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

QUESTIONS

Attempt all questions in the spaces provided

1. Evaluate (3mks)
   -19 + (6-8) ÷ 2 x 5
        16 ÷ 4 x -3
2. Express the following numbers as products of their prime factors (3mks)
   1. 357
   2. 5929
3. Find the GCD of 72, 96 and 300 (3mk)
4. Express 0.872872872………….as a fraction (3mks)
5. Show how the following calculations are performed using number line (4mks)
   1. -2 + (-2) + -3 + (-1)
   2. -7 – (-8)
6. Evaluate (3mks)
   4 ½ - (5 ¹/₅ + ⁴/₅ of ²⁵/₃)
7. Charles spent ¼ of his net salary on school fees. He spent ¼ of the remainder on electricity and water bills. He then spent 1/9 of what was left on transport. If he finally had sh 3400, what was his net January salary (3mks)
8. Which of the following numbers is divisible by 11, 3, and 4 (3mks)
   1. 2596
   2. 5896
   3. 1052
9. All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
   1. Write down the number formed. (1mk)
   2. Test whether or not the number formed in 16 (a) above is divisible by 11. (2mks)
10. A man is x years old now. In 10 years time, he will be twice as old as he was 5 years ago. How old will he be in 10 years time? (3mks)
11. Evaluate: ¼ + ¹/₅ ÷ ½ of ¹/₃
                    ½ of ( ⁴\₅ – ¾ + ½ )                   (3mks)
12. The sum of ³/₈, ²⁰/₃ and x is 6⁵⁷/₁₂₀. Find x. (2mks)
13. Evaluate without using tables or calculators. (3mks)
    0.036 × 0.0049
      0.07 × 0.048
14.                     
15.                     
16. A shop keeper sells a shirt for Kshs.350 thereby making a profit of 40%. Calculate the buying price of the shirt (3mks)
17. Evaluate:     (3marks)
    44 -(-28)  -  82 × -12 - 24
    12 × -2        96 ÷ -12 × 9 
18.                      ]
19. A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n. (3marks)
20. Reduce the following expression onto a single fraction.(3 marks)
    4x - 5  - 2x - 1
       2            6
21.                        
22. Convert 7 into a decimal (3mks)
                 8
23. If X: Y =1:2 and Y: Z =3:5 find X: Y: Z (3mks)
24. A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes. Find the maximum area of one plot. (4marks)
25. The ratio of John’s earnings to Musa’s earnings is 5:3 if johns earning’s increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musa’s earnings if the sum of their new earnings is sh 9600. (3mks)
26. Convert into percentage (3mks)
    1. 0.03%
27. Three Lorries, each making five trips per day, transport 2500 crates from a factory to a distributor in two days. How many Lorries, each making six trips a day, are needed to transport 10000 such crates in a day? (3mks)

MARKING SCHEME

Attempt all questions in the spaces provided

1. Evaluate (3mks)
   -19 + (6-8) ÷ 2 x 5
        16 ÷ 4 x -3
   num: -19 + (-2) ÷ 2 × 5
   -19 - 2  ÷ 2 × 5
   -19 - 1 × 5
   - 24
   
   Den: 16 ÷ 4 x -3
   4  ×  -3
   - 12
   
   -24
   -12
   = 2
2. Express the following numbers as products of their prime factors (3mks)
   1. 357 
      
      3 × 7 × 17
   2. 5929
      
      7 × 3 × 29
3. Find the GCD of 72, 96 and 300 (3mk)
   

   2	72	96	30
   3	36	48	15
   	12	16	5

   = 2 × 3
   = 6
4. Express 0.872872872………….as a fraction (3mks)
   r = 0.8728
   10r = 8.72828
   -100r = 87.2828
   1000r = 872.828
   10000r = 8728.28
   100r = 87.28
   9900r  =  8641   r = 8641
   9900       9900         9900
5. Show how the following calculations are performed using number line (4mks)
   1. -2 + (-2) + -3 + (-1)
      
      = -8
   2. -7 – (-8)
      
      = +1
6. Evaluate (3mks)
   4 ½ - (5 ¹/₅ + ⁴/₅ of ²⁵/₃)
   
