Instructions to candidates
 Write your name and class in the spaces provided above.
 Sign and write the date of examination in the spaces provided above.
 The paper contains TWO sections: Section I and Section II.
 Answer ALL the questions in Section I and any five questions from Section II
 All answers and working must be written on the question paper in the spaces provided below each question.
 Show all the steps in your calculations, giving your answers at each stage in the spaces below each question.
 Nonprogrammable silent electronic calculators and KNEC Mathematical tables may be used, except where stated otherwise.
For Examiner's use only.
SECTION 1
1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  TOTAL 
SECTION II
17  18  19  20  21  22  23  24  TOTAL 
QUESTIONS
SECTION I
Attempt ALL questions in this section.
 Use logarithms to evaluate the value of
Give your answer correct to 4 significant figures. (3marks)  Make x the subject of the formula (3marks)
 Without using a calculator or mathematical tables, express in surd form and simplify. (3marks)
 Find the centre and radius of a circle whose equation is 3x^{2} + 3y^{2} + 18x  12y +39 = 12 (3marks)
 Under a transformation whose matrix is , an object of area 12cm^{2} mapped onto an image whose area is 60cm^{2}. Find the possible values of x. (3marks)

 Expand the binomial (2marks)
 Using the first 4 terms of the binomial above solve for 1.75^{5 }(2 marks)
 Solve for x in the equation 3 sin^{2}x + 8cosx = 0 for 0° ≤ x ≤ 360° (3marks)
 Given 4.50 ÷ 5.0; Find the percentage error in the quotient. Give your answer to 4 s.f. (3marks)
 Find the equation of tangent to the curve y = (2x^{2}+1) (x3) at x = 1. (3 marks)
 Given that (3 marks)
 Use the trapezoidal rule to approximate the area bounded by the curve y = x^{2}3x+10 and the xaxis by using 4 trapezoids of equal width from x = 4 to x = 0 (3 marks)
 Maina bought a new laptop on hire purchase. The cash value of the laptop was Ksh. 56,000. He paid a deposit of Ksh. 14,000 followed by 24 equal monthly installments of Ksh.3500 each. Calculate the monthly rate at which the compound interest was charged. (3marks)
 Water flowing at a rate of 2m/sec through two pipes of diameter 3cm and 5cm respectively deliver water to a 6 cm diameter pipe. Calculate the speed of flow in the 6 cm pipe if a^{1}. are kept full. Give your answer in m/sec (3 marks)
 A quantity A is partly constant and partly varies inversely as a quantity B. Given that A = 10 when B= 2.5 and A = 10 when B = 1.25, find the value of A when B = 1.5. (4marks)
 A coffee dealer mixes two brands of coffee, x and y to obtain 40kg of the mixture worth Ksh. 2,600. If brand x is valued at Ksh. 70 per kg and brand y is valued at Ksh. 55 per kg. Calculate the ratio in its simplest form in which brands x and y are mixed. (3marks)
 The figure below shows a circle centre O. AB and PQ are chords intersecting externally at a point C. AB = 9cm, PQ= 5cm and QC = 4cm. Find the length of BC. (3marks)
SECTION II
Answer five questions only in this section.
 The marks of 50 students in a mathematics test were taken from a form 4 class and recorded in the table below.
Marks 2130 3140 4150 5160 6170 7180 8190 91100 Frequency 2 5 7 9 11 8 5 3  On the grid provided, draw a cumulative frequency curve of the data, using 1cm to represent students and icm to represent 10 marks.
(3marks)  From your curve in (a) above;
 Estimate the median mark (1mark)
 Determine the interquartile deviation (2marks)
 Determine the 10th to goth percentile range. (2marks)
 It is given that students who score over 45 marks pass the test. Use your graph in (a) above to estimate the percentage of students that pass.
(2marks)
 On the grid provided, draw a cumulative frequency curve of the data, using 1cm to represent students and icm to represent 10 marks.
 The table below shows the rate at which income tax was charged for all income earned in the year 2015
Taxable income per month in k£ Rate of tax per k£ 1  236 10% 237472 15% 473  708 20% 709  944 25% 945 and above 30%  A tax of Ksh 1200 was deducted from Mr. Rono's monthly salary. He was entitled to a personal relief of Ksh 1064 per month. Calculate his monthly
 Gross tax in k£. (1mark)
 Taxable income in Ksh (5marks)
 He was entitled to a house allowance of Ksh 3000 and medical allowances of Ksh 2000 calculate his monthly basic salary in Ksh. (2mark)
 Every month the following deductions were made from his salary electricity bill of sh. 680, water bill of sh 460, cooperative shares of sh 1250 and loan repayment of sh 2000 calculate his net salary in Ksh. (2marks)
 A tax of Ksh 1200 was deducted from Mr. Rono's monthly salary. He was entitled to a personal relief of Ksh 1064 per month. Calculate his monthly

