INSTRUCTIONS
- The paper contains two sections A and B.
- Answer all questions in section A and any five questions from section B 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.
- Non-programmable silent electronic calculator and mathematical tables may be used except where stated otherwise.
SECTION A (50 MARKS)
Answer all questions in this section
- Use logarithm table to evaluate. (4mks)
- Three sisters, Ann, Beatrice and Caroline together invested Ksh. 48,000 as capital and started a small business. If the share of profit is Ksh. 2,300, Ksh. 1,700 and Ksh. 800 respectively, shared proportionally. Find the capital invested by each of them. (3mks)
- Make t the subject of formula in
(3mks) - Without using a calculator or mathematical tables, express in surd form and simplify. (3mks)
√3
1 − cos 30º - Expand and simplify (3x − y)4 hence use the first three terms of the expansion to approximate the value of (6 − 0.2)4. (4mks)
- Find x without using tables if 3 + log23 + log2x = log25 + 2 (3mks)
- Find the value of m for which the matrix transforms an object into a straight line. (3mks)
- In the figure below PT is a tangent to the circle at T, PQ = 9cm, SA = 6cm, AT = 8cm and AR = 3cm. Calculate the length of;
- AQ (2mks)
- PT (1mk)
- A right angled triangle has a base of 15.3 cm and height 7.2 cm, each measured to the nearest 3 mm. Determine the percentage error in finding the area of the triangle, giving your answer to 2 decimal places. (3mks)
- Given that sin x=0.8, without using a mathematical table and calculator find tan(90-x) (3mks)
- The point B(3,2) maps onto B1(7,1) under a translation T1. Find T1 (2mks)
- Using a ruler and a pair of compasses only, construct triangle ABC in which BC = 6cm, AB = 8.8cm and angle ABC= 22.50. (3mks)
- Two grades of tea A and B, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by mass. The mixture is then sold at sh 160 per kg. Find the percentage profit on the cost price. (3mks)
- The first, the third and the ninth term of an increasing AP, makes, the first three terms of a G.P. If the first term of the AP is 3, find the difference of the AP and common ratio of GP. (4mks)
- The matrix maps a triangular object of area 7 square units onto one with area of 35 square units. Find the value of x. (4mks)
- The equation of a circle is given by x2 + 4x + y2 − 2y-4=0. Determine the centre and radius of the circle (3mks)
SECTION B (50 MARKS)
Answer any five questions in this section
- A bag contains 3 black balls and 6 white balls. If two balls are drawn from the bag one at a time, find the:
- Probability of drawing two white balls:
- With replacement (2mks)
- Without replacement (2mks)
- Probability of drawing a black ball and white ball:
- With replacement (3mks)
- Without replacement. (3mks)
- Probability of drawing two white balls:
- In the triangle below P and Q are points on OA and OB respectively such that OP:PA = 3 : 2 and OQ : QB = 1 : 2. AQ and PQ intersect at T. Given that OA = a and OB = b.
- Express AQ and PQ in terms of a and b. (2mks)
- Taking BT=kBP and AT=hAQ where h and k are real numbers.
- Find two expressions for OT in terms of a and b. (2mks)
- Use the expression in b(i) above to find the values of h and k. (4mks)
- Give the ratio BT:TP. (2mks)
- Complete the table below for the functions y=3cosx − 2 for 0°≤ x ≤360° (2mks)
x 0 30 60 90 120 150 180 210 240 270 300 330 360 y = 3cosx − 2 - Plot the graph of y=3cosx − 2 in the graph provided below. (3mks)
- From the graph
- Find the amplitude of the wave. (2mks)
- The period of the wave. (1mk)
- Find the solution to 3cosx = 2 (2mks)
- Plot the graph of y=3cosx − 2 in the graph provided below. (3mks)
- A plane leaves an airport A (41.5°N, 36.4°W) at 9:00am and flies due north to airport B on latitude 53.2°N. Taking π as 22/7 and the radius of the earth as 6370 Km,
- Calculate the distance covered by the plane in km (4mks)
- The plane stopped for 30minutes to refuel at B and flew due east to C, 2500km from B. Calculate:
- position of C (3mks)
- The time the plane lands at C if its speed is 500km/h (3mks)
- The curve given by the equation y=x2+1 is defined by the values in the table below.