7. Charles spent ¼ of his net salary on school fees. He spent ¼ of the remainder on electricity and water bills. He then spent 1/9 of what was left on transport. If he finally had sh 3400, what was his net January salary (3mks)
   1/x × fees
   1/4 of 3/4x = bills
   3/16x = bills
   1/9 of 3/16x
   133/144x → transport
   131/144x - 3400
8. Which of the following numbers is divisible by 11, 3, and 4 (3mks)
   1. 2596
      +(2 + 9) - (5 + 6) = 0 it is divisible by 11
      2 + 5 + 9 + 6 = 22 - not divisible by 3
      96/4 = 15 - divisible by 4
   2. 5896
      +(5 + 9) - (8 + 6) = 0 - divisible by 11
      5 + 8 + 9 + 6 = 28 - not divisible by 3
      96 is divisible by 4
   3. 1052
      (1 + 5) - (10 + 2) = 4 - divisible by 11
      1 + 0 + 5 + 2 = 8 - not divisible by 3
      52 - divisible by 4
9. All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
   1. Write down the number formed. (1mk)
      7 5 3 2
   2. Test whether or not the number formed in 16 (a) above is divisible by 11. (2mks)
      (7 + 3) - (5 + 2) = 3
      not divisible by 11
10. A man is x years old now. In 10 years time, he will be twice as old as he was 5 years ago. How old will he be in 10 years time? (3mks)
    

    	now	5 years ago	10 years time
    man	x	(x - 5)	2(x - 5)

    x + 10 = 2x - 5
    x - 2x = -5 - 10
    -x = -15
    x = 15
    
    10 years time
    - x + 10 = 15 + 10
    = 25
11. Evaluate: ¼ + ¹/₅ ÷ ½ of ¹/₃
                    ½ of ( ⁴\₅ – ¾ + ½ )                   (3mks)
    Num: 1/4 + 1/5 ÷ 1/2 of 1/3
    1/4 + 1/5  ÷ 1/6
    1/4 + 6/5 = 1⁹/₂₀
    
    Den: 1/2 of (4/5 - 3/4 + 1/2)
    1/2 of 11/20
    ¹¹/₄₀
    
    1⁹/₂₀ - ¹¹/₄₀
    = 1⁷/₄₀
12. The sum of ³/₈, ²⁰/₃ and x is 6⁵⁷/₁₂₀. Find x. (2mks)
    ³/₈ + ²⁰/₃ + x = 6⁵⁷/₁₂₀
    ¹⁶⁹/₂₄ + x = 6⁵⁷/₁₂₀ - ¹⁶⁹/₂₄
    x = 6⁵⁷/₁₂₀ - ¹⁶⁹/₂₄
    x = ¹⁷/₃₀
13. Evaluate without using tables or calculators. (3mks)
    0.036 × 0.0049
      0.07 × 0.048
    0.036 × 0.0049   × 1000000  
      0.07 × 0.048    × 1000000  
         36 × 49     
    7 × 48 × 100
    = ²¹/₄₀
14.                     
15.                     
16. A shop keeper sells a shirt for Kshs.350 thereby making a profit of 40%. Calculate the buying price of the shirt (3mks)
    sp = 350
    350 - 140%
          - 100%
    350 × 100
         140
    b.p = 250
17. Evaluate:     (3marks)
    44 -(-28)  -  82 × -12 - 24
    12 × -2        96 ÷ -12 × 9 
    44 + 28
       -24
    = 72
    -24
    64x - 12 - 24
    = 72/-24 - 28/-72
    = -⁴⁷/₁₈
18.                      
19. A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n. (3marks)
    

    3	3	7	11	13
    7	1	7	11	13
    11	1	1	11	13
    15	1	1	1	13
    	1	1	1	1

    3 × 7 × 11 × 13 = 3003
    n = 3003 + 1 = 3004
20. Reduce the following expression onto a single fraction.(3 marks)
    4x - 5  - 2x - 1
       2            6
    3(4x - 5) - (2x - 1) = (12x - 15) - (2x - 1)
           2            6               6
    = 12x - 15 - 2x + 1
                    6
    = 12x - 2x - 15 + 1
                 6
    = 10x - 14
            6
21.                        
22. Convert 7 into a decimal (3mks)
                 8
    0.875
23. If X: Y =1:2 and Y: Z =3:5 find X: Y: Z (3mks)
    X Y Z
    1:2
       3: 5
    3:6:10
24. A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes. Find the maximum area of one plot. (4marks)
    
    = 840 × 396
    =332640 m²
    G.C.D 
    

    2	840	396
    2	420	198
    3	210	99
    	70	33

    12 × 12 = 144m²
25. The ratio of John’s earnings to Musa’s earnings is 5:3 if johns earning’s increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musa’s earnings if the sum of their new earnings is sh 9600. (3mks)
    100/112 × 5600 = 5000
    J:M = 5:3
    3/5 × 5000 = 3000
    musas new earnings = 9600 - 5600
    = sh.4000
    musa's change in earnings = 4000 - 1000
    = 3000
    % change = 1000 × 100
                         3000
    =33¹/₃
26. Convert into percentage (3mks)
    1. 0.03%
       3/100 × 100 = 3%
27. Three Lorries, each making five trips per day, transport 2500 crates from a factory to a distributor in two days. How many Lorries, each making six trips a day, are needed to transport 10000 such crates in a day? (3mks)
    3 × 5 × 10000 × 2 
       6         2500    1
    = 20 lorries