Algebra Questions with Answers for Grade 10

Grade 10 algebra questions with answers are presented.

  1. Which real numbers are equal to their cubes?
    Solution on Video

  2. Write 410-2 as a decimal.
    Solution on Video

  3. Write 0.1210-3 as a decimal.

  4. Write 2 log3 x + log3 5 as a single logarithmic expression.

  5. Factor the algebraic expression 6x2 - 21 x y + 8 x z - 28 y z.
    Solution on Video

  6. Factor the algebraic expression (x - 1)2 - (y - 2)2.
    Solution on Video

  7. Factor the algebraic expression x2 - z4.

  8. Evaluate the algebraic expression |-2 x - y + 3| for x = 3 and y = 5

  9. Simplify the algebraic expression -2(x - 3) + 4(-2 x + 8)

  10. Expand and simplify the algebraic expression (x + 3)(x - 3) - (-x - 9)

  11. Which property is used to write a(x + y) = a x + a y

  12. Simplify ( 8 x3 ) / ( 2 x-3)

  13. Simplify (-a2b3)2(c2)0

  14. For what value of k is the point (-2, k) on the line with equation -3 x + 3 y = 4?

  15. For what value of a will the system given below have no solutions?
    2 x + 6 y = -2
    -3 x + a y = 4

  16. Which equation best describes the relationship between x and y in this table?
    x y
    0 -4
    4 -20
    -4 12
    8 -36
    A) y = - x/4 - 4
    B) y = - x/4 + 4
    C) y = - 4x - 4
    D) y = - 4x + 4

  17. Which equation best represents the area of the rectangle below?

    problem.
    A) area = 2(x+1) + 2(x-1)
    B) area = 4(x+1)(x-1)
    C) area = 2x2
    D) area = x2 - 1

  18. Which line given by its equation below contains the points (1, -1) and (3, 5)?
    A) -2y -6x = 0
    B) 2y = 6x - 8
    C) y = 3x + 4
    D) y = -3x + 4

  19. Solve the equation 2|3x - 2| - 3 = 7.

  20. Solve for x the equation (1/2)x2 + mx - 2 = 0.

  21. For what values of k the equation -x2 + 2kx - 4 = 0 has one real solution?

  22. For what values of b the equation x2 - 4x + 4b = 0 has two real solutions?

  23. Function f is described by the equation f (x) = -x2 + 7. What is the set of values of f(x) corresponding to the set for the independent variable x given by {1, 5, 7, 12}?

  24. Find the length and width of a rectangle whose perimeter is equal to 160 cm and its length is equal to triple its width.

  25. Simplify: |- x| + |3 x| - |- 2 x| + 3|x|

  26. If (x2 - y2) = 10 and (x + y) = 2, find x and y.

Answers to the Above Questions

  1. 0 , 1 , -1 are all equal to their respective cubes.
  2. 0.04
  3. 0.00012
  4. = log3 x2 + log3 5 = log3(5x2)
  5. = 3x(2x - 7y) + 4z(2x - 7y) = (2x - 7y)(3x + 4z)
  6. = [(x - 1)- (y - 2)][(x - 1)+ (y - 2)] = (x - y + 1)(x + y - 3)
  7. = (x + z2)(x - z2) = (x + z2)(x + z)(x - z)
  8. = |-2(3) - (5) + 3| = |-8| = 8
  9. = -2x + 6 -8x + 32 = -10x + 38
  10. = x2 - 9 + x + 9 = x2 + x
  11. distributivity
  12. 4 x6
  13. a4b6
  14. k = -2/3
  15. a = -9
  16. C. y = - 4x - 4
  17. D. area = (x + 1)(x - 1) = x2 - 1
  18. B. 2y = 6x - 8
  19. solution set : {7/3 , -1}
  20. solution set : {-m + sqrt(m2 + 4) , -m - sqrt(m2 + 4)}
  21. k = 2 , k = -2
  22. all values of b less than 1
  23. {6 , -18 , -42 , -137}
  24. width = 20 cm and length = 60 cm
  25. |-x| + |3x| - |-2x| + 3|x| = 5|x|
  26. x = 7 / 2 , y = - 3 / 2

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