Page 1 of 4

CAMPION COLLEGE

END OF TERM EXAMINATION

5TH

FORM MATHEMATICS PAPER 2

Instructions: (1) This paper consists of two sections with 7 questions. Answer ALL

questions from section 1 and ONLY ONE question from section 2.

(2) All working must be clearly shown.

(3) The use of silent electronic calculators is allowed.

(4) DO NOT WRITE ON THIS PAPER.

(5) DO NOT ATTACH THIS PAPER TO YOUR ANSWER SHEETS.

SECTION 1 [55 MARKS]

Answer ALL questions in this section. All working must be clearly.

Question 1

(a) Calculate the exact value of

(i)

5

1

2

12

4

3

7

11

(4mks)

(ii) 15.0

24.02 (2mks)

(b) The cash price of a bicycle is $319.95. It can be bought on hire purchase by making

a deposit of $69.00 and 10 monthly installments of $28.50 EACH.

(i) What is the TOTAL hire purchase price of the bicycle? (2mks)

(ii) Calculate the difference between the total hire purchase price and the cash price. (1mk)

(iii) Express your answer in (ii) above as a percentage of the cash price. (2mks)

Total : 11 marks

Question 2

(a) (i) Solve the inequality 733 xx (3mks)

(ii) If x is an integer, determine the SMALLEST value of x that satisfies the inequality

in (a) (i) above. (1mk)

(b) Solve the pair of simultaneous equations.

2

2

xy

xy

(6mks)

Total : 10 marks

Page 2 of 4

Question 3

The diagram below shows the graph of 322 xxy for the domain 24 x .

Use the graph above to determine:

(a) the scale used on the x-axis (1mk)

(b) the minimum value of y (1mk)

(c) the x value for the minimum y value (1mk)

(d) the value of y for which 5.1x (2mks)

(e) the values of x for which 0y (2mks)

(f) the range of values of y, giving your answer in the form bya ,where a and b

are real numbers. (2mks)

Total : 9 marks

Question 4

The table below shows the ages, to the nearest year, of the persons who the clinic during a particular week.

(a) Copy and complete the table to show the cumulative frequency. (2mks)

(b) Using a scale of 2cm to represent 10 years on the x axis and 1cm to represent 5

persons on the y axis, draw the cumulative frequency curve for the data. (5mks)

(c) Use your graph drawn at (b) above to estimate:

(i) the median data. (2mks)

(ii) the probability that a person who visited the clinic was 75 years or younger. (2mks)

Draw lines on your graph to show how these estimates were obtained.

Total : 12 marks

Page 3 of 4

Question 5

Two yachts leave a harbour H. The first yacht sails on a bearing of 072 for 30 km to a location A and then

stops. The second yacht sails on a bearing of 140 for 50 km to a location B and then stops.

(a) Draw a diagram to represent the information given above. (4mks)

(b) Find angle AHB. (1mk)

(c) How far apart are the two yachts when they both have stopped to the nearest whole number? (4mks)

(d) Find the bearing of the yacht at A from the yacht at B. (5mks)

Total : 14 marks

SECTION 2 [ 20 MARKS ]

Answer ONLY ONE question in this section. All working must be clearly shown.

Question 6 Algebra, Functions and Relations

(a) The shaded area in the diagram below shows the solution of a set of inequalities in x and y.

The variable x represents the number of boys in a cricket club and y represents the number

of girls in the cricket club.

Use the graph above to answer the questions which follow.

(i) State, using arguments based on the graph, whether the cricket club can have as members:

(a) 10 boys and 5 girls

(b) 6 boys and 6 girls. (4mks)

(ii) Write down the set of THREE inequalities that define the shaded region. (4mks)

(ii) A company sells uniforms for the club and makes a profit of $3.00 on a boy's

uniform and $5.00 on a girl's uniform.

(a) Write an expression in x and y that represents the total profit made by the

company on the sale of uniforms. (1mk)

(b) Calculate the minimum profit the company can make. (4mks)

Page 4 of 4

(b) (i) Express the quadratic function 261 xx in the form 2hxak ,

where a, h and k are constants. (5mks)

(ii) Hence, state:

(a) the maximum value of 261 xx (1mk)

(b) the equation of the axis of symmetry of the quadratic function. (1mk)

Total : 20 marks

Question 7 Vectors and Matrices

(a) M is the matrix

qp

4 3. If M is a singular matrix and p = 2, calculate the value of q. (3mks)

(b) nA 3 and

3 4

2 mB . Given that 3 11AB , calculate the values of m and n. (5mks)

(c) A superstore sells 3 models of cell phones. Model A costs $40 each, model B costs $55 each and model

C costs $120 each. The weekly sales for 2 weeks in June were:

Week 1 Week2

2 model A no model A

5 model B 6 model B

3 model C 10 model C

(i) Write down a matrix of size 23 which represents the sales for the two weeks. (1mk)

(ii) Write down a matrix of size 31 which represents the cost of the different models

of each cell phones. (1mk)

(iii) Write down the multiplication of the two matrices which represents the superstores

takings from the sale of cell phones for each of the two weeks. (2mks)

(d) , are the vectors a and b. C is the point on AB such that C is 3

4 along AB.

(i) Express in terms of a and b.

(a) AB (2mks)

(b) (3mks)

(ii) If D is the point that is 2

3 along AC, find the vector . (3mks)

Total : 20 marks

Total Test: 75 marks

END OF EXAM