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

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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)
    Maths F1 ET3 2122 Q5
  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)
    Maths F1 ET3 2122 Q9
  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)
    Maths F1 ET3 2122 Q12
  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)
    Maths F1 ET3 2122 Q17

SECTION B
Attempt any 3 questions

  1. 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)
  2.  
    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)
  3. 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)
  4.  
    1. Calculate the volume of the log of wood below. (2mks)
      Maths F1 ET3 2122 Q20i
    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)
  5. 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
 Maths F1 ET3 2122 Ans3
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 + 1x –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  Maths F1 ET3 2122 Ans17

Area (5 x 4) 2 + (4 x 3) 2 + (5 x 3) 2
40 + 24 + 30 = 94cm2

 B1

 

 B1

 

 

 

 A1

 Sketch
  18  Maths F1 ET3 2122 Ans17

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  Maths F1 ET3 2122 Ans18 new

 B1
 B1
 B1
 B2
 B1

 

 

 B1
 B1
 M1
 A1

  Angle of  ABC
 Point C
 For Δ
⊥ bisector
 Circle








 20
  1.  
    1. Time taken = arrival − departure time
                         = 1600 hr − 0830 hrs
                         = 7hrs 30 min
      7 x 60 + 30= 450 minutes
    2. 1340hrs − 1310 hrs = 30 minutes
                      30 x 60  = 1800 seconds
    3. 1600 − 1200 = 4.00 p.m.
    4. speed = d/t 
                  = 300 = 40 km/h
                      7.5
      Time taken = 4hrs 20 min
  2. 1010h 
      420 +
     1420h
         35 +
     1435h
       120    
     1555h/3.55pm
   
 21
  1. 5.6m = 560 cm
    V=πr2l = 22⁄7 x 14 x 14 x 560
                = 344,960 cm3
  2. Mass = density x volume
             = 0.5 x 344,960
             =172,480g
        1000g = 1 kg
    172480g = ?
    172480 =172.40 kg
      1000
  3.  
    1. S.A = πdl+2πr2
             = 22⁄7 x 28 x 560 + 2 x 22⁄7 x 14 x 14
             = 49,280 + 1,232
             =  50,512cm2 
    2. 50512⁄1000 = 5.0512m2 
           1m2     = kshs 50
      5.0512m2 = ?
      50 x 5.0512 = Kshs 252.56
   
  22  Maths F1 ET3 2122 Ans21    

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