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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 4*10-2 as a decimal.

    Solution on Video

  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.
    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 |-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.


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