The diagram below shows a frustum made by cutting off a small cone on a plane parallel to the base of the original one. The frustum represent a bucket with the open end diameter of 36cm and diameter of the bottom 24cm. the bucket is 18cm deep as shown (Take Õ = 22/7)

Calculate the:

(a) Volume of the small cone cut off.                (3mks)

(b) Volume of the original cone                             (2mks)

(c) The capacity of the bucket in liters                    (2mks)

The table below shows some values of the function y = 2x² – 7x -1   for    -1 < x < 5X

a) Complete the table above by filling in the missing values of y       (2mks)

b) Draw the graph of the function y = 2x² – 7x – 1 for -1 < x < 5 by using the scale 2cm to represent 1 unit on the X-axis. 2cm to represent 5 units on the Y – axis    (4mks)

c) By drawing suitable straight lines on the same axes, find the approximate roots of the following equations?

(i) 2x² – 7x - 1 = 0                (2mks)

(ii) 2x² - 4x + 3 = 0                  (2mks)

Mesurements of a maize field using a base line XY were recorded as shown below in a field book as follows: (take XY = 400cm)

(a) Use a scale of 1cm to 40m to draw the map of the maize field. (5mks)

(b) Find the area of the maize field in hectares. (5mks)

The speeds of a number of vehicles passing a 50kph limit sign were found to be as follows:

1. Calculate the mean speed in kph of the above distribution     (4mks)

2. Calculate the medium speed of the distribution    (2mks)

3. Draw a histogram to illustrate the information. 1cm to represent 5 units on the x- axis 1cm to represent 10 units on the y - axis   (4mks)

1. Without using a protractor, construct triangle ABC, such that BC = 10cm, angle ABC = 60⁰ and angle BCA = 45⁰ (let BC be the base)             (4mks)

2. Construct the perpendicular bisector of lines BC on the above diagram. Draw the circumference of triangle ABC.                (3mks)

3. Find the radius of the circumference hence determine the area of the circle drawn.                 (3mks)

Given that the position vectors of points A and B are  a =   and  b = respectively find:

a)  BA                                     (1mk)

b)  |BA|                                    (2mks)

Without using a calculator, evaluate:                       (3mks)

Express in the form of .where a and b are integers           (3mks)

The angle elevation of the top of a tower is 35⁰ from a point P and is 54⁰ from another point L, 3metres nearer the foot of the tower which lies on the line PL and at the same level with P and L. Calculate the height of the tower. (4mks)

In a triangle UVW, (not drawn to scale) VW = 14cm, UW = 10cm and UV = 20cm. Find the largest angle and hence determine its size.     (3mks)