Mathematics Questions and Answers - Form 1 End Term 3 Exams 2021

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

1. Evaluate     −4 of ((−4 + -15 ÷ 5) + −3 − 4 ÷ 2)         (3mks)
                                  84 ÷ −7 + 3 − −5
2. Express the following number in terms of their prime factors.(2mks)
    196
3. 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)
4. 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)
5. 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)
6. Using tables to find the Square root of 0.146 (2mks)
7. 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)
                                             
8. 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)
9. The exterior angle of a regular polygon is an eighth of the interior angle. How many sides does the regular polygon have? (3 marks)
10. Express each of the following as a fraction; (2 mks)
                           
11. Find the ratio of x: z if x: y=9:10 and y:z=5:3. (3mks)
12. In the figure below, lines AB and LM are parallel.
                     
    
    1. Find the values of the angles marked x, and z. (2 mks)
13. Solve for y in the following equation;(3mks)
     y+3   +   y−3 =  1 
      3             4       12
14. 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)
15. The diagram below show a triangular prism.
    Find the surface area of the prism. 5mks
                         
    SECTION II(Answer ALLquestions in this section)
16. 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

    
    
    1. At what time in 24hour clock system:
       1. The vehicle leaves town A. 2mks
       2. The vehicle arrives in town D. 2mks
       3. How long does it take to travel from town A to D. 4mks
       4. If the distance between the two towns A and D is 900km, find the average speed of the vehicle. 2mks
17.  
    1. 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      A

       E40   D100   B50

    2. Calculate the area of the above piece of land in hectares. (5mks)
18. Use a ruler and a pair of compasses only in this question.
    1. Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 60⁰. (4mks)
    2. Measure
       1. Side AC. (1mk)
       2. ∠ ACB. (1mk)
    3. 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

1. =  −4 of ((−4−3)+−3−2
        −12+3+5
   = −4 of (−7+−5)
       −4
   =  48 = 
      −4
2. 196 =2 × 2 × 7 × 7
         =2² × 7²
3. GDC
    

   2	36	84	90
   3	18	42	45
   	6	14	15

4. (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
5. No. = 72 × 50 × 210
            45     60  
         =280
   
   
6. √0.146 = √14.6 × 10⁻²
               =3.821 ×  10⁻¹
               = 0.3821
7. A =  θ   πr²
          360
   5.25 = 30 × 22 × r²
            360    7
   r²  =  5.25 × 360 × 7
              30 × 22
   r² = 20.045
     r= 4.477
8. J : A : H
   3 : 7 : 9
   3 + 7 + 9 = 19
     ³/₁₉  = 60,000
   Profit = 60,000 × 19
                              3
           = 380,000
9.  
   
   
   x + ¹/₈x = ⁹/₈x
   ⁹/₈x = 180
   x = 180 × ⁸/₉
       = 160⁰
   Ext. ∠ = 20⁰
   No. of sides = 360
                         20
                     = 18 sides
   
   
10.       r = 3.7272
    
     100r  = 372.72
        −r =      3.72
       99r =  369
      
          r = 369
                 99
    
    
11. x:y = (9:10)5
    y:z = (5:3)10
    
          =(45:50)
            (50:30)
    x:z = 45:30
          =   9:6
          =   3:2
12.  
            
13.  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
14.  100,000 × 77.24 = 7,724,000
    
    
15.  Hyp =√ 36 + 9
            = √45  = 6.7
    A_Δ =½ × 6 × 6 × 2 = 36cm²
    A_L = 12 × 6.7 × 2 =   160.8cm²
    A_L =           6 × 12 = + 72.0cm²
                             SA = 232.8cm²
    
    SECTION II
    
    
16.  
    1. 0820hrs
    2.   1200
       +  400
          1600 hrs
    3.   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
    4. S = D
             T
          = 900km
             3240hrs
        S = 42.19km/hr
17.  
    1.  
       
       
       
       
    2. A_A= ½ × 2 × 2.5 =2.5cm²
       A_B = ½ × 5.5 × 7.5 = 20.625cm²
       A_C = ½ × 2.5 × 7 = 8.75cm²
       A_D = ½ × 4 × 2    = 4cm²
       A_E = ½ × 9 × 8.5 = 38.25cm²
       A_F = ½ × 5 × 6    =   15cm²
                                      89.125     
       1cm = 20m 
       1cm²= 400m²   
       89.15cm² = x
        x = 400m² × 89.15cm²
                    10,000m² 
          = 3.566ha
18.  
    1.  
       
    2.  
       1. AC = 7.5cm
       2. ∠ ACB =54⁰
    3. A_Δ = ½ × b × h
            =½ × 7 × 7
            = 24.5cm²