 An arithmetic progression is such that the first term is 5, the last term is 135 and the sum of progression is 975.
 The number of terms in the series. (3marks)
 The common difference of the progression. (3marks)
 The sum of the first three terms of a geometric progression is 27 and first term is 36. Determine the common ratio and the value of the fourth term. (4marks)
 An arithmetic progression is such that the first term is 5, the last term is 135 and the sum of progression is 975.
 The diagram below shows a straight line 2x + y = 8 intersecting the curve y = 2x^{2}  4x + 4 at the points P and Q.
 Find the coordinates of P and Q. (3marks)
 Calculate the area of the shaded region. (4 marks)
 Find the coordinates of the stationary points on the curve y = 2x^{2}  4x + 4 (3 marks)
 The diagram below shows the frustum of a rectangular based pyramid. The base ABCD is a rectangle of side 24cm by 12cm. The top EFGH is a rectangle of side 14cm by 7cm.Each of the slanting edges of the frustum is 13cm.
Determine the: Altitude of the frustum (4marks)
 Angle between the line AG and the base ABCD (3marks)
 Volume of the frustum (3marks)
 The probability that three candidates; Anthony, Beatrice and Caleb will pass an examination are 3/4, 2/3 and 4/5 and respectfully. Find the probability that:
 All the three candidates will pass (2marks)
 All the three candidates will not pass. (2marks)
 Only one of them will pass (2marks)
 Only two of them will pass. (2marks)
 At most two of them will pass. (2marks)
 In the figure below PQR is a tangent to the circle at Q. TS is a diameter and TSR and UV are straight lines. QS is parallel to TV. Angles SQR = 40° and TQV = 55°.
 Find the following angles giving reasons each case.
 ∠QTS (2marks)
 ∠QRS (2marks)
 ∠QVT (2marks)
 ∠QUT (2marks)
 Given that QR8cm, and SR = 4cm. Find the radius of the circle. (2marks)
 Find the following angles giving reasons each case.
 A firm has a fleet of vans and trucks. Each van can carry 9 crates and 3 cartons. Each truck can carry 4 crates and 10 cartons. The firm has to deliver not more than 36 crates and at least 30 cartons.
 If x vans and y trucks are available to make the delivery. Write down inequalities to represent the above information. (4 marks)
 Use the grid provided, to represent the inequalities in (a) above (4 marks)
 Given that the cost of using a truck is four times that of using a van, determine the number of vehicles that may give minimum cost (2 Marks)
MARKING SCHEME
 Use logarithms to evaluate value of. Give your answer correct to 4 significant figures
 Make x the subject of the formula
(2p)^{2} = x+2w
4x + 3R
4P^{2}(4x + 3R) = x+ 2w
16P^{2}x + 12P^{2}R=x+2w
16P^{2}x  x = 2w 12P^{2}R
x^{2}(16P^{2} 1)=2w12P^{2}R
X = 12w  12P^{2}R
16P^{2}  1  Without using calculator or mathematical tables, express in surd form and simplify
 Find centre and radius of a circle
x^{2} +y^{2} +6x4y= 9
(x + 3)^{2} + (y2)^{2} = 9 + 9 + 4
Centre (3,2)
Radius = 2 units  Find the possible values of x
(x  1)(x + 1)3 = 60
12
x^{2} 13=5
x^{2} = 9
x = ±3 
 Expand binomial
coef: 1, 5, 10, 10, 5,1
1.2^{5} (1)° +5.2^{4}(1)^{1} + 10.2^{3}(1)^{2} + 10.2^{2}(1)^{3} +5.21(1)^{4} + 1.2°(1)^{5}
4x 4x 4x 4x 4x 4x
32  20 + 5  5 + 5  1
x x^{2} 8x^{3} 128x^{4} 1024x^{5}  Using first 4 terms of the binomial above solve or 1.75^{5}
(20.25)^{5} = (2 ^{1}/_{4}x) 0.25 = ^{1}/_{4}x
x = 1
4 x 0.25
X = 1
= 3220+5  5
= 16.375
 Expand binomial
 solve for x
 find percentage error in the quotient in 4 s.f
 Find equation of tangent to the curve
y = (2x^{2} + 1)(x  3)
y=2x^{3} 6x^{2} + x  3
dy = 6x^{2} 12x+1
dx
X = 1
dy = 6 12 +1 = 5
dx
@x=1
y = 6
Equation
y + 6= 5
x  1
y + 6 = 5+5
y=5x  1  Find /AB/
AB = 2ij2k
i +21  3h
i3j+k  Approximate area bounded by the curve
x 4 3 2 1 0 y 6 10 12 12 10
A = ^{1}/_{2}(16 + 2(34))
A = ^{1}/_{2} × 84
A = 42 square units  Calculate monthly rate at which compound interest was charged
Total interest amount = 34,000
Principal = 56,000
(C.P. Dep14.000)
42,000
84,000  42,000 (1 + R)^{24}
100
84.000 = (1 +B)^{24}
42,000 100
^{24}√2 = (1+R)
100
1.02931 = R
100
R = 2.93% P.m  Calculate speed of flow in the 6cm pipe if all are kept frull
Vol. delivered by 2 pipes in 1 sec. ^{22}/_{7} x 1.5^{2} x 200 = 1414^{2}/_{7}cm
 ^{22}/_{7} x 2.5^{2} x 200 = 27500cm^{3}= 3928^{4}/_{7}cm^{3}
Total Vol. 5342^{6}/_{7}
^{22}/_{7 }x 3^{2} x h=5342^{6}/_{7}
h =5342^{6}/_{7 }x 7
22 x 9
h= 188^{3}/_{9}speed = 1.889m/sec
 Find value o A when B1.5
 Calculate the ratio in its simplest form in which brands x and y are mixed Cost of 1kg mixture
2600 = 65
40
2 : 1  Find length of BC
x(x +9)= 9 x 4
x^{2} + 9x 36 = 0
Section II

