CXC general proficiency Mathematics Exam: Mathematics May/June 2008

SECTION 1

Answer ALL the questions in this section.

All working must be clearly shown.

1. (a) (i) Using a calculator, or otherwise, determine the EXACT value of
(3.9 × 0.27)+ √0.6724 (2 marks)

(ii) Express as a single fraction.
(2 1/2- 4/5)/(3/4) (3 marks)

(b) In this question, use CAN $1.00 = JA $72.50
(i) On a vacation in Canada, Steve used his credit card to buy a camera for CAN $250.00.
What is the value of the camera in Jamaican dollars? (2 marks)

(ii) Steve's credit card limit is JA $30 000.00. After buying the camera, how many Canadian dollars does he have left on his credit card for spending? (3 marks)

(Total 10 marks)

(2) (a) Find the value of EACH of the following when a = 2, b = -1, c = 3
(i) a(b + c) (1 mark)

(ii) (〖4b〗^2- 2 ac)/(a+b+c) ( 2 marks)

(b) Change the following statements into algebraic expressions.
(i) Four times the sum of x and 5 (1 mark)

(ii) 16 larger than the product of a and b. (2 marks)

(c) Solve the equation.
15 - 4x = 2(3x + 1) (2 marks)

(d) Factorise completely.
(i) 6a^2 b^3+ 12a^4 b (2 marks)

(ii) 2m^2+ 9m-5 (2 marks)

Total 12 marks

(3) At a career guidance seminar, a servey was done to find out the type of careers that Form 5 students were likely to choose.

The results were shown in the table below.

Career-Lawyer-Teacher-Doctor-Artist-Salesperson
Number-240-189-t-216-330
of students

There are 1080 students surveyed.
(a) Calculate the value of t, the number of students who were interested in becoming doctors. (2 marks)

(b) (i) The data above are to be represented on a pie chart. Calculate the size of the angle in each sector of the pie chart. (4 marks)

(ii) Using a circle of radius 4cm, construct a pie chart to represent the data. (4 marks)

Total 10 marks

Questions 4 was typed and posted by our buddy, Sansha. Here is the link to her wonder work, http://www.caribexams.org/node/485.

12. A ship leaves Port R, sails to Port S and then to Port T.
The bearing of S from R is 112°.
The bearing of T from S is 033°.
The distance RT is 75km and the distance RS is 56km.
(a) Draw a diagram showing the journey of the ship from R to S to T.
Show on the diagram
(i) the north direction (1 mark)

(ii) the bearings 112° and 033° (2 marks)

(iii) the points R, S, and T (1 mark)

(iv) the distances 75km and 56km. (1 mark)

(b) Calculate
(i) the size of angle RST (1 mark)

(ii) the size of angle RTS (3 marks)

(iii) the bearing of R from T. (2 marks)

(c) The ship leaves Port T and travels due west to a point X which is due north of R.
(i) Show on your diagram the journey from T to X. (1 mark)

(ii) Calculate the distance TX. (3 marks)

Total 15 marks

14. (a) X and Y are two matrices where
X=(â– (-2&0@5&1))and Y=(â– (4&-1@3&7))
Evaluate X^2+ Y (4 marks)

(b) The matrix (■(1&2@1&3)) maps Q (1, 2) to Q’ (5, 7)
Find the 2 × 2 matrix which maps Q’ back to Q. (2 marks)

(c) The vertices of triangle DEF are
D(5, 12), E(2. 7) and F(8, 4)
Triangle DEF undergoes an enlargement with centre, O, and scale factor, k. Its image is D’E’F’ where
D (5, 12) – D’ (7.5, 18)
Determine the value of k.

Hence write down the coordinates of E’ and F’. (4 marks)
(ii) D’E’F’ undergoes a clockwise rotation of 90° about the origin.
Determine the 2 × 2 matrix that represents a clockwise rotation of 90° about the origin.

Determine the coordinates of D”E”F”, the image of D’E’F’, under this rotation.

Determine the 2 × 2 matrix that maps triangle DEF onto triangle D”E”F”. (5 marks)

Total 15 marks

END OF TEST

Friends! We are very sorry that this paper didn’t complete. You see, the rest of the questions have diagrams which is time consuming to produce and most importantly can’t post. Sansha and I were trying to post a scanned version but it was picture like. Does anyone know how to import the text in the scanned paper to Microsoft Word so that it can be posted?