Simplify completely

Simplify the expression. (4 mks)

x - 1 - 2x + 1 Hence solve the equation
x 3x

x - 1 - 2x + 1 = 2
x 3x 3

If 2/3 is added to the numerator of a certain fraction the fraction will be increased by 1/21 and if 1/2 is deducted from its denominator that fraction becomes 2/9. Find the reciprocal of the fraction.

Without using a calculator or mathematical tables, evaluate.

A polygon of n sides has half of the interior angles 1500 each and the rest 1700 each. Find the value of n.

Kanyau toured Switzerland from Germany. In Switzerland he bought his wife a present worth 72 Deutsche marks.

Find the value of the present in
a) Swiss Francs
b) Kenya shillings correct to the nearest sh, if
1 Swiss Franc = 1.25 Deutsche marks
1 Swiss Franc = 48.2 Kenya shillings

Given that Sin x = 3/4 find without using tables or calculators.
a) Cos x
b) Tan (90 - x)

In the figure below, O is the centre of the circle. PQ is parallel to OR and PQO = 400, find <PRO.

A colony of insects was found to have 250 insects at the beginning. Thereafter, the number of insects doubled every two days. Find the number of insects after 16 days.

The cash price of a music system is kshs. 30,000. It can be bought under hire purchase terms by paying a deposit of kshs. 10,000 and twelve monthly installments of Kshs. 3,200 per month. Determine the percentage rate of interest per month.

A square whose vertices are P(1, 1), Q(2, 1), R(2, 2) and S(1, 2) is given an enlargement with centre at (0, 0).

Find the images of the vertices if the scale factor is 3.

Kairietu is now four times as old as her daughter and six times as old as her son. Twelve years from now, the sum ofthe ages of her daughter and son will differ from her age by 9 years. What is Kairietu’s present age?

In the figure below O is the centre of the circle diameter AB. <AXP = 900, AX = 4cm and PX = 10cm.
Calculate the radius of the semi-circle.

Given that a = 5i + 4j, b = 3i - 2j and c = 7i + 10j; find the scalars m and n such that ma + nb = c

Solve the simultaneous inequalities and represent the solution on a number line; 4 - 2x < 8 and 2 - 3x > - 7

The figure below is a cone whose base radius is 7cm and slant height 14cm. The net of the cone is a sector of a circle.

a) Find the angle substended at the centre of the sector. (1 mk)
b) Draw the net of the solid. (2 mks)

The following data shows the sample of age distribution in years of the people who reside in a certain village in Murang’a.

Age group Frequency
1 - 5 4
6 - 10 8
11 - 20 8
21 - 30 6
31 - 50 40
51 - 55 3
56 - 65 3
a) Complete the histogram of the given data below. (6 mks)
b) Calculate the mean age of the given sample in the village. (4 mks)

a) Copy and complete the following table for y = 2x2 + 4x - 5 (2 mks)
x -4 -3 -2 -1 0 1 2
2x2 32 2 0 8
4x -16 -4 0 8
-5 -5 -5 -5 -5 -5 -5 -5
y 11 -7 -5 11
b) i) Draw the graph of y = 2x2 + 4x - 5 (3 mks)
ii) Use the graph of b (i) above to solve the equation 2x2 + 4x - 5 = 0 (1 mk)
c) To solve the equation 2x2 + x - 7 = 0 a straight line must be drawn to intersect the curve y = 2x2 + 4x - 5.
i) Find the equation of the line. (1 mk)
ii) Draw the line and hence estimate the roots of the equation 2x2 + x - 7 = 0. (3 mks)

The diagram below is a right pyramid on a rectangular base.
Given that the volume of the solid is 280m3 and its base area is 60cm2 and that AB : BC = 3 : 5, determine
i) The height of the pyramid. (2 mks)
ii) The length and width of the base. (4 mks)
iii) The slant edge of the pyramid. (4 mks)

The table below shows measurements, in metres made by surveyor in his field book.
F
420
G 100 380 D70
300 C100
220 E40
H60 140
80 B60
A
i) Using an appropriate scale draw the region. (5 marks)
ii) Find the area in hectares of the filed. (5 marks)

A cross country route has five sections AB, BC, CD, DE and EA. B is 2km on a bearing of 0500 from A. C is 5km from B.
The bearing of B from C is 3000. D is 4km on a bearing 2300 from C. E is 2.5km on a bearing 0250 from D. Use the scale
1cm for 0.5km to draw the diagram representing the cross country route.
From the diagram determine. (6 mks)
i) The distance in km of A from E. (2 mks)
ii) The bearing of E from A. (2 mks)

A bus travels from Murang’a to Meru a distance of 320km at a speed of x km/h. If the speed is reduced by 20km/h the bus would take 48 minutes more.
a) Form an equation to represent the given information and simplify it. (4 mks)
b) Find the speed of the bus. (3 mks)
c) Determine the time taken by the bus for the whole journey. (1 mk)
d) Another car is moving from Meru to Murang’a at a speed of 80km/h. Determine their relative speed. (2 mks)

a) Construct a triangle ABC in which AB = 4.3cm, BC = 5.0cm and CA = 6.3cm using a pair of compass and ruler only.
(3 mks)
b) Construct an escribed circle centre O opposite angle CAB and measure radius of the circle. (3 mks)
c) Measure the acute angle subtended by BC at the centre of the circle. (2 mks)
d) Determine the area of triangle OBC. (2 mks)

A particle starts from rest and moves with an acceleration, a, given by a = (10 - t)m/s2. Given that velocity, Vm/s is 2m/s; when time; t seconds is 1 sec.
a) Express in terms of t;
i) Its velocity after t seconds. (3 mks)
ii) Its displacement after t seconds. (2 mks)
b) Calculate its velocity when t = 3 seconds (2 mks)
c) Calculate the maximum velocity attained. (3 mks)