Use a tables to find the value of x  if 2^x = 3. Give your answer correct to 4sf.

Make x the subject of the formula:

It would take 18 men 12 days to dig a piece of land. If they work for 8 hours a day, how long
will it take 24 men if they work 12 hours to cultivate three quarters of the same land.

Kinyua bought soya and millet at sh.65 per kg and sh.40 per kg respectively. He then mixed
them and sold the mixture at sh.60 per kg making a profit of 20%. Determine the ratio of soya
to millet in mixture.

Chord AB is of length 8cm and the maximum distance between chord and lower part of circle
is 2cm. Determine the radius of the circle.

Use the inverse matrix method rule to solve simultaneous equations.
2x + y = 10
2x + 2y = 14

Solve

Construct a circle centre K and radius 2.5cm. Construct a tangent from a point Q which is
6cm from K to touch the circle at M. Measure the length QM.

Given 4.6 ÷ 2.0 find
(a) the absolute error in the quotient. (2mks)
(b) the percentage error in the quotient correct to four significant figures. (1mk)

A variable P varies jointly with the square of R and inversely with the square root of Q.
If R is increased by 10% and Q decreased by 20%, what is the percentage change in the
value of P.

The figure below shows a circle with segments cut off by a triangle whose longest side AB
is the largest possible chord of a circle. Determine the area shaded given that AB = 14cm
and AC = BC.

A bucket in the shape of a frustrum as shown in the diagram. It has diameters of 36cm and 24cm.

Calculate the volume of the bucket.

Without using a Mathematical tables or a calculator, evaluate.

Find the length represented by y in the figure below.

(a) Expand (1 + 2x)⁸ in ascending powers of x up to and including the term x³. (1mk)
(b) Hence evaluate (1.02)⁸to 3d.p. (2mks)

The difference between the exterior and interior angle of a regular polygon is 100ï‚°. Determine the
number of sides of the polygon.

(a) Fill the table below for the curves given by y = 3 sin (2x + 30^o) and y = Cos 2x for 
values in the range O < x < 180^oï‚°. (2mks)

(b) Draw the graphs of y = 3 Sin (2x + 30^o) = Cos 2x on same axes. (2mks)

(c) Use your graph to solve the equation y = 3 Sin (2x + 30^o) and y = Cos 2x. (2mks)
(d) Determine the following from your graph:
(i) Amplitude of y = 3 Sin (2x + 30^o). (1mk)
(ii) Period of y = 3 Sin (2x + 30^o) . (2mks)
(iii) Phase difference for y = 3 Sin (2x + 30^o). (1mk)

OAB is a triangle in which OA  a and OB  b. M is a point on OA such that OM: MA = 2: 3
and N is another point on AB such that AN: NB = 1: 2. Lines ON and MB intercept at X.
(a) Express the following vectors in terms of a and b.
(i) AB (1mk)
(ii) ON (1mk)
(iii) BM (1mk)
(b) If OX = KON and BX = hBM express OX in two different ways. Hence or otherwise
find the values of h and K. (6mks)
(c) Determine the ratio OX: XN. (1mk)OAB is a triangle in which OA  a and OB  b. M is a point on OA such that OM: MA = 2: 3
and N is another point on AB such that AN: NB = 1: 2. Lines ON and MB intercept at X.
(a) Express the following vectors in terms of a and b.
(i) AB (1mk)
(ii) ON (1mk)
(iii) BM (1mk)
(b) If OX = KON and BX = hBM express OX in two different ways. Hence or otherwise
find the values of h and K. (6mks)
(c) Determine the ratio OX: XN. (1mk)

(a) Using only a ruler and a pair of compasses draw a line AB of length 8cm long.
Hence draw the locus of all points P such that angle APB = 52.5ï‚°. (5mks)
(b) If the region above represents a map of an estate drawn to a scale of 1cm representing 1km.
Show the region to be fenced if AMB ï‚£ 90ï‚° by shading the unwanted region. (3mks)
(c) Find the area of this region. (2mks) (a) Using only a ruler and a pair of compasses draw a line AB of length 8cm long.
Hence draw the locus of all points P such that angle APB = 52.5ï‚°. (5mks)
(b) If the region above represents a map of an estate drawn to a scale of 1cm representing 1km.
Show the region to be fenced if AMB ï‚£ 90ï‚° by shading the unwanted region. (3mks)
(c) Find the area of this region. (2mks)

The data below is a daily record of sugar sold in one of the supermarkets in Kerugoya town which
sells any proportion in kg of sugar.

(a) How many people bought sugar from this supermarket on that day. (1mk)
(b) Calculate mean of sugar bought that day. Calculate also the standard deviation from
this data. (4mks)

(c) Draw a cumulative frequency curve of the data above and determine the number of
people who bought sugar between 1.2 and 1.9kg. (5mks)

A plane take of f from airport P at (0^oï‚°, 40^oï‚°W) and flies 1800 nautical rules due East to Q then
1800 nautical rules due South to R and finally 1800 nautical rules due West before landing at S.
(a) Find to the nearest degree the latitudes and longitudes of Q, R and S. (4mks)
(b) If the total flight time is 16 hours, find the average speed in knots for the whole journey.
(3mks)
(c) Find the time taken to fly from R to S, given that this was two hours shorter than the time
taken from P to Q to R. (2mks)

The 2^nd and 5^th terms of an arithmetic progression are 8 and 17 respectively. The 2^nd, 10^th and
42^nd terms of the A.P. form the first three terms of a geometric progression. Find
(a) the 1^st term and the common difference. (3mks)
(b) the first three terms of the G.P and the 10th term of the G.P. (4mks)
(c) The sum of the first 10 terms of the G.P. (3mks)

A girl’s school has a store a far off distance for food. It has 20 sacks of rice and 35 sacks of maize.

The weight, volume and number of meal rations for each sack are as follows.

A delivery van is to carry the largest possible total number of meals. It can carry up to 600kg in
weight and 2m³ in volume.
(a) If a load is made up of x sacks of rice and y sacks of maize, write four inequalities other
than x > 0, y > 0 which satisfy these conditions. (3mks)
(b) Illustrated these inequalities graphically by shading unwanted region. (4mks)

(b) Write down an expression for the number of meals that can be provided from x sacks of
rice and y-sacks of maize. Use your graph to find best values to take for x and y. (3mks)