(Time – Two hours and a half)

Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer.

Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided.

SECTION A (40 Marks)

Attempt all questions from this Section

Question 1.

a) What number must be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has a factor 2x – 3 ? [3]

b) D, E, F are mid points of the sides BC, CA and AB respectively of a Δ ABC. Find the ratio of the areas of Δ DEF and Δ ABC. [3]

c) A man borrowed a sum of money and agrees to pay off by paying Rs 3150 at the end of the first year and Rs 4410 at the end of the second year. If the rate of compound interest is 5% per annum, find the sum borrowed. [4]

Question 2.

a) The y-axis is a line of symmetry for the figure ACBD where A, B have co-ordinates (3, 6), (– 3, 4) respectively. (i) Find the co-ordinates of C and D. (ii) Name the figure ACBD and find its area. [3]

b) PAQ is a tangent at A to the circumcircle of Δ ABC such that PAQ is parallel to BC, prove that ABC is an isosceles triangle. [3]

c) A rectangular piece of paper 30 cm long and 21 cm wide is taken. Find the area of the biggest circle that can be cut out from this paper. Also find the area of the paper left after cutting out the circle. [Take π = 22/7][4]

Question 3.

a) Construct a 2 × 2 matrix whose elements aij are given by aij = i + j. [3]

b) The point P (– 4, – 5) on reflection in y-axis is mapped on P’. The point P’ on reflection in the origin is mapped on P”. Find the co-ordinates of P’ and P”. Write down the single transformation that maps P onto P”. [3]

c) Let A = {1, 2, 3}, B = {1, 2, 3, 4} and R = {(x, y) : (x, y) ∊ A × B, y = x + 1}, then (i) find A × B (ii) write R in roster form (iii) write domain and range of R (iv) find R –1 in roster form (v) write R –1 in set builder form (vi) represent R and R –1 by arrow diagrams.

Question 4.

a) Without using trigonometric table, evaluate : 7(sin 27˚/cos 63˚) + 3(cos 21˚/sin 69˚) – 7(tan 36˚/cot 54˚) [3]

b) Prabha saves Rs 1250 per month and invests in a cumulative deposit account giving interest at the rate of 8.5% per annum compounded quarterly. In order to have a total amount of nearly Rs 56000, how many instalments must she deposit ? [3]

c) In a class test, the marks obtained by 11 students are : 13, 17, 20, 5, 19, 7, 6, 11, 15, 17. Find (i) mean (ii) median (iii) upper quartile (iv) lower quartile. [4]

SECTION B (40 marks) Attempt any four question from this section.

Question 5.

a) Take any two different matrices A and B of order 2 × 2, and verify that AB ≠ BA. [3]

b) The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area (iii) volume.[3]

c) Which is better investment : 7% Rs 100 shares at Rs 120 or 8% Rs 10 shares at 13.50 ? [4]

Question 6.

a) Solve the quadratic equation : 3 x2 – x – 7 = 0 and give your answer correct to two decimal places. [3]

b) An integer is chosen at random form 1 to 100. Find the probability that the number is : (i) is...