Post Code : P.O BOX 3000 - 80113 ISIOLO
July 2024
2:30 minute
Exam code: 441122
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | Total |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
17 | 18 | 19 | 20 | 21 | 22 | 23 | Total |
---|---|---|---|---|---|---|---|
Answer all questions
Without using a calculator or mathematical tables, work out (4mks)
Solve for x and y in: (3mks)
Two similar containers have masses 768kg and 324kg respectively. If the surface of the smaller container has the surface area of 2,430cm2 , what is the area of the corresponding surface of the larger container. (3mks)
The cost price of 31 inch flat LG TV screen is Ksh 36,500. Mary bought a screen on hire purchase price by paying a deposit of Ksh 12,000 and 15 monthly installments of Ksh 2050 each. Calculate the monthly rate of interest she was charged. Give your answer to 2 decimal places. (4mks)
Expand and hence simplify the expression (3mks)
Express the following in surd form and simplify by rationalizing the denominator. (3mks)
Solve the simultaneous equalities and state the integral values of : (3mks)
The volume (v) of an inflated balloon varies as the cube of the diameter (d). The volume is 14.23cm3 when its diameter is 3.5 cm. what is the volume of the balloon when its diameter is 4.5cm? (3mks)
The figure below shows a circle centre O, radius 8.4cm. The chord EF = 8.4cm. calculate the area of the unshaded region (3mks)
In June 2009, a cleaner salary was Ksh 15,300. Given that the company increases the cleaner’s money by ksh 800 every month of May since. What was the cleaner’s salary in May 2014? (3mks)
Make g the subject of the formular: (3mks)
Use the matrix method to solve the simultaneous equations: (3mks)
In the diagram below ; PQ = 10cm and RS = 14cm. find the length of QR (3mks)
Use table of square roots and reciprocals only to evaluate. (3mks)
Solve for x in the equation. (3mks)
The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number. (3mks)
Answer any five questions
The table below shows income tax rates in Kenya in a certain year
Total income per year |
Rate in shillings per Kenyan pound |
1 - 325 |
2 |
326 - 650 |
3 |
651 - 975 |
4 |
976 - 1300 |
5 |
1301 - 1625 |
7 |
over 1625 |
7.5 |
Mr. King’ori earned a basic salary of ksh13, 120 and a house allowance of ksh3, 000 per month. He claimed a tax relief from a married person of ksh 455 per month
a) Calculate :
(i) The tax payable without relief (4mks)
(ii) The tax paid after relief (2mks)
b) A part from the income tax, the following month deductions are made; a service charge of ksh 100, a health Insurance fund of ksh and 2% of his basic salary as widow and children pension scheme. Calculate:
(i) The total monthly deductions made from King’ori’s income (2mks)
(ii) Mr. King’ori’s net income from his employment (2mks)
A trailer 30m long moving at an average speed of 60km/h started from station A towards station B at 4.00am ,a bus moving at an average speed of 90km/h and 20m long started also travelling from A towards B at 4.30am .
find:
a) The time the bus caught up with the trailer (4mks)
b) The time in seconds the bus took to pass the trailer completely (3mks)
c) How far from A did the bus completely overtake the trailer (3mks)
The figure below shows triangle OAB in which M divides OA in the ratio 2:3 and N divides OB in the ratio 4:1, AN and BM intersect at X
a) Given that OA = a and OB = b, express in terms of a and b:
(i) AN (1mk)
(ii) BM (1mk)
b) If AX = sAN and BX = tBM, where s and t are constants, write an expression for OX in terms of a,b , s and t (2mrks)
c) Find the values of s (4mks)
d) Hence write OX in terms of a and b (2mks)
(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)
x |
-5 |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
y |
24 |
14 |
|
|
-4 |
-6 |
|
|
0 |
6 |
14 |
24 |
(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)
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) Express as single fraction in its simplest form (2mks)
(b) When driven into a town a car travels x km on each litre of petrol.
i. Find in terms of x, the number of litres of petrol used when the car is driven 200km in town. (1mk)
ii. When driven out of town the car travels (x +4) km on each litre of petrol. It uses 5 litres less petrol to cover 200km out of town to cover same distance in town. Use this information to write down an equation involving x, and show if simplified to x2 + 4x – 160 = 0 (3mks)
(c) Solve the equation x2 + 4x – 160 = 0 (3mks)
(d) Calculate the volume of petrol when the car is driven 40km in town (1mk)