1. Simplify the following expression: (22x103)2 16,000,000
2. Find the product of (4x-5)(2x+3) 8x2 + 2x -15.
3. Factor the following trinomial: 6x2 - 13x + 6 (3x-2)(2x-3)
4. Use the quadratic formula to solve: 2x2 + 7x - 5 = 0 x = (-7 +/- sqrt(89))/4
5. Find all solutions to the following equation: x4 - 11x2 + 28 x = 2, -2, sqrt(7), -sqrt(7)
6. Find all solutions to the following equation: | 3x - 1 | = 7 x = -2, 8/3
7. Solve the inequality and sketch the solution on the real number line: 4 - 2x < 12 x > -4 (graph missing)
8. Plot the points and find the slope of the line passing through (-3, -1) and (1, 7). slope = 2 (graph missing)
9. Sketch the graph of the quadratic function. Identify the vertex and intercepts: f(x)=x2
- 11x + 28
x-intercept: (4, 0) and(7, 0). y-intercept: (0, 28). Vertex: (11/2, 37/4). (graph missing)
10. Divide by long division: (4x3 - 8x2 - 11x + 5) / ( x + 4) 4x2 - 24x + 85 - 335/(x+4)
11. Divide by synthetic division: (3x3 - 17x2 + 15x - 25)/(x-5) 3x2 - 2x + 5
12. Evaluate the following expression: log2(47). 14
13. Write the following expression as the logarithm of a single expression: 2log5x
+ 3log5y - 5log5z
log5(x2y3/z5)
14. Solve the following system of equations: 3x - 5y = 13, 2x + 5y = 7. x= 4, y = -1/5
15. Solve the following system of equations: 6x - 5y = 1, 4x + 7y = 11. x =1, y=1
16. Find the midpoint of the interval with endpoints -2 and 15. 13/2
17. Suppose in the interval [a,b], a = -2. Find b if the midpoint of the interval is 7. b = 16
18. Find the point that is five-ninths of the way from -4 to 23. 11
19. If 4 is midway between a and b and 8 is two-thirds of the way from a to b, what are a and
b?
a = -8, b = 16
20. What is the set of letters in the state name MISSISSIPPI? How many elements are in that
set?
{ M, I, S, P }, 4
21. How many elements are in the set {1, 2, {3, 4}, {5, 6, 7} }? 4
How many elements are in the set {1,2,3,4,5,6,7}? 7
22. What is the power set of {a, b}? { {}, {a}, {b}, {a,b} }
23. What is the power set of the empty set? { {} }
What is the power set of { {} }? { {}, {{}} }
24. Let A = {a, b, c, d, e} and B = {c, d, e, f, g}.
What is A intersect B? {c, d, e}
What is A union B? {a, b, c, d, e, f, g}
What is A - B? {a, b}
25. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}?
How many elements are in 2A? 212
How many elements in 2A contains the number 10? 211
How many elements in 2A does not contain the number 10? 211