. It can be bought on hire
purchase by making a deposit of 15% and 10 monthly installments of $120
EACH.
(i) Calculate the amount deposit to be made on the television set.
(1 mark)
(ii) What is the TOTAL hire purchase price? (2 marks)
(iii) Calculate the difference between the TOTAL hire purchase price
and the cash price. (1 mark)
(iv) Express your answer in (iii) above as a percentage of the cash
price writing your answer to 2 significant figures. (2 marks)
(c) Calculate the TOTAL amount of money a man would receive if he invested
$2000 in a credit union for 2 years at an interest rate of 5% per annum. (3 marks)
TOTAL 12 MARKS
3
4. 3) (a) EC $1.00 = US $0.37
Jillian converted $500 EC to US to take with her to the Virgin Islands.
(i) How much US did Jillian receive if the exchange rate stated above
was used? (2 marks)
(ii) She spent US $100 and converted the remainder back to EC $.
How much EC $ did she receive (to the nearest cent) assuming
that the buying and selling rates are the same? (3 marks)
(b) The basic rate per hour earned by a mason for a 40-hour week is $50. If he
worked for 52 hours in one week and his overtime rate is time and a half,
calculate his basic wage for that week. (4 marks)
(c) A vehicle which was purchased 2 years ago for $20 000 depreciates by 5%
yearly. What is the present value of the vehicle? (3 marks)
TOTAL 12 MARKS
4) (a) Use algebraic statements to express each statement below.
i. Three apples and two oranges cost $15.25
ii. Four times the sum of x and 5
iii. I think of a number, doubled it then add five to it.
(3 marks)
(b) Simplify the expressions
(i) 5( x y ) 7( x 3 y ) (2 marks)
4 x 2 3x 4
(ii) (3 marks)
6x3
3x 4 x 2
(iii) (2 marks)
5y y
(c) Simplify
x3 x2
(3 marks)
3 5
TOTAL 13 MARKS
5) (a) Factorize completely
i. 3mn 6n 2 (1 mark)
ii. xy 3 x 2 y (2 marks)
iii. 4 x 2 25 (2 marks)
iv. 3sx 3sy 2tx 2ty (2 marks)
4
5. (b) Given that a 2 , b 3 and c 4 , calculate
b 2 4ac
(3 marks)
2a
a
(c) Given that a * b 2a
b
Evaluate 8 * 4 in its simplest form (2 marks)
(d) Solve for x
(i) x 2 5 x 14 (3 marks)
x x
(ii) 10 (3 marks)
2 3
TOTAL 18 MARKS
6) (a) A survey was conducted among 40 students. 30 students like reading the
Searchlight newspaper. 20 students like reading the News newspaper and 5 like
reading neither.
N
i. Copy and complete the Venn diagram above to represent the given
information. (2 marks)
ii. Calculate how many students like reading both papers. (3 marks)
iii. How many students like reading the News newspaper only?(1 mark)
(b) The figure below is a Venn diagram showing a Universal set. and two
subsets, G and H . The numerals in the diagram represent members of the sets.
i. List the members of the set
a. G H
b. G H
c. (G H )
ii. Determine the
value of n(G H
(4 marks)
TOTAL 10 MARKS
5
6. A
7) (a) The diagram to the right, not drawn to scale, 10 m
shows a vertical pole AC, which is supported by
a straight wire AB 10 metres long and pinned to
to horizontal ground some 6 metres away from
the foot of the pole.
B C
(i) Calculate in metres, AC the length of the pole. 6m
(2 marks)
(ii) Calculate the size of the angle formed at B, which is angle ABC. (3 marks)
(b) The diagram below, not drawn to scale, shows PQR , which represents the
cross section of a roof. QS Is perpendicular to PSR
Using the dimensions shown on the diagram, calculate, correct to 3 significant
figures.
i. the length QS (2 marks)
ii. the measure of RQS (3 marks)
iii. the area of triangle PQR (3 marks)
TOTAL 13 MARKS
8) The diagram below, not drawn to scale, shows a triangular prism with right-
angled isosceles triangles at both ends. Angle ABC 90 and AB = BC = 4cm
i. Calculate the area of triangle ABC. (2 marks)
The volume of the prism is 72 cm2
ii. Calculate the length of the edge CD (3 marks)
iii. Calculate, to one decimal place, the length of the edge AC
(2 marks)
iv. State the number of faces, edges and vertices of the prism (3 marks)
TOTAL 10 MARKS
6
7. 9) (a) Find the surface area of the cuboid below with the given dimensions. (4 marks)
5 cm
5 cm
22
(b) In this question, use
7
i. A piece of wire is bent to form a square of area 121 cm2. Calculate
a. The length of each side of the square
b. The perimeter of the square (3 marks)
ii. The same piece of wire is bent to form a circle
a. The radius of the circle
b. The area of the circle (4 marks)
TOTAL 11 MARKS
10) Given that f(x) = x – 2 and g (x) = 3x + 4
(a) f (2) (1 mark)
(b) g (-3) (2 marks)
(c) f -¹ (x) (2 marks)
(d) g-¹ (x) (3 marks)
(e) fg (x)
(4 marks)
TOTAL 12 MARKS
END OF TEST!
7
