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.
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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?

.

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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