Mathematics Paper 02 - Christmas End of Term 1 Exam-(2012-2013)

Time: 2hrs 40 mins

Form 4:1 and 4:2

Teachers: Miss R. Rampersad & Mr. L.Sammy

Instructions: This paper consists of two sections, A and B.

Answer ALL questions in both sections. Show ALL working.

1. (a) Calculate the exact value of

8

13

×212

2−56

(3 marks)

(b) Express 0.0402

i) exactly

ii) correct to2 decimal places

iii) correct to 2 significant figures

iv) in standard form ( 4 marks)

c)The Peters’ family consists of Mr. Peters, his wife and two children. Mr. Peters’ monthly salary is $2,800.

Table showing income tax allowances for a year are calculated as follows:

HusbandWifeEach child

$1000$ 600S200

Table showing Tax Rates for a year

Chargeable Income Rate of taxFor every dollar of the first $12 000“ “ “ “ “ next $ 8 000

5 cents15 cents

0.71

“ “ “ “ “ next $20 000 35 centsCalculate for Mr. Peters,

(i) His salary for the year. (1 mark)

(ii) His total allowances. (2 marks)

(iii) His chargeable income. (1 mark)

(iv)The amount he has to pay as income tax. (2 marks)

(v) The percent of his salary paid as income tax. (2 marks)

Total 15 marks

2.a) Express as a single fraction: 3p + q (2 marks)

b) Ninety tickets were sold for a concert. x tickets were sold for $3.00 each and the rest of the

tickets were sold for $4.00 each.

Write an expression in x to represent the number of tickets sold at

(i) $3.00 each

(ii) $4.00 each.

(iii) If the total sales on all tickets amounted to $300.00, how many of the tickets costing $3.00

were sold? (4 marks)

(c) Calculate the values of x for which

7- 4x >15 (3 marks)

Total 9 marks

5.a) Using a ruler, pair of compasses and a pencil only:

i) Construct a triangle CDE in which DE= 10cm, DC= 8cm and angle CDE = 45o. (4 marks)

ii) Construct a line, CF, perpendicular to DE such that F, lies on DE. (2 marks)

iii) Using a protractor, measure and state the size of angle DCE. (1 mark)

b) Given that a b=ab - b

Evaluate

i) 4 8

ii) 2 (4 8) ( 4 marks)

c) Fresh Farms Dairy sells milk in cartons in the shape of a cuboid with internal dimensions 6cm by 4cm by 10cm.

2 p

a

(i) Calculate in cm3 the volume of milk in each carton. (2 marks)

(ii) A recipe for making ice- cream requires 3 litres of milk. How many cartons of milk should be

bought to make the ice- cream? ( 3 marks)

(iii) One carton of milk is poured into a cylindrical cup of internal diameter 5cm. What is the

height of milk in the cup? Give your answer to 3 significant figures.

[ Use π = 3.14] ( 4 marks)

Total 20 marks

17) The functions f and g are defined by:

f(x) = x + 1 g(x) = 2x – 1

a) Calculate g(-3) ( 1 mark)

b) Find in its simplest form:

i) f -1(x) (1 mark)

ii) g -1(x) (1 mark)

iii) fg(x) (2 marks)

iv) (fg)-1(x) (3 marks)

c) Show that (fg)-1(x)= g -1f -1(x) (3 marks)

Total 11 marks

18) Given that:

f: x 3 - x

g: x x + 2

Milk

6cm

4cm

10cm

x- 5

3

a) Calculate g(2) (1 mark)

b) State the value of x for which g(x) is not defined. (1 mark)

c) Derive an expression for gf(x) (3 marks)

d) Calculate the value of f -1(4) (4 marks)

Total 8 marks

19) a) The table below shows the corresponding values for P and r.

P m 4 62.5r 0.2 2 n

Given that P varies directly as r3, calculate the values of m and n. ( 6 marks)

b) When y varies directly as the square of x, the variation equation is written as y= kx2, where k is a constant.

i) Given that y = 50 when x =10, find the value of k. ( 2 marks)

ii) Calculate the value of y when x=30 (2 marks)

c) If S varies directly as (r + 1), and S= 8 when r = 3, calculate the value for r when S = 50.

(4 marks)

Total 14 marks

END OF TEST