Evaluate without using tables or a calculator;

A wholesaler sold a radio to a retailer making a profit of 20%. The retailer later sold the radio for ksh. 1560 making a profit of 30%. Calculate the amount of money the wholesaler had paid for the radio.

Given that 9^2y × 2^x = 72, find the value of x and y.

Use logarithms, correct to 4 decimal places to evaluate.

A line L passes through point (3, 1) and is perpendicular to the line 2y = 4x + 5.

Determine the equation of the line L.

A spherical ball is 15cm in diameter. What is its surface area?

Simplify the expression:

Given the inequalities x – 5 < 3x – 8 < 2x − 3, find the integral values of x.

Triangle A¹B¹C¹ is the image of triangle ABC under the transformation represented by the matrix. If the area of triangle A¹B¹C¹ is 140cm², find the area of triangle ABC.

In the figure below, the tangent ST meets chord VU produced at T. Chord SW passes through the centre O, of the circle and intersects chord VU at X. Line ST = 12cm and UT = 8cm.

(a) Calculate the length of chord VU. (2 marks)

(b) If WX = 3cm and VX : XU = 2 : 3, find SX. (2 marks)

The product of the matricesand is a singular matrix, find the value of P.

If , find the values of a and b where a and b are rational numbers.

Without using a calculator, evaluate, giving your answer as a fraction in its simplest form.

On a certain day, the probability that it rains is 1/7 . When it rains, the probability that Mukai carries an umbrella is 2/5. When it does not rain the probability that Mukai carries an umbrella is 1/6 . Find the probability that Mukai carried an umbrella that day.

A Kenyan businessman bought goods from Japan worth 2950000 Japanese Yen. On arrival in Kenya
a custom duty of 20% was charged on the value of the goods. If the exchange rates were as follows:
1 US dollar = 118 Japanese Yen
1 US dollar = 76 Kenyan shillings
Calculate the duty paid in Kenyan shillings.

The size of an interior angle of a regular polygon is 6½ times that of an exterior angle.
Determine the number of sides of this polygon.

The figure below represents a cone of height 12cm and base radius of 9cm from which a similar
smaller cone is removed, leaving a conical hole of height 4cm.

Calculate:
i) The base radius of conical hole. (1 mark)

ii) The volume, in terms of of the smaller cone that was removed. (2 marks)

i) Determine, slant height of the original cone. (1 mark)

ii) Calculate, in terms of , the surface area of the remaining solid after the smaller cone is
removed. (5 marks)

a) Solve the equation, (4 marks)

b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m²
i) Calculate the perimeter of the floor. (4 marks)

ii) A rectangular carpet is placed on the hall leaving an area of 64m². If the length of the carpet
is twice its width, determine the width of the carpet. (2 marks)

The figure below represents a solid cuboid ABCDEFGH with a rectangular base.
AC = 13cm, BC = 5cm and CH = 15cm.

Determine the length of AB. (1 mark)

Calculate the surface area of the cuboid. (3 marks)

Given that the density of the material used to make the cuboid is 7.6g/cm³, calculate its mass in kilograms. (4 marks)

Determine the number of such cuboids that can fit exactly in a container measuring 1.5m by 1.2m
by 1m. (2 marks)

A motorist left Embu for Nairobi, a distance of 240km, at 8.00a.m and travelled at an average speed of 90km.h. Another motorist left Nairobi for Embu at 8.30a.m and travelled at 100km/h. Find:
(i)The time they met. (6 marks)

(ii)How far they met from Nairobi. (4 marks)

The table below shows the heights, measured to the nearest cm, of 101 pawpaw trees.

Height (cm)	20-24	25-29	30-34	35-39	40-44	45-49	50-54	55-59
Frequency	2	15	18	25	30	6	3	2

(a) State the modal class. (1 mark)

(b) Calculate to 2 decimal places:
i) The mean height (4 marks)

ii) The difference between the median height and the mean height. (5 marks)

In a triangle ABC, BC = 8cm, AC = 12cm and angle ABC = 120^o
a. Calculate the length of AB, correct to one decimal place (4 marks)

b. If BC is the base of the triangle, calculate correct to one decimal place:
The perpendicular height of the triangle. (2 marks)

c. The area of the triangle. (2 marks)

d. The size of angle ACB (2 marks)

A trader bought 2 cows and 9 goats for a total of ksh. 98,200. If she had bought 3 cows and 4 goats,
she would have spent ksh. 2200 less
a) Form two equations to represent the above information. (2 marks)

b) Use matrix method to determine the cost of a cow and that of a goat. (4 marks)

c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat.
Calculate the total amount of money she received. (2 marks)

d) Determine, correct to 4 significant figures the percentage profit the trader made from the sale of the animals. (2 marks)

The displacement, S metres of a moving particle from point O, after t seconds is given by:
S = t³ – 5t² + 3t + 10
a) Find S when t = 2 (2 marks)

b) Determine:
(i)The velocity of the particle when t = 5sec (3 marks)

(ii) The value of t when the particles is momentarily at rest . (3 marks)

(c) Find the time, when the velocity of the particle is maximum. (2 marks)