INSTRUCTIONS TO CANDIDATES
- This paper consists of two sections: Section I and Section II
- Answer all questions in section land 3 questions in Section II.
- Show all the steps in your calculations
- Marks may be given for correct working even if the answer is wrong.
- Non- programmable silent electronic calculators and KNEC Mathematical tables may be used.
QUESTIONS
SECTION I: 40MKS
- Evaluate −4 of ((−4 + -15 ÷ 5) + −3 − 4 ÷ 2) (3mks)
84 ÷ −7 + 3 − −5 - Express the following number in terms of their prime factors.(2mks)
196 - Three tanks are capable of holding 36, 84 and 90 litres of milk. Determine the capacity of the greatest vessel which can be used to fill each one of them an exact number of times. (2 mk)
- The cost of 5 skirts and 3 blouses is sh. 1750. Mueni bought three of the skirts and one of the blouses for sh.850. Find the cost of each item. (3 mks)
- Forty five men can construct a road 210m long in 60 days. What length would be constructed by 72 men in 50 day assuming that all work at the same rate? (3mks)
- Using tables to find the Square root of 0.146 (2mks)
- The figure below shows a circle centre O. ChordAB subtends 300 at the centre. If the area of the shaded section is 5.25cm2, find the radius of the circle ( Take π = 22/7) (3mks)
- Juma, Ali and Hassan share the profit of their business in the ratios 3:7:9 respectively. If Juma receives Ksh 60000. How much profit did the business yield? (2mks)
- The exterior angle of a regular polygon is an eighth of the interior angle. How many sides does the regular polygon have? (3 marks)
- Express each of the following as a fraction; (2 mks)
- Find the ratio of x: z if x: y=9:10 and y:z=5:3. (3mks)
- In the figure below, lines AB and LM are parallel.
- Find the values of the angles marked x, and z. (2 mks)
- Solve for y in the following equation;(3mks)
y+3 + y−3 = 1
3 4 12 - A Kenyan company received US Dollars 100,000.The money was converted into Kenya shillings in a bank which buys and sells foreign currencies as follows:
Buying Selling
(in Kenya shillings) (in Kenya shillings)
1 US Dollar 77.24 77.44
1 Sterling Pound 121.93 122.27
Calculate the amount of money, in Kenya shillings, the company received. (3mks) - The diagram below show a triangular prism.
Find the surface area of the prism. 5mks
SECTION II(Answer ALLquestions in this section) - The table below shows a time table for a public surface vehicle operating between two towns A and D via town B and C.
town Arrival time Departure time A 8:20am B 10:40pm 11:00am C 2:30pm 2:50pm D 4:00pm - At what time in 24hour clock system:
- The vehicle leaves town A. 2mks
- The vehicle arrives in town D. 2mks
- How long does it take to travel from town A to D. 4mks
- If the distance between the two towns A and D is 900km, find the average speed of the vehicle. 2mks
- At what time in 24hour clock system:
-
- The table below shows measurements, in metres, made by a surveyor in his field book. Using a scale of 1cm to represent 20m construct a diagram to represent this information. (5mks)
F50
C120
G
280
250
200
150
100
40
AE40
D100B50
- Calculate the area of the above piece of land in hectares. (5mks)
- The table below shows measurements, in metres, made by a surveyor in his field book. Using a scale of 1cm to represent 20m construct a diagram to represent this information. (5mks)
- Use a ruler and a pair of compasses only in this question.
- Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 600. (4mks)
- Measure
- Side AC. (1mk)
- ∠ ACB. (1mk)
- On the same diagram, drop a perpendicular from C to meet AB at D. Measure CD hence calculate the area of the triangle (4mks)
MARKING SCHEME
SECTION I
- = −4 of ((−4−3)+−3−2
−12+3+5
= −4 of (−7+−5)
−4
= 48 =
−4 - 196 =2 × 2 × 7 × 7
=22 × 72 - GDC
2 36 84 90 3 18 42 45 6 14 15 - (5s + 3b = 1750)1
(3s + b = 850)3
5s + 3b = 1750
9s + 3b = 2250
4s = 800
4s = 800
s = 200
b = 850 − 3s
= 850 − 3 × 200
= 250 - No. = 72 × 50 × 210
45 60
=280 - √0.146 = √14.6 × 10−2
=3.821 × 10−1
= 0.3821 - A = θ πr2
360
5.25 = 30 × 22 × r2
360 7
r2 = 5.25 × 360 × 7
30 × 22
r2 = 20.045
r= 4.477 - J : A : H
3 : 7 : 9
3 + 7 + 9 = 19
3/19 = 60,000
Profit = 60,000 × 19
3
= 380,000 -
x + 1/8x = 9/8x
9/8x = 180
x = 180 × 8/9
= 1600
Ext. ∠ = 200
No. of sides = 360
20
= 18 sides - r = 3.7272
100r = 372.72
−r = 3.72
99r = 369
r = 369
99 - x:y = (9:10)5
y:z = (5:3)10
=(45:50)
(50:30)
x:z = 45:30
= 9:6
= 3:2 -
- 12(y + 3) +12(y − 3) = 1 ×12
3 4 12
4(y +3) + 3( y−3)=1
4y + 12 +3y − 9 =1
7y −3 =1
7y=−2
y= −2
7 - 100,000 × 77.24 = 7,724,000
- Hyp =√ 36 + 9
= √45 = 6.7
AΔ =½ × 6 × 6 × 2 = 36cm2
AL = 12 × 6.7 × 2 = 160.8cm2
AL = 6 × 12 = + 72.0cm2
SA = 232.8cm2
SECTION II -
- 0820hrs
- 1200
+ 400
1600 hrs - 2240hrs
−0820hrs
1420hrs form A to B
2400hrs
−2240hrs
1h 20 min
1100hrs from Midnight
1430
−1100hrs
3h 30min from B to C
20 min.
1600hrs
−1450hrs
1h 10 min
Time taken =1420 + 120 + 1100 + 330 + 20min + 110
= 3240hrs - S = D
T
= 900km
3240hrs
S = 42.19km/hr
-
-
- AA= ½ × 2 × 2.5 =2.5cm2
AB = ½ × 5.5 × 7.5 = 20.625cm2
AC = ½ × 2.5 × 7 = 8.75cm2
AD = ½ × 4 × 2 = 4cm2
AE = ½ × 9 × 8.5 = 38.25cm2
AF = ½ × 5 × 6 = 15cm2
89.125
1cm = 20m
1cm2= 400m2
89.15cm2 = x
x = 400m2 × 89.15cm2
10,000m2
= 3.566ha
-
-
-
-
- AC = 7.5cm
- ∠ ACB =540
- AΔ = ½ × b × h
=½ × 7 × 7
= 24.5cm2
-
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