 On graph provided draw a cumulative frequency curve of the data, using 1 cm to represents students and lcm to represent 10 marks
 from curve
 Estimate median mark
^{1}/_{2} x 60 = 30^{th} = 65  Determine interquartile deviation
Q3 = ^{3}/_{4} x 60 = 45^{th} 71.5
Q1 = ^{1}/_{4} x 60 = 15^{th} 51.5
20.0
Interquartile=^{1}/_{2} x 20 = 10  Determine 10th to 90th percentile range
10th = 10 x 60 = 6th = 39
100
90th = 90 x 60  54th = 84
100
 Estimate median mark
 Use graph to estimate percentage of students that pass
50 students passed
= 50 x 100
60
= 83^{1}/_{3}% passed
 On graph provided draw a cumulative frequency curve of the data, using 1 cm to represents students and lcm to represent 10 marks

 Calculate his monthly
 Gross tax in K£
= 1200 + 1064 = Ksh. 2264
2264
20
= K£ 113.2  Taxable income in Ksh.
1st brachet = 236 x 10/100 = K£ 23.6
2ndbrachet = 236 x 0.15 = K£ 35.4
3rdbrachet = 236 x 0.2 = K£ 47.2
4thbrachet = a x 0.25 K£ 7.0
a = 7  28
0.25
Taxable income
2.6 x 3+28 736
= K£ 736 x 20
=Kshs. 14,720
 Gross tax in K£
 Calculate his monthly basic salary in Ksh.
Basic salary  14,720(3,000+ 2,000)
= Ksh. 9.720  Calculate net salary in Ksh.
Net salary
14,720  (1,200 +680 + 460 + 1250 + 2000)
=Kshs. 9,130
 Calculate his monthly


 The number of terms in the series
Sn = n(a+1)
2
975 = n(5+135)
2
n = 975 x 2
130
n = 15  The common difference of the progression
S_{15} = n (2a + (n  1)d
975 = 15 (2x5 + (151)d)
2
975 = 10 + 14d
7.5
130 + 10 = 14d
d=13
 The number of terms in the series
 Determine common ratio and the value of the fourth term
a+ar+ar^{2 = }27
36 + 36r + 36r^{2} = 27
36r^{2}+ 36r+9 = 0
4r^{2} + 4r + 1 = 0


