## Write 3cos? + 4sin? in the form Rcos(? – ?), and hence solve the equation 3cos? + 4sin? = 2 [9 marks]

QUESTION 1

a) i) Find the minimum value of x2 – 5x – 7 and state the value of x

when the minimum value occurs. (3 marks)

ii) Rationarise the denominator of (2 marks)

b) i) If are the roots of the equation 2×2 – 5x – 1 = 0, find the value of . (2 marks)

ii) The expression ax4 + bx3 – x2 + 2x + 3 has remainder 3x + 5 when

it is divided by x2 – x – 2. Find the values of a and b. (3 marks)

c) Find the sum of odd numbers between 11 and 199 inclusive. (4 marks)

d) Given that sin Find the value of (i) sin 2 (3 marks)

e) Eliminate from the equations x = 2 tan and y = tan 2 . (3 marks)

f) i) Find the probability of getting three heads in five tosses of unfair

coin in which the probability of getting a head is (3 marks)

ii) Find the mean and standard deviation of the numbers 2, 3, 4, 5, 6 and 7(3 marks)

g) How many arrangements can be made of the letters in the word

TROTTING? In how many of these are N and G next to each other? (3 marks)

QUESTION 2

a) Find an equation with integral co-efficients, whose roots are the squares

of the roots of the equation 2×2 + 5x – 6 = 0 (5 marks)

b) Find the greatest value of:

-10 + 14x – 2×2 and state the value of x at which it occurs. Sketch the curve

of y = -10 + 14z -2×2. Showing clearly the line of symmetry of the curve.(5 marks)

c) Solve by factorization the equation 2×2 – 5x + 3 = 0 (5 marks)

d) The sum to infinity of a geometrical progression with a positive common

ratio is 9 and the sum of the first two terms is 5. Find the first four terms

of the progression. (5 marks)

QUESTION 3

a) A committee of six is to be formed from nine women and three men. In how

many ways can the members be chosen so as to include at atleast one man?(6 marks)

b) i) Find the middle term in the expansion of (6x + (4 marks)

ii) What is the value of the constant term in the expansion of:

(4 marks)

c) Express 24 sin x + 7cosx in the form R sin (x + and hence solve the

equation 24 sin x + 7 cos x + 15 = 0 (7 marks)

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