INSTRUCTION TO STUDENTS:
 This paper consists of two Sections; Section I and Section II.
 Answer ALL the questions in Section I and only five questions from Section II.
 Show all the steps in your calculation, giving your answer at each stage in the spaces provided below each question.
 Marks may be given for correct working even if the answer is wrong.
 KNEC Mathematical tables may be used, except where stated otherwise.
 Candidates should answer the questions in English.
Ensure that all the pages are printed and no question(s) are missing.
SECTION 1 (50 Marks)
Answer all Questions from this Section
 Use logarithms correct to 4 decimal places to evaluate. 4mks
 A car was valued at ksh.500,000 in January 2017.Each year ,its value depreciates at 12% p.a.Find after how long would the value depreciate to 350,000 . 3mks
 Simplify (3mks)
 Two fruits juices A and B are mixed together .Juice A cost sh.50 per litres.What is the ratio if the cost is sh.59 per litre of the mixture? 3mks
 Find the centre and radius of the circle whose equations is
x^{2}+y^{2} – 2x + 4y +1=0 3mks
 Find the standard deviation for the following set of data 3mks
16,42,41,6,20,28,19,23,15
 The diagram below shows a circle ABCDE .The line FEG is a tangent to the circle at point E.Line DE is parallel to CG.
State giving reasons the sizes of; AEG 2mks
 ABC 2mks
 Find the value of x given that log(x2) + 2 =log (3x +1) + log 25 . 3mks
 Find the percentage error in the calculation of the volume of a sphere whose radius is 4.9cm. 3mks
 In a right angled triangle ,the two sides enclosing the right angle measure (3x 2) cm and (x+2)cm.If the area of the triangle is 36cm^{3}.Find the length of these two sides. 3 mks

 Expand (ab)^{5} 1mks
 Use the first three terms of the expansion in (a) in ascending power to find the approximate value of (1.98)^{5} (2mks)
 The first term of geometric sequence is 16 ,and the fifth term is 81.Find the sum of the first 10 terms . (3mks)
 Solve the equation sin sin (^{1}/_{2}x30)=cos cos x^{0} 2mks
 The angle at vertex of a cone is 90^{0}.If the slant height is √4 cm,find without using tables .
 The diameter of the cone 2mks
 The height of the cone. 2MKS
 Under a transformation whose matrix is Q = (x2 2x^{2}),a triangle whose area is 12cm^{2} is mapped onto a triangle whose area is 50cm^{2}.Find the two possible values of a . 3mks
 Make L the subject of the formula below.
f= 2mks
SECTION B(50MKS)Answer only five questions from this section

 Complete the table given below by filling the blank spaces. 2mks
X
0
15
30
45
60
75
90
105
120
135
150
165
180
4cos 2x
4.00
2.00
20
3.46
2.00
0
2.00
4.00
2sin(2x+30)
1.00
1.73
2.00
1.73
0
1.00
1.73
.2.00
1.73
0
1.00
 On the grid provided draw the graph of y = 4cos 2xn and y =2 sin (2x+30) for O^{0 }≤x≤180^{0 }. 5mks

 State the amplitude of y=4cos 2x . 1mk
 Find the period of y =2sin (2x+30)^{0}
 Use your graph to solve
4cos 2x 2sin (2x+30) =0 1mk
 Complete the table given below by filling the blank spaces. 2mks
 The figure below is a square based pyramid ABCDV with AD=DC=6cm and height VO=10cm.
 State the projection of VA on the base ABCD 1mk
 Find
 The length of VA . 3mks
 The angle between VA and ABCD . 2mks
 The angle between VDC and ABCD 2mks
 Volume of the pyramid. 2mks
 The table below gives marks obtained in a mathematics test by 47 candidates.
Marks
3135
3640
4145
4650
5155
5660
No of candidates
4
6
12
15
8
2
 Calculate the mean score 3mks
 On the grid provided draw a cumulative frequency graph and use it to estimate
 The median 2mk
 The semiinterquartile range. 3mks
 In order to pass the test a pupil had to score more than40 marks. Calculate the percentage of pupils who passed. 2mks

 In a form 4 Class there are 22 girls and 18 boys. The probability that a girl completes the secondary education course is^{3}/_{5} whereas that of a boy is ^{2}/_{3} .A student is picked at random from the class .Find the probability that the student picked
 Is a boy and will complete the course. 2mks
 Will complete the course. 2mks
 Is a girl and will not complete the course. 2mks
 A bag contains 5 blue balls, 8 red balls and 3 green balls being similar in shape and size .A ball is picked out at random without replacement and its colour noted, use a tree diagram to determine the probability that at least one of the first two balls picked is green. 4mks
 In a form 4 Class there are 22 girls and 18 boys. The probability that a girl completes the secondary education course is^{3}/_{5} whereas that of a boy is ^{2}/_{3} .A student is picked at random from the class .Find the probability that the student picked
 Two quantities P and R are connected by the equation P=Kr^{n} where k and n are constants. The table of values of P and r is given below.
 State the linear equation connecting P and r. 1mk

 Using a suitable scale draw a suitable line graph from the above data on the grid provided . 5mks
 Using your graph estimate the values of k and n. 3mks
 Find the equation connecting P and r. 1mk

 P,Q and R are three quantities such that P varies directly as the square of Q and inversely as the square root of R.
 Given that P=12 when Q=24 and R=36,find P when Q=27 and R=121. 3mks
 If Q increases by 10% and R decreases by 35% find the percentage increase in P. 4mks
 If Q is inversely proportional to the square root of P and P=4 when Q=3.Calculate the value of P when Q = 8. 3MKS
 P,Q and R are three quantities such that P varies directly as the square of Q and inversely as the square root of R.
 A community water tank is in the shape of a cuboid of base 6m by 5m and a height of 4m.A feeder pipe of diameter 14cm suppliers water to this tank at the rate of 40cm /s
Calculate the; Capacity of the tank in litres. 2mks
 Amount of water ,in litres delivered to this tank in one hour. 3mks
 The time taken for the tank to fill . 2mks
 The community consumes a full tank a day,with each family consuming an average of 150 litres per day.If each family pays a uniform rate of sh.350 per month,find the total amount of money due monthly. 2mks
 In the diagram O is the centre of a circle radius 11cm .OX=5cm and BX=12cm.
 Find the length of XA. 3mks
 Find the size of angle XOA . 3mks
 Find the area of the shaded part. 4mks
MARKING SCHEME