Mathematics Questions and Answers - Form 1 End Term 3 2022 Exams

SECTION A (50MARKS)
Attempt all the questions in the spaces provided.

1. Without using a calculator, evaluate; (3 mks)
   (⁵/₆ − 1²/₃ + 1¼  x 1⁵/₇)
2. Use substitution method to solve the following simultaneous equations. (3 mks)
   3x + 2y = 23
   2x – y = 6
3. A fruit juice dealer sells the juice in packets of 300ml, 500ml and 750ml. Find the size of the smallest container that can fill each of the packets and leave a remainder of 200ml.(3 mks)
4. The size of an interior angle of a regular polygon is 150°. Find the number of sides of the polygon. (3 mks)
5. Find the area of the shaded region in the figure below (use π = 3 .14) (3 mks)
   
6. Solve the equation; (3 mks)
   x + 1 – x – 3 = 4
      2          3
7. Show that 8260439 is exactly divisible by 11 using divisibility test. (2 mks)
8. Without using a calculator, evaluate; (3 mks)
   36 – 8 × –4 –15 ÷ –3
    3 × –3 –8(+6–(–2))
9. The figure below (Not drawn to scale) shows the cross section of a metal bar of length 3 metres. The ends are equal semi circles. Determine the mass of the bar in kg if the density of the metal is 8.87g/cm³ (3 mks)
   
10. A Kenyan bank sells and buys foreign currency as show in the table below.
    

    	Buying (kshs)	Selling (kshs)
    1 Us dollar	95.34	95.87
    1 UK pound	124.65	125.13

    A tourist arrived in Kenya with 15000 pounds and converte4d into Kenya shillings at a commission of 8% . He later used half of the money before changing the balance into dollars at no commission. Calculate to the nearest dollar the amount he received.       (3 mks)
11. Three years ago, John was three times as old as Jane. In two years time, the sum of their ages would be 62 years. Calculate the difference in their ages five years ago. (3 mks)
12. In the figure below <MNO = 54° and <PLM = 50°, PN = NM and PO is parallel to LM. Find the value of <LPM
    (3 mks)
    
13. Use the table of squares and square roots to evaluate; (3 mks)
    √ 0.000125
        0.0225²
14. Wanjiru, Atieno and Jeptoo shared the profit of their business in the ratio of 8:7:9 respectively. If Atieno received sh 63,000, find how much profit the business realised.    (3 mks)
15. Five men each working 10 hrs a day take two days to cultivate acre of land. How long will two men each working six hours a day take to cultivate three acres of land. (3 mks)
16. A wholesale sold a radio to a retailer making a profit of 20% . The retailer later sold the radio for Kshs 1560 making a profit of 30%. Calculate the amount of money.    (3 mks)
17. Sketch the net of the solid below and find its total surface area. (3 mks)
    

SECTION B
Attempt any 3 questions

18. Measurement of a maize filed using baseline XY were recorded as shown below.
    Measurements are in metres. Take XY=400m
    

    To R 80   To S 160

    Y   360   280  200   40    X

    80 to Q   200 to P

    1. Using a scale of 1cm to represent 40m, draw the map of the coffee farm. (4mks)
    2. Calculate the area of coffee farm in hectares. (6mks)
19.  
    1. Using a ruler and a pair of compasses only construct a triangle ABC such that AB = AB=4cm, BC=5cm. and <ABC=120°. Measure AC. (4mks)
    2. Construct a circle which passes through vertices of a triangle ABC. Measure the shortest distance from the centre of the circle to point B. (4mks)
    3. Calculate the area of the circle draw. (2mks)
20. The travel timetable below shows the departure and arrival for a bus plying between two towns A and E, 300 kilometres apart.
    

    Town	Arrival	Departure
    A     B     C     D     E	1000h   1310h  1510h  1600h	0830h    1020h    1340h    1520h

    1.  
       1. How long does the bus take to travel from town A to E in minutes. (2mks)
       2. How long does it take at town C in seconds? (1mk)
       3. At what time does it arrive at town E in 12 hour system. (1mk)
       4. What is the average speed for the whole journey (3mks)
    2. A service vehicle which left Mombasa for Nairobi at 1010h had a puncture after travelling for 4h 20 minutes. Fixing a new tyre took 35 minutes. The vehicle then travelled for another hour 20 minutes to reach Nairobi at what time did it arrive at Nairobi? (3mks)
21.  
    1. Calculate the volume of the log of wood below. (2mks)
       
    2.  If the density of the wood is 0.5g/cm³. Find the mass in Kg (2mks)
    3.  
       1. Calculate the surface area of the log of wood in cm². (4mks)
       2. The log was painted. If the cost of paint was Ksh 50 per cm². Calculate the total cost of the paint. (2mks)
22. Three towns A and B are situated in such that away B is on a bearing of 280° from town C. If town A is 190km from town C and town B is 160km from town C. If town A is 190km from town C and town B is 160km from town C on scale.
    1. Draw the position of three town A, B and C on scale. (4mks)
    2. Find the bearing of A from B (2mks)
    3. Find the distance between A and B. (2mks)
    4. A motorist travelled from A to B then to C and back to A at an average speed of 80km/h. Find the time taken.(2mks)

