Mathematics Questions and Answers - Form 1 Mid Term 2 Exams 2023

QUESTIONS

1. Express each of the following numbers as product of prime factors. (3mks)
   1. 256
   2. 1078
   3. 81
2. 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 of them exact times. (3mks)
3. Perform the following operation on a number line. (2mks)
   1. +5-(-2)
   2. +4-(+7)
4. 3 bells ring at interval of 40 minutes, 45 minutes and 60minutes. If they ring simultaneously at 6:30am, at what time will they ring together? (3mks)
5. Evaluate ½{3/5 + ¼(7/3-3/7) of 1 ½ ÷ 5 } (3mks)
6. Convert the following into fractions.
   1. 0.73 (2mks)
   2. 0.23 (2mks)
7. A water melon vendor had 1500 water melons. He sold 800 on the first day and 250 on the second day. He added 470 on the remaining stock on the third day.
   1. How many water melons did he have at the end? (2mks)
   2. If he sold all the water melons at an average cost of sh. 100 each. How much money did he collect? (2mks)
8. 3/5 of the pupils in a school are boys. If there are 96 girls in the school, how many pupils are there in the school? (3mks)
9. Express the following number in standard form
   1. 0.000718 (1mk)
   2. 156700 (1mk)
10. Use tables to find.
    1. 423² (1mk)
    2. √0.067 (2mks)
11. Find the difference in value between the largest number and the smallest number formed by digits 5,2 and 8. (3mks)
12. The first four even numbers are written in descending order to form a number.
    1. Write down the number. (1mk)
    2. Find the total value of the thousands digits in the number. (2mks)
13. A number n is such that when it is divided by 30, 36 and 45 the reminder is always 7. Find the smallest possible value of n. (3mks)
14. Which of the following number is divisible by both 3 and 4?
     120, 744, 306, 9564, 1504, 192, 86 and 36. (3mks)
15. If x=-2, y=-6 and z=4, find the value of 4xyz. (3mks)
16. By how much is the product of 9/5 and 8 ¼ greater than 5? (2mks)
17. The distance between two schools M and K is 6km. A market is situated between M and K such that it is one third of the distance from M. How far is the market from K? (2mks) 

MARKING SCHEME

1. Express each of the following numbers as product of prime factors. (3mks)
   1. 256
      • 
   2. 1078
      • 
   3. 81
      • 
2. 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 of them exact times. (3mks)
   • 
3. Perform the following operation on a number line. (2mks)
   1. +5-(-2)
      • 
   2. +4-(+7)
      • 
4. 3 bells ring at interval of 40 minutes, 45 minutes and 60minutes. If they ring simultaneously at 6:30am, at what time will they ring together? (3mks)
   

   5	40	45	60
   4	8	9	12
   2	2	9	3
   3	1	9	3
   3	1	3	1
   	1	1	1

   5 x 4 x 2 x 3 x 3
   =360/60 minute
   =6 hrs
   
   1630
   +600
   1230
   
   = 12:30 pm
5. Evaluate ½{3/5 + ¼(7/3-3/7) of 1 ½ ÷ 5 } (3mks)
   • BODMAS
     7/3 - 3/7 
     
     49 - 9 = 40
         21     21
     1/4 x 40/21 = 10/21
     
     10/21 of 3/2 = 5/7
     5/7 - 5 = 5/7 x 1/3 = 1/7 
     3/5 + 1/7 = 21 + 5 = 26 = 13
                          35       35
6. Convert the following into fractions.
   1. 0.73 (2mks)
      • x = 0.737373
        10x = 7.37373
        100x = 73.7373
        
        100x - x = 73.7373 - 0.7373
        
        99x/99 = 73/99 = 73/99
        
        0.23 = 23/100
   2. 0.23 (2mks)
7. A water melon vendor had 1500 water melons. He sold 800 on the first day and 250 on the second day. He added 470 on the remaining stock on the third day.
   1. How many water melons did he have at the end? (2mks)
      • 1500 - 800 - 250 = 450
        450 + 470 
        = 920 watermelons
   2. If he sold all the water melons at an average cost of sh. 100 each. How much money did he collect? (2mks)
      • 1500 + 470 = 1970 watermelon
        (1970 x 100)
        = 197000 
8. 3/5 of the pupils in a school are boys. If there are 96 girls in the school, how many pupils are there in the school? (3mks)
   • 3/5 - boys
     2/5 - girls 
     2/5 - 96
     5/5 x 5/2 x 96 
     
     = 240 pupils
9. Express the following number in standard form
   1. 0.000718 (1mk)
      • 7.18 x 10^-4
   2. 156700 (1mk)
      • 1.567 x 10⁵
10. Use tables to find.
    1. 423² (1mk)
       • (4.23 x 10²)² -> 17.893 x 10⁴ = 178930
    2. √0.067 (2mks)
       • = 2.5884 x 1/10 = 0.25884
11. Find the difference in value between the largest number and the smallest number formed by digits 5,2 and 8. (3mks)
    • largest number -> 852
      smallest number -> 258
      852 - 256 = 594
12. The first four even numbers are written in descending order to form a number.
    1. Write down the number. (1mk)
       • 8642
    2. Find the total value of the thousands digits in the number. (2mks)
       • 8 x 1000 = 8000
13. A number n is such that when it is divided by 30, 36 and 45 the reminder is always 7. Find the smallest possible value of n. (3mks)
    • 3 x 3 x 5 x 2 x 3
      = 270
      = 270 + 7 
      = 277
14. Which of the following number is divisible by both 3 and 4?
     120, 744, 306, 9564, 1504, 192, 86 and 36. (3mks)
    • 120, 192 and 36
15. If x=-2, y=-6 and z=4, find the value of 4xyz. (3mks)
    • 4x - 2x - 6x x 4
      -8x - 24 
      = 192
16. By how much is the product of 9/5 and 8 ¼ greater than 5? (2mks)
    • 9/5 x 33/4 = 297/20 - 5/1  
      
      297 - 100 = 197
             20         20
      by 9¹⁷/₂₀
17. The distance between two schools M and K is 6km. A market is situated between M and K such that it is one third of the distance from M. How far is the market from K? (2mks) 
    
    1/3 of 6 = 2 km
    (6 - 2) = 4 km