 Find the coordinates of P and Q
2x^{2}  4x + 4 = 2x + 8
2x^{2}  4x + 2x + 48 = 0
2x^{2}  2x  4 = 0
x^{2}  x 2 = 0
x=1 ± 3
2
x = 2 or1
P(1, y=8(2x1)
P(1, 10)
X = 2, Y = 8 (2 x 2)
= 4
Q = (2,4)  Calculate the area of the shaded region
Area of trapezium
A= ^{1}/_{2} (10 + 4) × 3
= 7x 3 = 21
Area under curve
*(2x^{2}  4x + 4)dx
12x^{3}  2x^{2} + 4x + c)^{2}t
3
= (16  8 + c)  (2  2  4 + c)
3
= 16 + c + 20  c
3 3
Area = 12 sq units
Shaded area
= 2112 = 9 square units  Find coordinates of stationery points on the curve
@ Stationary point
oy=0
ox
oy = 4x  4 = 0
ox
4π = x
X = 1
When x=1
y = 2  4 +4
y = 2
Coordinates A stationary point is (1,2)
 Find the coordinates of P and Q
 Determine
 Altitude of the frustum
 Angle between line AG and the base ABCD
= √720  5.590
= 21.24
TanD = 11.74
21.24
= 28.93°  Volume of the frustum
12 = x + 11.74
7 x
12x = 7x + 82.18 X = 15.436
V=^{1}/_{3 }x 24 x 12 x 28.176  ^{1}/_{3 }x 14 x 7 x 16.436
= 2704.896536.909
= 2167.987cm^{2}
 Altitude of the frustum
 Find probability that:
 All the three candidates will pass
P(ABC)= 3/4 x 2/3 x 4/5 = 2/3  All the three candidates will not pass
P(A'B'C')= 1/4 x 1/3 x 1/5 = 1/60  Only one of them will pass
=P (A'B'C') + P(A'B'C) + P(ABC)
=(3/4 x 1/3 x 1/5) + (1/4 x 2/3 x 1/5) + (1/4 x1/3 x 4/5)  Only two of them will pass
= P (ABC') + P (AB'C) + P (A'BC)
= (3/4 × 2/3 × 1/5) + (3/4 × 1/3 × 4/5) + (1/4 × 2/3 × 4/5)
= 1/10 + 1/5 + 2/15 = 13/30  Almost two of them will pass
P (one or 2 passes)
=3/20 + 12/20
=7/12
 All the three candidates will pass

 Fins the following angles giving reasons each case
 <QTS
<QTS = <SOR = 40°
(Alternate seg. Theorem)  <ORS
<TSQ = 90  40  50°
<OSR = 180  50o = 130°
(Angles on a straight line adds up to 180°)
<QRS180(130+40) 10°
(Angles in a triangle adds up to 180)  <OVT
<SQR905535°
<SOR = <QVT = 35°
(Alternate angles)
(check for a complete reason)  <OUT
<QUT = <OST 50°
(angles subtended by the same chord in the same segment are equal)
 <QTS
 Given that QR8cm, and SR = 4 cm, Find the radius of the circle
Ts=diameter = x
8^{2} = (x + 4) 4
64 = 4x + 16
4x = 48
x= 12
Diameter = 12cm
Radius  6cm
 Fins the following angles giving reasons each case

 if x vans and y trucks are available to make delivery. Write down inequalities to represent the above information
 9x + 4y ≤ 36
 3x + 10y ≥ 30
 y > 0
 x>0
 Use grid provided, to represent the inequalities in (a) above
 Given that cost of using a tuck is four times that of using a van, Determine number of vehicles that may give minimum cost
y=4 cost of trucks=y
x = then cost of van = 1/4y
1 van, 3 trucks
 if x vans and y trucks are available to make delivery. Write down inequalities to represent the above information
Download Mathematics Paper 2 Questions and Answers  Sukellemo Joint Mock Examinations July 2020.
Tap Here to Download for 50/
Get on WhatsApp for 50/
Why download?
 ✔ To read offline at any time.
 ✔ To Print at your convenience
 ✔ Share Easily with Friends / Students
Join our whatsapp group for latest updates