Mathematics Questions and Answers - Form 1 End Term 1 2021

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MATHEMATICS
FORM 1
END TERM EXAM
TERM 1 2021

INSTRUCTIONS

  • Answer all the questions
  1. Work out: (4 mks)
    1. (-7) + (-4) = 
    2. (-20) ÷ (+4) =
    3. (+18) x (-2) =
    4. (+10) – (+7) =
  2. Use square and square root tables to evaluate: (3 mks)
    3.4742 + √1287
  3. Arrange the following fractions in descending order. (3 mks)
    2/3, 8/9, 7/12, 5/7
  4. Express the following recurring decimal into a fraction

    1. Mathf1et121q4a (3 mks)

    2. Mathf1et121q4b(2 mks)
  5. A bus service number 4 leaves a terminus every 20 minutes. Service bus 8 and 3 leaves ever 25 and 30 minutes respectively. If all the three services leave together at 6.00 a.m, at what other times during day time do they leave together? (4 mks)
  6. A man spends 1/3 of his salary on rent and 2/5 of the remainder on food. He saves the rest of his Income. If his savings amount to sh 4,200, find his income. (3 mks)
  7. Simplify the following expressions:- (2 mks)
    1. 2a + 3b + 4a – b
    2. ax – ay + bx – by
            a + b                      (2 mks)
  8. Work out:
    1 ¼ + 2 3/5 - 4/5 of 3 1/3 (3 mks)
  9. Test whether the following numbers are divisible by 11. (6 mks)
    1. 8260439
    2. 8151
    3. 4132
  10. Find the square root of each of the following using factor method.
    1. 1764 (2 mks)
    2. 625 (2 mks)
    3. 441 (2 mks)
  11. Without using a calculator, evaluate the following leaving your answer as a simple fraction.(3 mks)

    1. Mathf1et121q11a

    2. Mathf1et121q11b
  12. Express as a single fraction.
    Mathf1et121q12(3 mks)
  13. Mr. Kimanthi keeps Turkeys and chicken. The number of turkeys exceeds the number of chickens by 6. During the outbreak of a disease, ¼ of the chicken and 1/3 of the turkeys died. If he lost total of 30 birds, how many birds did he have altogether? (4 mks)
  14. Four farmers took their goats to the market. Salim had x goats, Mohammed two more goats than Salim and Koech had 3 times as many goats as Mohammed whereas Okoth had 10 goats less than both Mohammed and Koech.
    1. Write a simplified expression with one variable, representing the total number of goats.(3mks)
    2. Three butchers bought all the goats and shared them equally. If each butcher got 17 goats, how many did Okoth sell to the butchers? (3 mks)
  15. Melisa ate 1/5 of her birthday cake and gave 2/3 of the remainder to her friends. The rest was kept for her two sisters who were absent. If the two sisters shared their piece equally, what fraction of cake did each sister eat? (3 mks)
  16. A company registered a gross profit of five billion, three hundred and sixty eight million, five hundred and seventy nine thousand and seventy nine shillings. Round off this figure to the nearest hundred millions and express it in standard form. (3 mks)
  17. Simplify the following algebraic equations: 

    1. Mathf1et121q17a(2mks)
    2. 7x – 7xy
         7 - 7y                     (2 mks)


MARKING SCHEME

  1. Work out: (4 mks)
    1. (-7) + (-4) = -11
    2. (-20) ÷ (+4) = -5
    3. (+18) x (-2) = -36
    4. (+10) – (+7) = +3
  2. Use square and square root tables to evaluate: (3 mks)
    3.4742 + √1287
    • (3.474)2 = 12.041 + 28= 12.069
      √1287=√(12.87 X 102)
      =(3.5777+99) X 10
      =3.5876 X 10
      =35.876
      =12.069 + 35.876
      = 47.945

  3. Arrange the following fractions in descending order. (3 mks)
    2/38/97/125/7
    • 2/3 X 100= 66.6
    • 8/9 X 100= 88.87
    • 7/12 X 100= 58.33
    • 5/7 X 100= 71.43
      Ans = 8/9, 5/7, 2/3,7/12
  4. Express the following recurring decimal into a fraction

    1. Mathf1et121q4a (3 mks)
      Let
      r = 0.375375
      10r= 3.753753
      100r= 37.537537
      1000r= 375.375375
      1000r-r= 375.375-0.375375
      999r=375
      r=375/999
      r= 125/333 

    2. Mathf1et121q4b(2 mks)
      let 
      r=0.6666
      10r= 6.666
      10r-r= 6
      9r=6
      r=6/9
      r=
      2/3
  5. A bus service number 4 leaves a terminus every 20 minutes. Service bus 8 and 3 leaves ever 25 and 30 minutes respectively. If all the three services leave together at 6.00 a.m, at what other times during day time do they leave together? (4 mks)
     2  20 25  30 
     2  10 25  15 
     3  5  25  15
     5  5  25  5
     5  1  5  1
       1  1  1
    2x2x3x5x5= 300 minutes
    300/60= 5 hours
      6:00
    +5:00
    11:00 am


  6. A man spends 1/3 of his salary on rent and 2/5 of the remainder on food. He saves the rest of his Income. If his savings amount to sh 4,200, find his income. (3 mks)
    • 3/3-1/3=2/3
      2/5 of 2/3= 2/5 x 2/3= 4/15
      1/3 + 4/15= 5/15 + 4/15

