Algebra Questions for Grade 10 with Solutions on Videos

Grade 10 algebra questions with answers presented at the bottom of the page and several questions has detailed solutions on videos..

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.
   Solution on Video
   
   
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.
   Solution on Video
   
   
8. Evaluate the algebraic expression |-2 x - y + 3| for x = 3 and y = 5
   Solution on Video
   
   
9. Simplify the algebraic expression -2(x - 3) + 4(-2 x + 8)
   Solution on Video
   
   
10. Expand and simplify the algebraic expression (x + 3)(x - 3) - (-x - 9)
    Solution on Video
    
    
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?
    Solution on Video
    
    
15. For what value of a will the system given below have no solutions ?
    2 x + 6 y = -2
    -3 x + a y = 4
    Solution on Video
    
    

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.
    Solution on Video
    
    

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?
    Solution on Video
    
    
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 the triple its width.
    
    
25. Simplify: |- x| + |3 x| - |- 2 x| + 3|x|
    Solution on Video
    
    
27. If (x² - y²) = 10 and (x + y) = 2, find x and y.
    Solution on Video
    
    

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)
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