# Algebra Questions, for Grade 10, on simplifying, factoring, evaluating expressions and solving equations are presented along with their answers.

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 - 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? .
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.

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

More High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
More Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
More Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
Author - e-mail