Algebra Questions with Answers for Grade 10

Grade 10 algebra questions with answers are presented.



  1. Which real numbers are equal to their cubes?

  2. Write 4*10-2 as a decimal.

  3. Write 0.12*10-3 as a decimal.

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

  5. Factor the algebraic expression 6x2 - 21xy + 8xz - 28yz.

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

  7. Factor the algebraic expression x2 - z4.

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

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

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

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

  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 -3x + 3y = 4?

  15. For what value of a will the system given below have no solutions?

    2x + 6y = -2
    -3x + ay = 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
    1. y = - x/4 - 4
    2. y = - x/4 + 4
    3. y = - 4x - 4
    4. y = - 4x + 4

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

    problem.

    1. area = 2(x+1) + 2(x-1)
    2. area = 4(x+1)(x-1)
    3. area = 2x2
    4. area = x2 - 1

  18. Which line given by its equation below contains the points (1, -1) and (3, 5)?

    1. -2y -6x = 0
    2. 2y = 6x - 8
    3. y = 3x + 4
    4. 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| + |3x| - |-2x| + 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. 0.02

  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|

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Updated: 14 March 2009 (A Dendane)