Algebraic Expressions Questions and Answers - Form 1 Topical Mathematics

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Questions

  1. Five years ago, a mother’s age was four times that of her daughter. In four years to come, she will be 2 ½ times the age of her daughter. Calculate the sum of their present ages
  2. Simplify;
    1. 6a – 2b + 7a – 4b + 2

    2. algebraic expressions 3bq
  3. Simplify
    algebraic expressions 4q
  4. Given that x + y = 8 and x2 + y2 = 34
    Find;
    1. the value of x2 + 2xy + y2
    2. Find the value of ; 2xy
    3. x2 – 2xy + y2
    4. Value of x and y
  5. Simplify the expression.
    algebraic expressions 6q
  6. Simplify the expression
    2/3(3x -2) – 3/4(2x -2)
  7. Simplify by factorizing completely:
    algebraic expressions 8q
  8. Simplify as far as possible.
    algebraic expressions 9q
  9. Simplify:

    1. algebraic expressions 10aq
    2. hence solve:-
      algebraic expressions 10bq
  10. Factorize completely the expression
    75x2 – 27y2
  11. Simplify
    algebraic expressions 13q
  12. Simplify the expression:- 
    algebraic expressions 14q
  13. Given that (x-3) (Ax2+bx+c) = x3-7x-6, find the value of A, B and C
  14.  
    1. solve for y in 8x(22)y=6x2y-1
    2. Simplify completely
      algebraic expressions 16bq
  15. Simplify the expression.:
    algebraic expressions 17q
  16. Simplify
    algebraic expressions 18q
  17. The sum of two numbers is 15. The difference between five times the first number and three times the second number is 19. Find the two numbers.
  18. Simplify the following expressions by reducing it to a single fraction
    algebraic expressions 20q
  19. Simplify the expression:-
    algebraic expressions 21q

Answers

  1. Let the daughter’s age 5yrs ago be x
    Mother 4x
    come;
    Daughter = x + 9
    Mother = 4x+ 9
    4x + 9 = 5/2(x +9)
    4x + 9 = 2.5x + 22.5
    1.5x = 13.5
    x = 9
    Mother = 41yrs
    14 + 41 =55
  2.  
    1. 6a + 7a – 2b – 4b + 2
      = 13a – 6b + 2

    2. algebraic expressions 2ba

  3. algebraic expressions 3a
  4.  
    1. From x + y and x2 + y2 = 34
      X = 8 – y
      Substituting for x in x2 – y2 = 34
      (8 – y) (8 – y) + y2 = 34
      64 – 8y – 8y + y2 + y2 = 34
      64 – 16y + 2y2 = 34
      2y2 – 16y + 64 – 34 = 0
      2y2 – 16y + 30 = 0
      y2 = 8y + 15 = 0
      y (y – 3) – 5 (y-3) = 0 (y-5) (y – 3)
      y is either 5 or 3
      but x – y = 8
      x is either 5 0r 3
      x2 + 2xy + y2 = 32 + 2 x 3 x 5 + 25
      = 9 + 30 + 25 = 64
    2. 2xy = 2 x 3 x 5 = 30
    3. x2 – 2xy + y2 = 9 – 2 x 3 x 5 + 25 = 4
    4. x - y = 8 and x2 + y2 = 34
      x = 8 – y
      (8 – y)2 + y2 = 34
      y2 – 8y + 15 = 0
      y2 – 3y – 5y + 15 = 0
      y(y -3) – 5(y – 3)
      (y-3) = 0 y = 3
      (y-5) = 0 y = 5
      x + 3 = 8, x = 5 or x + 5 = 8
      x = 3
      x is either 3 or 5
      y is either 3 or 5

  5. algebraic expressions 5a

  6. algebraic expressions 6a

  7. algebraic expressions 7a

  8. algebraic expressions 8a

  9. algebraic expressions 9a
  10.  3( 25x2 – 9y2)
    3(5x + 3y)(5x – 3y)
  11. Factorizing the numerator
    = p(p2 – q2) + q(p2-q)
    = (p+q) (p2-q2)
    = (p+q) (p+q) n(p-q)
    Factorising the denominator
    (p+q) (p+q)
    Numerator = p - q
    Denominator
  12. ( 3x + 2y ) ( 3x - 2y )
    ( 3x + 2y ) ( 3x - 2y )
    3x + 2y
    4x + 3y
  13. (x – 3) (AX2 +BX + C) = x3 – 7x – 6
    AX3 + BX2 +CX – 3AX2 – 3BX – 3c = x3 – 7x – 6
    A = 1
    B – 3A = 0
    B – 3 x 1 = 0
    B = 3
    -3c = -6
    c = 2
  14.  
    1. 8(22)y = 6 x 2y – 1
      let t = 2y
      8t2 = 6t – 1
      8t2 – 4t – 2t + 1 = 0
      (4t – 1) (2t – 1) = 0
      t = ¼ or ½
      t = 2y = ¼ = 2-2
      y = -2
      or t = 2y = ½ = 2-1
      y = -1
      y = -2 or -1

    2. algebraic expressions 14ba

  15. algebraic expressions 15a

  16. algebraic expressions 16a
  17. Let the numbers be a and b
    a + b = 15 x3
    5a – 3b = 19 x 1

    3a + 3b = 45
    5a – 3b = 19
    8a = 64
    a = 8
    b = 7

  18. algebraic expressions 18a

  19. algebraic expressions 19a

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