Algebra - Class 8 Mathematics Revision Notes

Algebra

Worked Exercise

1. What is the value of x in the equation?
   2(3x – 2) = 3x + 8
   1. 12 
   2. 3
   3. 5
   4. 4
      Working 2 (3x – 2 ) = 3x + 8
      Step 1: Open brackets 6x – 4 = 3x + 8
      Step 2: Collect like terms and simplify 6x – 3x = 8 + 4 3x = 12 x = 4
      The correct answer is D (4)
2. Francis has r shillings. John has s shillings. Ouma has sh.150 less than the total money of both Francis and John. Which one of the following expressions gives the total amount of money do the three men have?
   1. 2r + 2s – 150
   2. r + s – 150
   3. 2r + 2s + 300
   4. r + s + 300
      Working
      Francis = r
      John = s
      Ouma = r + s - 150
      Total money = r + s + r + s – 150
      = 2 r + 2s – 150
      The correct answer is A (2r + 2s – 150)
3. If x = 2, y = z - x and z = 3, What is the value of
   3x – 4y + 2z  
   2 (x + 2y – z)
   1. 8
   2. 5
   3. 7
   4. 4
      Working
      Substitute the values of x, y, and z
      = (3x2) – (4x1) + (2x3)
             2 (2+2 x 1 - 3)
      = ⁸/₂ = 4
      The correct answer is D (4)
4. In a meeting there were 30 women than men and three times as many men as children.If there were 1,360 people altogether. What was the number of children in the meeting?
   1. 220
   2. 190
   3. 600
   4. 570
      Working Men 3x
      Children x
      Women 3x + 30
      Total 7x + 30 = 1360
      7x = 1360- 30
      7x = 1330
      x = 190
      Children are 190
      The correct answer is B (190)
5. What is the value of p in the equation?
   ¾(8p- 4) = 4p +7
   1. 2
   2. 5 
   3. 5½
   4. 2 ³/₈
      Working
      ¾(8p - 4) = 4p +7
      6p – 3 = 4p + 7 (opening brackets)
      6p – 4p = 7 + 3 (collecting like terms)
      2p = 10
      p = 5 (Simplifying)
      The correct answer is B (5) 
6. Omammo is two years older than Temo and three years younger than Mbeti. The sum of their ages is 64 years. If Omamo’s age is m, which of the following equations below can be used to find Omamo’s age?
   1. 3m + 1 = 64 
   2. 3m – 1 = 64
   3. 3m – 5 = 64
   4. 3m + 5 = 64
      Working
      Omamo = m
      Temo = m- 2
      Mbeti = m + 3
      Total age = 64
      X + m – 2 + m + 3 = 64
      m + m + m – 2 + 3 = 64
      3m + 1 = 64
      The correct answer is A (3m + 1 ) = 64
7. What is the simplified form of 5x + (8x – 2y)
   1. 37x – 8y
   2. 7x –
   3. 28x – 2y
   4. 7x – 2y
      Working
      5x + ¼(8x – 2y ) open brackets
      5x + 2x – ½y simplify
      = 7x – ½y
      The correct answer is B (7x – ½y)