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

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