A telephone bill includes Ksh.4,320 for local calls, Ksh.3,260 for trunk calls and a rental charge of Kshs.2,080 .A value added tax (V.A.T.) is then charge at 15%.

Two valuables A and B are such that A varies partly as the square of B. Given that A = 30,when B = 9, and A= 16 when B = 14, Find A and B.

Three people Odawa, Mliwa and Amina contributed money to purchase a flour mill. Odawa contributed ⅓ of the total amount, Mliwa contributed ⅜ of the remaining amount and Amina contributed the rest of the money. The difference in contribution between Mliwa and Amina was sh.40,000.

Calculate the price of the flour mill.

Simplify;

P^{2} + 2pq + q^{2} P^{3} – pq^{2} + p^{2}q – q^{3}

P

Number.

(a) Write down the number formed

(b) State the total value of the second digit in the number formed in (a) above

A curve is given by the equation: u = 5x^{3} – 7x^{2} + 3x +2) Gradient of the curve at x = 1

Solve for x in the equation 32^{(x-3)} ÷8 ^{(x-4)} = 64÷2^{x}

A plane flying at 200 knots left an airport A (30^{0}S, 31^{0}E) and flew due North to an airport B ( 30^{0} N, 31^{0}E)

- (a) Calculate the distance covered by the plane, in nautical miles
- (b) After a 15 minutes stop over at B, the plane flew west to an airport C ( 30
^{0}N, 13^{0}E) at the same speed.

The probability of three darts players Akinyi, Kamau, and Juma hitting the bull's eye are 0.2, 0.3 and 1.5 respectively.

- (a) Draw a probability tree diagram to show the possible outcomes
- (b) Find the probability that:
- (i) All hit the bull's eye
- (ii) Only one of them hit the bull's eye
- (iii) at most one missed the bull’s eye

(a) Complete the following table for the equation y = x^{3} + 2x^{3}

- (b) On the grid provided draw the graph y = x
^{3}+ 2x^{2}for -3 ≤ x ≤ 1.5. Take the scale: 2cm for 1 unit on the x- axis and 1 cm for 1 unit on y – axis - (c) By drawing a suitable line on the same grid, Estimate the roots of the equation: x
^{3}+ 2x^{2}– x – 2 =0

Answer