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

QUESTIONS

1. Write in words 77707707. (2 Marks)
2. The sum of three consecutive whole numbers is 54. Find the numbers. (3 Marks)
3. A number n is such that when it is divided by 27, 30 or 45, the remainder is 3. Find the smallest value of n. (3 Marks)
4. Use the number line to perform the following operations.
   1. (-10)-(-3) (2 Marks)
   2. (+1)-(-8)(2 Marks)
   3. (-3)+(-4) (2 Marks)
5. If x= -4, y= -12 and z=8, find the values of :
   1. 4y - 6x+ 2z (3 Marks)
   2. ^4xy/_2z +y (3 Marks)
6. solve ²/₅ of(6 ²/₅ - ¹/₂ (1 ²/₃+¹/₃)×¹/₅)(3 Marks)
7. A farmer has 165 orange trees on his farm. 38 trees have 97 oranges each, 79 trees have 176 oranges each, the rest have 59 oranges each. How many oranges are there altogether?(3 Marks)
8. Simplify; (3 Marks)
   2x + 3 - 3x - 1
      4           6
9. Given that 1.05 = 1^a/_b Find the value of a and b (3 Marks)
10. On a certain day, a student measured the temperature inside a deep freezer and found that it was -3°c while the room temperature was 24°c. What was the temperature difference between the room and the deep freezer? (3 Marks)
11. Using tables find the:
    1. Square of 4.973 (2 Marks)
    2. Square root of 0.146(2 Marks)
12. An integer p is two-thirds of another and their difference is 10. Find the two integers.(3 Marks)
13. Check whether 7544 is divisible by 6 (3 Marks)
14. Write the following in standard form: (3 Marks)
    1. 0.00121
    2. 4521.021
    3. 26342
15. Evaluate without using tables or a calculator       1.33×0.51       correct to three decimal places. (3 Marks)
                                                                                0.19×0.0017
16. Find the square root of 1764 using factor method.(3 Marks)
17. Remove the brackets and simplify."2b+a[3-2(a-5) ](3 Marks)
18.                  
    1. Three bells are programmed to ring after an interval of 15 minutes, 25 minutes and 50 minutes. If they all rang together at 6.45am, when will they next ring together? (3 Marks)
19.  A bookstore had 30816 exercise books which were packed in cartons. Each contained 24 exercise books. The mass of an empty carton was 2kg and that of a carton full of exercise books is 12kg.
    1. How many cartons were there? (3 Marks)
    2. What was the total mass of the empty cartons? (3 Marks)
    3. What was the total mass of the books alone? (4 Marks)

MARKING SCHEME

1. Seventy seven million, seven hundred and seven thousand, seven hundred and seven
2. Let the number be x, x + 1, x + 2
   x + x + 1 + x + 2 = 54
   3x + 3 = 54
   3x = 54 - 3
   3x = 52
   x = 17
   x + 1 = 18
   x + 2 = 19
3. L.C.M of 27, 30 and 45 = 270
   n = 270 + 3
   n = 273
4.        
   1. -7
   2. +9
   3. -7
5.                
   1. = 4(-12) - 6(-4) + 2(8) Substitution
      =-48 + 24 + 16
      = -8
   2. = 4(-4)(-12) + (-12) substitution
                2(8)
      = 192 + (-12)
          16
      = 12 + (-12)
      = 0
6. = 2/5 of {32/5 - 1 x 1/5}
   = 2/5 of {31/5}
   = 62/25
   = 2¹²/₂₅
7. 38 = 97 oranges each
   79 = 176 oranges each
   Rest 165 - (38 + 79) = 48
   Total oranges = (38 x 97) + (79 x 176) + (48 x 59) = 20422 oranges
8. 2x + 3 - 3x - 1
        4          6
   = 3(2x + 3) - 2(3x - 1)
                  12
   = 6x + 9 - 6x + 2
                12
   = ¹¹/₁₂
9. r = 1.050505
   10r = 10.50505
   100r = 105.0505
   100r - r = 105.0505 - 1.0505
   99r = 104
   r = 104/99
   r = 1⁵/₉₉ 
   a = 5
   b = 99
10. = 24 - (-3)
    = 24 + 3
    = 27ºC
11.         
    1. 24.701 add 30 = 24.731
    2. 0.146 = 14.6 x 10^-2
       square root = 3.821 x 10^-1
       = 0.3821
12. Let the other integer be a,
    p = ²/₃a
    a - ²/₃a = 10
    3a - 2a = 30
    a = 30, p = 20
13. 7544 is divisible by 2 since the last digit is an even number.
    7+5+4+4=20
    7544 is not divisible by 3 since the sum of its digits is not divisible by 3
    Therefore, 7544 is not divisible by 6
14.           
    1. 0.00121 = 1.21 x 10^-3
    2. 4521.021 = 4.521021 x 10³
15.    1.33 x 0.51  
    0.91 x 0.0017
    =    1.33 x 0.51     x 1000000
       0.91 x 0.0017       1000000
    = 19 x 7 x 17 x 3 x 100
              19 x 17
    = 7 x 3 x 100 = 2100
16. 1764 = 2 x 2 x 3 x 3 x 7 x 7
    = 2² x 3² x 7²
    √1764 = 2 x 3 x 7 = 42
17. 2b+a[3-2(a-5)]
    =2b+a(a-2a+10)
    =2b+a(-a+10)
    =2b-a²+10a
    = -a² + 10a + 2b
18. =L.C.M of 15, 25 and 50
    

    2	15	25	50
    3	15	25	25
    5	5	25	25
    5	1	5	5
    	1	1	1

    = 2 x 3 x 5 x 5 = 150 minutes
    = 2 hours 30 minutes
    = 6.45 am + 2 hours 30 minutes
    = 9.15 am
19.                        
    1. Number of carton =  30816
                                          24
       =284 Cartons
    2. (1284 x 2) = 2568 kg
    3. 1284 x 12=15408 kg
       Mass of books alone= (15408 – 2568)
       =12840kg