Algebra 3 Fall 2014 Final ReviewName:______
Equations: Slope: , Slope-intercept form: , Point-slope form:
Unit 1
1. Determine the numbers that are found in each set:
a. Natural numbers:______
b. Whole numbers:______
c. Integers:______
d. Rational numbers:______
e. Irrational numbers:______
f. Real numbers:______
2. Insert >, < or = to make the statement true.
a. 22 _____ 11 b. _____ 6 c. _____ 8
3. Simplify the following.
a. |-2| = _____ b. |4| = ____ c. |-5.6| =____
4. Write each fraction in lowest terms.
a. =_____ b. =______c. =______
5. Perform the indicated operation. Write your answer in lowest terms.
a. =______b. =______
c. =______d. =______
6. Simplify the following.
a. b.
7. Perform the indicated operation of real numbers:
a. b.
c. d.
8. Evaluate the following for x = 1, y = -4, and z = 2
a. b.
Unit 2
9. Simplify the following expressions.
a. b.
c. d.
e.
10. Translate the following into algebraic expressions or equations.
a. Subtract from ______
b. The difference of a number and five, divided by seven. ______
c. The sum of a number and six subtracted from two times a number decreased by one. ______
d. Five times a number less four is the same as twice the sum of the number and three. ______
11. Solve for x:
a. b.
c. d.
12. Formulas
a. Given ; . Find w.
b. Solve for w: .
c. Mike is trying to replace the carpet in his bedroom. His room is rectangular and has a width of 13. feet and a length of 20 feet. How much carpet will Mike need for his bedroom?
d. The normal body temperature for a human is 98.6 degrees Fahrenheit. Express this temperature in terms of degrees Celsius.
13. Solve the following word problems.
a. Greg gets paid $20 dollars an hour. If Greg’s paycheck at the end of week is $700 before taxes, how many hours did he work?
b. The sum of two consecutive even numbers is 178. What are the two numbers?
Unit 3
14. Graph the following using coordinate points. Find at LEAST three points:
15. Identify the intercepts of the following graphs:
16. Find the intercepts for the following equations:
a. b.
17. Graph the following equations by plotting intercepts:
18. Find the slope of the following:
a. Line through (4, -2) and (2, 5)
b. Line through (8, -1) and (3, -1)
19. Determine if the following lines are parallel, perpendicular, or neither.
- L1: (5, -1) and (4, 3); L2: (2, 3) and (-1, 15)
b. L1: (3, -2) and (0, -1); L2: (2, 5) and (3, 2)
c.
20. Find the slope and y-intercept of the following:
a. b. c.
21. Graph the following using slope-intercept form:
a.
22. Use point-slope form to find the following equations:
a. Find an equation of the line passing through (3, 4) with slope . Put in slope-intercept form.
b. Find an equation of the line perpendicular to the line and goes through the point (6, -1). Write the equation in slope-intercept form.
Unit 4
23. Solve for x. Write the answer in interval notation and graph.
a.
b.
c.
24. Write each Compound Inequality in inequality form and interval notation and then graph.
a. and
b. or
c.
25. Solve the following Absolute Value Equations.
a. b.
26. Solve the following Absolute Value Inequalities. Graph the answer and write in interval notation.
a.
b.
c.
27. Graph the following Linear Inequalities.
a. b.
28. Graph the following Systems of Linear Inequalities:
a.
b.
Unit 5
29. Determine if the following are solutions to the given system of linear equations:
a. 1) (3, -5)2) (-1, 3)
30. Solve the following systems by graphing. If a single point, write as an ordered pair:
a.
31. Solve the following systems by substitution. If a single point, write as an ordered pair:
a. b.
32. Solve the following systems by elimination. If a single point, write as an ordered pair:
a. b.
Unit 6
33. Determine if the following are solutions to the given system of equations.
a. 1) (5, -2, 4) 2) (3, -3, 1)
34. Solve the following systems. If a single answer, write as an ordered triple:
a. b.
35. Problem solving with systems:
a. The sum of three numbers is 110. The largest number is six more than three times the smallest. The remaining number is two more than twice the smallest What are the three numbers?
b. A jewelry maker spends $1650 on operating costs and $35 for each necklace made. The necklaces are then sold for $85 each. How many necklaces does the jewelry maker need to sell in order to break even?
c. John buys 3 pairs of jeans and 4 shirts for $195. Nathan buys 2 pairs of jeans and 5 shirts for $165 on the same day. How much does a pair of jeans cost? How much does a shirt cost?
Unit 7
36. Write in simplest form without zero or negative exponents.
a. b.
c. d. e.
f. g. h.
37. Determine the degree of the following polynomials. Then indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.
a. b. c.
38. Perform the indicated operations and simplify.
a.
b.
c.
d.
Unit 8
nth root rule:
39. Simplify each radical expression.
a. b.
40. Evaluate the following expression in radical form and simplify if possible.
a. b.
41. Evaluate the following expression in rational form and simplify if possible.
a. b. c.
42. Multiply/divide the following expressions. Then simplify if possible.
a. b.
c. d.
43. Perform the indicated operation.
a. b.
c. d.
Unit 9
44. Rationalize the denominator of the following. Simplify if possible.
a. b. c.
45. Rationalize the numerator. Simplify if possible.
a. b.
46. Solve the following radical equations. Check for extraneous answers.
a. b.
c.
47. Write in terms of i.
a. b.
c. d.
48. Perform the indicated operation. Write your answer in the form .
a. b.
c. d.
49. Find the powers of i.
a. b. c.