X 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Y 1.0 2.0 5.0 10.0 17.0 26.0 37.0 - Complete the table by filling in the missing values. (2mks)
- Sketch the curve for y=x2 + 1 for 0 ≤ x ≤6 (2mks)
- Use the mid-ordinate rule with 5 ordinates to estimate the area of the region bounded by the curve y=x2+1, the x-axis, the lines x = 0 and x = 6. (2mks)
- Use method of integration to find the exact value of the area of the region in (c) above. (2mks)
- Calculate the percentage error involved in using the mid-ordinate rule to find the area. (2mks)
-
- Using a ruler and pair of compasses only construct triangle PQR in which PQ = 7.5cm QR= 6.0cm and angle PQR = 60°. Measure PR (3mks)
- On same side of PQ as R
-
- Determine the locus of a point T such that angle PTQ = 60° (3mks)
- Construct the locus of M such that PM = 3.5cm. (2mks)
- Identify the region W such that PR≥3 and angle PTQ≥60° by shading the unwanted part. (2mks)
- OABCD is a right pyramid on a rectangular base with AB = 8 cm, BC = 6 cm, OA = OB = OC = OD = 13 cm. Calculate;
- the height of the pyramid. (3mks)
- the inclination of OBC to the horizontal. (2mks)
- the angle between;
- OB and DC (3mks)
- the planes OBC and OAD (2mks)
- the height of the pyramid. (3mks)
- The games master wishes to hire two matatus for a trip. The operators have a Toyota which carries 10 passengers and a Kombi which carries 20 passengers. Altogether 120 people have to travel. The operators have only 20litres of fuel and the Toyota consumes 4 litres on each round trip and the Kombi 1 litre on each round trip. If the Toyota makes x round trips and the kombi y round trips;
- write down four inequalities in x and y which must be satisfied . (2mks)
- Represent the inequalities graphically on the grid provided. (3mks)
- The operators charge shs.100 for each round trip in the Toyota and shs.300 for each round trip in the kombi;
- determine the number of trips made by each vehicle so as to make the total cost a minimum. (4mks)
- find the minimum cost. (1mk)
Marking Scheme
-
- A : B : C
2300 : 1700 : 800
23 : 17 : 8
23/48 : 17/48 : 8/48
Ann = 23/48 × 48, 000 = sh. 23,000
Beatrice = 17/48 × 48, 000 = sh. 17,000
Caroline = 8/48 × 48, 000 = sh. 8,000 -
-
- 1(3x)4(−y)° + 4(3x)3(−y)1 + 6(3x)2(−y)2 + 4(3x)1(−y)3 + 1(3x)°(−y)4
81x4 +− 108x3y + 54x2y2 − 12xy3 + y4
81x4 − 108x3y + 54x2y2 − 12xy3 + y4
3x = 6 −y = − 0.2
x = 2 y = 0.2
81x4 − 108x3y + 54x2y2
81(2)4 − 108×8×0.2 + 54× 4 × 0.04
324 − 172.8 + 8.64
= 159.84 - 3log22 + log23 + log2x = log25 + 2log22
log28 + log23 + log2x = log25 + log24
log2(8 × 3 × x) = log2(5×4)
24x = 20
24 24
x = 5/6 - Singular matrix
(m2 × 1) − (2m − 1)1 = 0
m2 − (2m − 1)1 = 0
m2 − 2m + 1 = 0
(m2 − m)(−m + 1) = 0
m(m − 1) − 1(m−1)
(m − 1)(m − 1) = 0
m − 1 = 0
m = 1 -
- 8 × 62 = 3AQ
3 3
AQ = 16 cm - 9 × 28 = PT2
PT = √(9 × 28)
= √252
= 15.8745 cm
- 8 × 62 = 3AQ
