Evaluate without using calculator or mathematical tables leaving your answer as a simplified fraction.

What is the exact value of

Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially Simiyu had five stones less than Nasike, how many stones did each have?

The figure below shows vectors a and b. Construct on the same grid, c given that

A cylinder of radius 14cm contains water. A metal solid hemisphere of radius 6.8cm is submerged into the water in the cylinder. Find the change in height of the water in the cylinder

At 90km/h, a car takes 2 hours to cover a distance A to B. How long would it take to cover the same distance if the car was travelling at 120km/h?

Solve for x and y in the equation

A sales man earns a basic wage of Ksh 1,500 per week. In addition , he is paid commission per week as follows:

Commission

For sales up to Ksh 50,000 0%

For sales above Ksh 50,000

i) For the first Ksh 25,000 2%

ii) For the next Ksh 25,000 2 ½ %

iii) For any amount above Ksh100, 000 5%

During that week, he sold goods worth Ksh 115,000.What was his total pay for that week?

The coordinates of the points P and Q are (1, -2) and (4, 10) respectively. A point T divides the line PQ in the ratio 2:1

a) Determine the coordinates of T (2mks)

b) Find the equation of the line perpendicular to PQ and passing through T. (2mks)

For the quadrilateral ABCD given below, find its image under reflection in the line y=0 followed by reflection in the line y= -x

. The figure below shows an arc ACE of a circle with centre O and radius 6cm. If BC=CD=4cm, calculate the area of the shaded region if DE=AB =1.53cm

. The diagram below shows part of the quadrilateral PQRS.

Given that 2RS=RQ and that PQRS is a cyclic quadrilateral, complete the diagram.

. A poultry farmer has twenty times as many hens as turkeys and three quarters as many ducks as turkeys.

a) If there are t, turkeys, write down a simplified expression in terms of t for the total number of birds on the farm. (1mk)

b) Given that he has 72 ducks, calculate as a percentage the sum of turkeys and ducks to the number of hens on the farm. (3mks)

. The sum of angles of a triangle is given by the expression (2a+b) 0 while that of a quadrilateral is given by (13a-b) ⁰ Calculate the values of a and b

The table below represents the marks scored by form 4 students in an end of term examination

Calculate the upper quartile.

. Determine the inequalities that represent and satisfy the unshaded region below.

The figure below shows a portable Kennel.

a) Calculate i) The total surface area of the walls and the floor. (2mks)

ii) The total area of the roof. (2mks)

b) The cost of roofing is Ksh 500 per square meter and that of making walls and floor is Ksh 600 per m2.Find the cost of making the Kennel. (2mks)

c) Find the cost of roofing another Kennel whose dimensions are 50% more than those of the given Kennel. (2mks)

d) Calculate the volume of air inside the Kennel in cm3. (2mks)

Given the coordinates of the points A, B and C as (3,-2); (6, 4) and (9, 3) respectively. a) Express the following vectors in terms of

i) AB (1mk)

ii) CB (1mk)

b) Calculate the magnitude from A to C through B. (3mks)

c) Determine the coordinates of the mid point of AC. (2mks)

d) If R divides AC externally in the ratio 3:1, determine the coordinates of R. (3mks)

. A flag post 12m long is fixed on top of a tower. From a point on horizontal ground, the angles of elevation of the top and bottom of the flag post are 460 and 330 respectively.
Calculate

a) The horizontal distance from the point on the ground to the base of the tower. (4mks)

b) The total height of the tower and the flag. (2mks)

c) The shortest distances from the point on the ground to

i) The top of the flag post. (2mks)

ii) The top of the tower. (2mks)

Four towns P, Q, R and S are such that town Q is 120km due east of town P. Town R is 160km due north of town Q, town S is on a bearing of 3300 from P and on a bearing of 3000 from R

a) Using ruler and compasses only, show the relative positions of towns P,Q,R and S. Take a scale of 1cm rep 50km. (5mks)

b) Determine i) The distance SP in km (2mks)

ii) The bearing of S from Q (1mk)

iii) How far north, S is, from line QP produced. (2mks)

The figure below shows two intersecting circles of centres C and D radii 16cm and 20cm respectively. The two circles subtend angles 2 1  and at their centres respectively and intersect at P and Q as shown

a) Given that the area of triangle PCQ is 80.14cm2,calculate the size of

i) The angle marked (2mks)
ii) The angle marked
(3mks)
b) Calculate the area of the shaded region. (5mks)

A private farmer in Mwea produced 14,400bags of rice in 2008. This was a decrease of 20% over the production in 2007. In 2009 he increased production by 30%. In 2010, he managed to produce 12,000 bags of rice.

a) Find the number of bags of rice he produced in;

i) 2007 (2mks)

ii) 2009 (2mks)

b) What was the percentage decrease in production in 2010 over that of previous year? (2mks)

c) Calculate the percentage decrease in production in 2010 over that in 2007 (2mks)

d) The price per bag of rice was Ksh 3500 in 2010, how much did he get if he sold 65% of the produce in that year. (2mks)

The diagram below (not drawn to scale) shows the position of a harbor H and three islands A,B and C. C is due North of H. The bearing of A from H is 062⁰ and angle HAB=1280 HA=54km and AB=31km

a) Calculate the distance HB (3mks)

b) Find the bearing of B from A (1mk)

c) Given that the bearing of A from C is 1330, calculate AC (3mks)

d) A light ship L is positioned due North of H and equidistant from A and H. Calculate HL. (3mks)

. The table below gives some of the values of x and y for the function in the interval

a) Complete the values in the table above. (1mk)

b) Use the values in the table to draw the graph of the function on the grid provided below. (2mks)

c) Using the graph and the mid- ordinate rule with 6 strips, estimate the area bounded by the curve, the x –axis, the y-axis and the line x=6 (3mks)
d) Using integration, calculate the exact area and hence find the percentage error made when mid-ordinate rule is used . Give your answer correct to 2d.p. (4mks)