Momanyi spent one eight of his February Salary on farming, half on school fees and two thirds of the remainder on food. Calculate his February salary and the amount he spend on school fees if he spent sh. 3200 on food.                     (3marks)

Makau, Wanjiru and Kemboi start a race at 9.03 a.m in the same direction to run round a circular course.  Makau makes the circuit in 252 seconds, Wanjiru in 308 seconds and Kemboi in 198 seconds.   If they start from the same point, at what time will they next be all at the starting point together?               (3marks)

Use squares square roots and reciprocal tables to evaluate              (3mks)

Simplify the expression                                 (3marks)

A square based brass plate is 2mm high and has a mass of 1.05kg.  The density of the brass is 8.4g/cm³.  Calculate the length of the plate in centimeters.                (3 marks)

The currency exchange rates of a given bank in Kenya are as follows;

 A tourist arrived in Kenya with 5,000 US dollars which he converted to Kenya shillings upon arrival. He spent ksh.214, 500 and converted the remaining to sterling pounds. How many pounds did he receive?                                                                                                   (3marks)

The figure below shows a simple tent.AF=FB=10cm, AB=12cm and BC=FE=AD=20cm. On the tent, a tight rope is tied as shown on the diagram from BD, DE and EA.  Draw the net of the tent and show the path of the rope on the net using the scale 1cm  rep.  5cm    (3marks)

Mrs Wekesa paid shs 12500 for a wrist watch after the shopkeeper gave her a discount of 2%. If the shopkeeper made a profit of 20%.calculate the price the shopkeeper bought from the manufacturer.                      (3marks)

Find the equation of a perpendicular bisector of line PQ if the coordinates of P and Q are       (-2,6) and (4,-2) respectively, in the form  y = mx + c           (3mks)

Complete the figure below by adding the correct missing features if it has a rotational symmetry of order 4 about O.                        (3mks)

The volumes of two similar cylindrical containers are 27cm³ and 125 cm³ respectively. Given that the height of the smaller container is 12cm, find the height of the larger container.     (3marks)

Without using calculator or mathematical tables, simplify               (4mks)

Form three inequalities that satisfy the unshaded region R.                          (3mks)

A railway line and a road are parallel to each other on a flat and level section of land. A 5 metre long car moving at a speed of 110kmh^-1 starts overtaking a train which is 495 metres and moving at 80kmh^-1 .How long will it take the car to completely overtake the train?       (3marks)

Evaluate without using tables or calculators              (3mks)

Solve for  in the equation               (4 marks)

Two circles with centres O and Q and radii 8cm intersect at points A and B as shown below.

Given that the distance between O and Q is 12cm and that the line AB meets OQ at X, find:

            (a)       the length of the chord AB.             (3marks)

            (b)       the reflex angle AOB.                     (3marks)

            (c)       the area of the shaded region.              (4marks)

In the figure below, EG is the diameter of the circle centre O. Points B, G, D, E and F are on the circumference of the circle. <BFD=50⁰ , <BEO=25⁰ and line ABC is a tangent to the circle at B

Giving reasons, calculate the size of

(a)  < CBD                                                  (2marks)

(b)  < BED                                                 (2marks)

(c) The reflex angle  BOD                          (2marks)

(d)  < EBA                               (2marks)

(e)  < BGD                               (2marks)

Every Sunday Alex drives a distance of 80km on a bearing of 074⁰ to pick up his brother John to go to church.  The church is 75km from John’s house on a bearing of S50⁰E.  After church they drive a distance of 100km on a bearing of 260⁰ to check on their father before Alex drives to John’s home to drop him off then proceeds to his house

(a)  Using a scale of 1cm to represent 10km, show the relative positions of these places.       (4 mks)

 (b)       Use your diagram to determine:

           (i)        the true bearing of Alex’s home from their father’s house.   (1 mark)

          (ii)       the compass bearing of the father’s home from John’s home. (1 mark)

          (iii)      the distance between John’s home and the father’s home.    (2 marks)

           (iv)      the total distance Alex travels every Sunday.                        (2 marks)

The data below shows the sample of age distribution of some of the people who reside in a Yoruba village in years.

(a) Complete the frequency distribution table above and hence

 i) Calculate the mean.                             (3mks)

 ii) Calculate the median.                               (2mks)

(b) Draw a frequency polygon from the given data on the grid below    (5mks)

The table below shows how income tax was charged on income earned in a certain year.

Mr. Gideon is an employee of a certain  company and earns a salary of  ksh.15,200 per month. He is housed by the company and pays a nominal rent of Ksh. 1050 per month. He is married and is entitled to a family relief of ksh. 450 per month.

(a) Calculate his taxable income in K£ p.a                         (2mks)

(b) Calculate his gross tax per month.                          (4mks)

(c) Calculate his net tax per month                              (2mks)

(d) Calculate his net salary  per month                             (2mks)

The figure below shows triangle ABC inscribed in a circle. AB = 6 cm, BC = 9cm and AC = 10cm.

Calculate:

a) The radius of the circle              (6mks)

b) The area of the shaded parts              (4mks)

(a) Using a ruler and a pair of compasses only, construct a triangle QRS in which angle QRS = 37¹ /₂ ⁰ , RS = 7cm and RQ = 6cm.     (4mks)

(b) Drop a perpendicular from Q to RS = to meet RS at T. measure QT,      (3mks)

(c) hence calculate the area of the triangle QRS.        (3mks)

(a) Complete the table below by filling in the blank spaces for the function    y = -x + x² – 6.     (2mks)

(b) On the grid provided draw a graph of y = -x + x² - 6 with the domain     (3mks)

(c) From the graph find the values of x which satisfies the expressions

    i.      –x + x² – 6 = 0                              (2mks)

    ii.   – x + x² – 6 = 5                             (3mks)