- Actual Area = 15.3 × 7.2 = 110.16
Max. Area = 15.45 × 2.35 = 113.5575
Min Area = 15.15 × 7.25 = 106.8075
|E| = 106.8075 − 113.5575
2
= 6.75/2 = 3.375
% E = |E| × 100
A.A
= 3.375 × 100
110.16
= 3.06372549
= 3.06 -
Sin x = 8/10 = 4/5
tan (90 −x) = 0
= 3/4 -
-
- 3/8(100) + 5/8(150) ⇒ Cost price
32.5 + 93.75 = sh. 131.25
profit = 160 − 131.25
% profit = Profit × 100
c.p
= 28.75 × 100
131.25
= 21.90476190
= 21.9048% - a, a+2d, a+8d
3, 3+2d, 3+8d
3+8d = 3+2d
3+2d 3
a+24d = a +12d + 4d2
0 = 4d2 − 12d
0 = 4d(d −3)
4d = 0 d − 3 = 0
d = 0 d = 3
r = 3 + 2(3)
3
= 3+6
3
= 9/3
r = 3 - |det| = A.s.f
A.s.f. = IA
OA
= 35/7
= 5
5 = 3y − 10
15 = 3y
y = 5 - x2 + 4x +(4/2)2 + y2 − 2y + (−2/2)2 = 4 + 4 + 1
(x+2)2 + (y−1) = 32
(x−a)2 + (y − b)2 = r2
∴ (a,b) = (−2,1) & r = 3 units -
-
-
-
- = P(BW) or P(WB)
= (3/9 × 6/9) + (6/9 × 3/9)
= 2/9 + 2/9
= 4/9 - = (3/9 × 6/8) + (6/9 × 3/8)
= 1/4 + 1/4
- = P(BW) or P(WB)
-
-
- AQ = AO + OQ
= −a + 1/3b
= 1/3b − a
PQ = −3/5a + 1/3b
= 1/3b − 3/5a -
- OT = OA + AT
= a + h(1/3b − a)
= a + 1/3hb − ha
= (1−h)a + 1/3hb
OT = OB + BT
= b + k(3/5a − b)
= b + 3/5ka − kb
= (1−k)b + 3/5ka - a
(1−h) = 3/5k
b
1/3h = 1 − k
h = 3 − 3k
1−(3−3k) = 3/5k
1 − 3+3k = 3/5k
−2 = −3k + 3/5k
5/12 × −2 = −12/5k × −5/12
k = 5/6
h = 3 − 3k
= 3 − 3(5/6)
= 3 − 5/2
h = 1/2
- OT = OA + AT
- BT:TP
k : 1 − k
5/6 : 1 − 5/6
6 × 5/6 : 5/6
BT:TP = 5:1
- AQ = AO + OQ
-
x 0 30 60 90 120 150 180 210 240 270 300 330 360 y = 3cosx − 2 1.0 −1.5 −4.9 −3.3 0.4 0.1 −3.8 −4.7 −1.0 1.0 −2.1 −5.0 −2.9 -
-
- 1 −−5 = 3 units
2 - 270°
- 3cos x − 2 = 0
18°, 117°, 150°, 249°, 282°
- 1 −−5 = 3 units
-
-
-
Distance = 11.7/360 x 2 x 22/7 x 6370
= 1,301.3km -
- θ/360 x 2 x 22/7 x 6730 cos 53.2 = 2500
66.6247θ = 2500
66.6247 66.6247
θ = 37.52
37.52 − 36.4 = 1.12°
∴ C(53.2°N, 1.12°E) - t = D/S
= 1301.3/500 + 2500/500
= 2 hrs 36 min + 5 hrs
= 7 hr 36 min
37.52° x 4 = 150.08
= 2 hrs 30 mins
0900h
0736
1636h
230
1906h
= 7.06 pm
- θ/360 x 2 x 22/7 x 6730 cos 53.2 = 2500
-
-
-
X 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Y 1.0 1.25 2.0 3.25 5.0 7.25 10.0 13.25 17.0 21.25 26.0 31.25 37.0 -
- A = 1(1.25 + 3.25+7.25+13.25+21.25+31.25)
= 1 (77.5)
= 77.5 sq. units - |E| = Approx. A − Actual Area
= 77.5 − 78
= 0.5 sq. units
%E = |E|/A.A × 100
= 0.5/78 × 100
= 0.64102564
= 0.6410 %
-
-
-
-
-
tanθ = 12/4
θ = tan-13
= 71.57° -
-
cos β = 4/13
β = cos-1 4/13
= 72.08° -
Tan r = 4/12
r = Tan-1 4/12
= 18.43°
∴2r = 36.87°
-
-
-
- 10x + 20y ≥ 120
4x + y ≤ 20
x ≥ 0
y ≤ 0 -
-
- 100x+300y = k (1,10)
100(1)+300(10) = k
100 + 3000 = k
k = 3100
100x + 300y = 3100
3100 3100 3100
x + _y_ = 1
31 10.3
Minimum cost (4,4)
= 4 Toyota trips
= 4 Kombi trips - 100x + 300y ⇒ cost
100(4) + 300(4) = 400 + 1200
= sh. 1600
- 100x+300y = k (1,10)
- 10x + 20y ≥ 120
Download Mathematics Paper 2 Questions and Answers - Kassu Jet Joint Exams 2020/2021.
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