      =9/15
      15/15 - 9/15= 6/15
      4200= 6/15
      =15/15 x 4200 x 15/6
      =4200 x 15/6= 700 x 15
      = 10500 
  7. Simplify the following expressions:- (2 mks)
    1. 2a + 3b + 4a – b
      • 2a + 4a +3b -b
        6a + 2b
    2. ax – ay + bx – by
            a + b                      (2 mks)
      • a(x-y) + b(x-y)
                a+b

        (a+b)(x-y
             a+b
      • x-y
  8. Work out:
    1 ¼ + 2 3/5 - 4/5 of 3 1/3 (3 mks)
    • 5/4 + 13/5 - 4/5 of 10/3
      5/4 + 13/5 - 40/15
      5/4 + 13/5 - 8/3
      75/60 + 156/60 - 160/60
      71/60
      111/60
  9. Test whether the following numbers are divisible by 11. (6 mks)
    1. 8260439
      8+6+4+9= 27
            2+0+3= 5
      27-5= 22
      Divisible
    2. 8151
      8+5=13
      1+1=2
      13-2= 11
      divisible
    3. 4132
      4+3=7
      1+2=3
      7-3=4
      Not divisible
  10. Find the square root of each of the following using factor method.
    1. 1764 (2 mks)
      √1764=√2x2x3x3x7x7
      =2x3x7=42
    2. 625 (2 mks)
      √5x5x5x5=5x5=25
    3. 441 (2 mks)
      √441=√3x3x7x7=3x7=21
  11. Without using a calculator, evaluate the following leaving your answer as a simple fraction.(3 mks)

    1. Mathf1et121q11a
      8+(-9) + (-20+4-6)
          -24         46-10-2

      -1 + (-22)
      -24      34
      1/24 + -11/17
      17 - 264
        408

      = -247/408

    2. Mathf1et121q11b
      • 5/6 of (13/3 - 23/6)
        5/6 of (26/6 - 23/6)
        5/6 of 3/6
        =15/36=5/12
      • 5/12 x 3/25 + 14/9 ÷ 7/3
        5/12 x 3/25 + 14/9 x 3/7
        1/20 + 2/3
        3/60 + 40/60= 43/60
        5/12 ÷ 43/60
        5/12 x 60/43
        25/43
  12. Express as a single fraction.
    Mathf1et121q12(3 mks)
    let r=1.9333333               let s = 0.252525
    r=1.93333                               s= 0.252525

    10r=19.333                           10s= 2.52525
    100r= 193.333                     100s= 25.2525
    100r -10r=193.33-19.333   100s-s=25.2525-0.2525
    90r=174                                99s= 25
    174/90 + 25/99
    87/45 + 25/99
    1082/495
  13. Mr. Kimanthi keeps Turkeys and chicken. The number of turkeys exceeds the number of chickens by 6. During the outbreak of a disease, ¼ of the chicken and 1/3 of the turkeys died. If he lost total of 30 birds, how many birds did he have altogether? (4 mks)
    • No of chickens=x
      no. of turkeys= x +6
      X/4 + (x+6)/3 = 30
      3x + 4x + 24=360
      7x= 360-24=334
      7x=334
      x= 48
      Turkeys = 48+6=54
      48+54= 102 birds

  14. Four farmers took their goats to the market. Salim had x goats, Mohammed two more goats than Salim and Koech had 3 times as many goats as Mohammed whereas Okoth had 10 goats less than both Mohammed and Koech.
    1. Write a simplified expression with one variable, representing the total number of goats.(3mks)
      • Salim = x
        Mohammed = x+2
        Koech = 3(x+2)= 3x +6
        Okoth= (3x+6)+(x+2) - 10= 4x -2
        Total no of goats
        = 2x +2 + 3x + 6 + 4x + 8 - 10= 9x + (16-10)= 9x + 6
    2. Three butchers bought all the goats and shared them equally. If each butcher got 17 goats, how many did Okoth sell to the butchers? (3 mks)
      • 17 x 3= 51 goats
        9x + 6 = 51
        9x=45
        x=5
        4x-2= 4(5) -2= 18 goats
  15. Melisa ate 1/5 of her birthday cake and gave 2/3 of the remainder to her friends. The rest was kept for her two sisters who were absent. If the two sisters shared their piece equally, what fraction of cake did each sister eat? (3 mks)
    • 5/5 -1/5
      4/5 x 2/3= 8/15
      1/5 + 8/15= 3/15 + 8/15= 11/15
      15/15 11/15= 4/15
      4/15 x 1/2= 2/15
      2/15 each
  16. A company registered a gross profit of five billion, three hundred and sixty eight million, five hundred and seventy nine thousand and seventy nine shillings. Round off this figure to the nearest hundred millions and express it in standard form. (3 mks)
    • 5 000 000 000
         368 000 000
                579 000
                        70
      5 368 579 070
      5 400 000 000
      5.4 x 109
  17. Simplify the following algebraic equations: 

    1. Mathf1et121q17a(2mks)
      ans = 7xb/6y


    2. 7x – 7xy
         7 - 7y                     (2 mks)
      • 7x(1-y)
        7(1-y)
        =x

 

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