Algebraic Expressions Questions and Answers - Form 1 Topical Mathematics

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. 
      
3. Simplify
   
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.
   
6. Simplify the expression
   ²/₃(3x -2) – ³/₄(2x -2)
7. Simplify by factorizing completely:
   
8. Simplify as far as possible.
   
9. Simplify:
   1. 
      
   2. hence solve:-
      
10. Factorize completely the expression
    75x² – 27y²
11. Simplify
    
12. Simplify the expression:- 
    
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=6x2^y-1
    2. Simplify completely
       
15. Simplify the expression.:
    
16. Simplify
    
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
    
19. Simplify the expression:-
    

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. 
      
3. 
   
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. 
   
6. 
   
7. 
   
8. 
   
9. 
   
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 2^y – 1
       let t = 2^y
       8t² = 6t – 1
       8t² – 4t – 2t + 1 = 0
       (4t – 1) (2t – 1) = 0
       t = ¼ or ½
       t = 2^y = ¼ = 2^-2
       y = -2
       or t = 2y = ½ = 2^-1
       y = -1
       y = -2 or -1
    2. 
       
15. 
    
16. 
    
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. 
    
19.