MARKING SCHEME

No.
1	(5/6 − 12/3 + 1¼  x 15/7) = 5/6 + 5/4 − 5/3) x 12/7 = (10 + 15 – 20) x 17             12               7 = 5/2 x 12/7 = 5/7	M1  M1  A1
		3
2	3x + 2y = 23 2x – y = 6 2x – y = 6 –y = 6 – 2x y = 2x – 6 3x + 2 (2x – 6) = 23 3x + 4x – 12 = 23 7x = 23 + 12 7x = 35 x = 5 2(5) – y = 6) 10 – y = 6 y = 4	M1       A1      A1	Substitution method must be used otherwise NO MARKS
		3
3	LCM   LCM = 22 × 3 × 53 = 1500L  1500 + 200 = 1700L	B1    M1      A1	Findingnthe LCM
		3
4	Exterior angle = 180° − 156°                          = 24 No. of sides = 360° = 15                         24°	M1  A1
		2
5	Area of bigger sector  36  x 3.142 x 10.5 x 10.5 = 34.641  360 Area of smaller sector  36  x 3.142 x 7 x 7 = 15 .396 360 Shaded = 34.641 – 15.396 = 19.245cm2	M1    M1    A1
		3
6	x + 1 – x –3 = 4     2        3 6 (x + 1)  – 6 (x – 3) = 6(4)    (   2   )        (   3  ) 3(x + 1)  – 2(x – 3) = 24 3x + 3 – 2x + 6 = 24 x+ 9 = 24 x = 24 – 9 x = 15	M1      M1      A1
		3
7	8260439 Sum of all digits odd positions = 8 + 6 + 4 + 9 = 27 Even positions = 2 + 0 + 3 + = 5 Difference = 27 – 5 = 22 22 is a multiple of 11 hence divisible by 11	M1      A1
		2
8	Numerator: 36 – 8x – 4 + 5 36 + 32 + 5 = 73 Denominator 3x – 3 + –8(8) =– 9 – 64                        = –73 N =  73 = –1 D   –73	M1    M1    A1
		3
9	Cross section area (2 x 7) + 22 x 72 = 168cm2                7 Volume = (168 x 300)cm3             = 50,400cm3 Mass v x d + 50,400 x 8.87                              1000               = 447.048kg	B1    M1    A1
		3
10	(15000 X 124 .65) 92                                100 Ksh 1720170 ½ x 1720170 = 860085 860085 = 8971.3675   95.87 = 8971 US dollars	M1    M1    A1
11	John       Jane 3 years ago      3x            x 2 years time    3x + 5      x + 5 3x + 5 + x + 5 = 62 4x + 10 = 62 4x = 52 x = 13 Difference = 39 – 13 = 26	M1    M1    A1	Difference does not change
		3
12	<PNM = 180 – 54 = 126° <NPM= <NMP=180 − 126=27° 2 <LMP= <NPM = 27° Hence <LPM=180 − (27+50) = 103°	B1  B1    A1
		3
13	√ 0.000125     0.02252 √0.000125 = 1.25 x     1                                       10000                    = 1.1180 x 1/100                    = 0.01118 0 .02252 = (2 .25)2 =    5.0625                      (100)         10000                =0.00050625   =       0.0118              0.00050625     = 22.084	B1      B1      A1
		3
14	W:A:J = 3:7 :9 Atieno =     7    =   7                3+7+9    19 7/19    = 63,000 19/19 = ? 63,000 x 19/7 = Ksh 171,000	M1    M1    A1
		3
15	Men Days Hrs Acres    5      2      10    1    2      ?       6     3 2 x 5 x 10 x 3 = 25 days    2        6     1	B1      M1
		2
16	130% = 1560 100% =    ? 1560 x 100 = 1200       130 120% = 1200 100% = ? 1200 x 100 = 1000       120	M1    M1    A1
		3
17	Area (5 x 4) 2 + (4 x 3) 2 + (5 x 3) 2 40 + 24 + 30 = 94cm2	B1    B1        A1	Sketch
18	Area of A= 1⁄2 x 200 x160= 16,000 m2 Area of B= 1⁄2(160+80)80= 9,600 m2 Area of C= 1⁄2 x 120 x 80 = 2,400 m2 Area of D= 1⁄2 x 40 x 200= 4,000m2 Area of E= 1⁄2(200+80)= 44,800m2 Area of F= 1⁄2 x 40 x 80 = 1,600m2 Total = 78,400m2           = 7.84 hectares	B1      B2    B1      B3    B1    A1	Baseline      Offsets    Complete Diagram    Every 2 correct  1 Mark    Area in m2
19		B1  B1  B1  B2  B1      B1  B1  M1  A1	Angle of  ABC  Point C  For Δ ⊥ bisector  Circle
20	Time taken = arrival − departure time                    = 1600 hr − 0830 hrs                    = 7hrs 30 min 7 x 60 + 30= 450 minutes 1340hrs − 1310 hrs = 30 minutes                 30 x 60  = 1800 seconds 1600 − 1200 = 4.00 p.m. speed = d/t              = 300 = 40 km/h                 7.5 Time taken = 4hrs 20 min 1010h    420 +  1420h      35 +  1435h    120      1555h/3.55pm
21	5.6m = 560 cm V=πr2l = 22⁄7 x 14 x 14 x 560             = 344,960 cm3 Mass = density x volume          = 0.5 x 344,960          =172,480g     1000g = 1 kg 172480g = ? 172480 =172.40 kg   1000   S.A = πdl+2πr2        = 22⁄7 x 28 x 560 + 2 x 22⁄7 x 14 x 14        = 49,280 + 1,232        =  50,512cm2  50512⁄1000 = 5.0512m2       1m2     = kshs 50 5.0512m2 = ? 50 x 5.0512 = Kshs 252.56
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