Algebra Final Exam Review Topics



Algebra Final Exam Review

How to use this study guide: Complete all Practice problems in this packet. Check with the answer key. If you need more work on a topic, see the Extra practice sections and select odd numbered problems. Check answers at the end of the Selected Answers section of your book.

Solving Equations (Chapter 3; sections 3.3-3.5):

Important skills: Solve multi-step linear equations, equations with variables on both sides, and proportions.

Extra practice: pg. 940, sections 3.3-3.5

Practice problems:

1) Solve [pic]

2) Solve [pic]

Graphing Linear Equations and Functions (Chapter 4; sections 4.1-4.7):

Important skills: Identify solutions of linear equations and write equations of horizontal and vertical lines, Calculate the x and y intercepts for a linear equation, calculate slope by using the slope formula, graph using slope and y-intercept, evaluate a function with f(x) notation

Extra practice: pg. 941 sections 4.2-4.7

Practice Problems:

3) What is the slope of the line that passes through the points [pic] and [pic] ? through the points (-3,6) and (-3,2)?

4) What are the x and y intercepts of these equations? [pic] and [pic]?

5) Which of these equations represent direct variation? A) [pic] B) [pic]

6) What is the constant of variation in the equation [pic]?

7) How do you recognize the graph of a direct variation equation?

8) What is the value of [pic] if [pic] ?

Writing Linear Equations (Chapter 5; sections 5.1-5.7):

Important Skills: Write the equation of a line: slope intercept form, point slope form, and standard form (“A” is an integer!); write equations of parallel and perpendicular lines, write an equation for a line of best fit for a set of points

Extra practice: pg. 942 sections 5.1-5.7

Practice Problems:

9) Write the equation of the line that passes through the points [pic] and [pic]

a. in Point-Slope form

b. in Slope-Intercept form

c. in Standard form

10) Write the equations of the vertical and horizontal lines that pass through the point [pic] ?

11) How do you recognize the equations of parallel lines?

12) How do you recognize the equations of perpendicular lines?

13) On page 296, do problems # 11, 13, 17 and 19.

14) Write the equation of the line through [pic] that is parallel to [pic].

15) Write the equation of the line through [pic] that is perpendicular to [pic].

16) On page 329, do problem #8.

Solving and Graphing Linear Inequalities (Chapter 6; sections 6.4 - 6.7):

Important skills: Find solutions to linear inequalities with two variables, graph linear inequalities with two variables, solve compound inequalities

Extra practice: pg. 943, sections 6.4-6.7

Practice problems:

17) Graph the linear inequality [pic]

18) Graph the linear inequality [pic]

19) Solve [pic]

20) Solve [pic]or [pic]

Systems of Equations and Inequalities (Chapter 7; sections 7.1-7.6):

Important skills: Solve systems of linear equations: graphing, substitution, elimination (add/subtract) and write a system of linear equations to represent a word problem

Extra practice: pg. 944, sections 7.1-7.6

Practice problems:

21) A linear system can have 0, 1, or infinitely many solutions. How do you determine the number of solutions to a system without actually solving?

22) Solve these systems by any method of your choosing (graphing, substitution, or elimination):

a) [pic] b) [pic] c) [pic]

23) Which ordered pair is a solution to the system [pic] and [pic]?

a) [pic] b) [pic] c) [pic] d) [pic]

24) On page 440, do problem #31.

Exponents (Chapter 8; sections 8.1-8.4)

Important skills: apply all exponent rules to simplify an expression

Extra practice: pg. 945, sections 8.1-8.4

Practice problems:

25) Simplify [pic]

26) Simplify [pic]

27) Simplify[pic]

28) Simplify [pic]

29) Simplify [pic]

30) Simplify [pic]

Polynomials and Factoring (Chapter 9; sections 9.1-9.7)

Important skills: Add, subtract, and multiply polynomials, factor polynomials, use the zero product property to solve equations in factored form

Extra practice: pg. 946, sections 9.1-9.7

Practice problems:

31) Subtract: [pic]

32) Add: [pic]

33) Multiply: [pic]

34) Simplify: [pic]

35) What are the roots of [pic] ?

36) Factor:

a) [pic]

b) [pic]

c) [pic]

d) [pic]

e) [pic]

f) [pic]

Quadratic Equations (Chapter 10; sections 10.3-10.6):

Important skills: Solve quadratic equations by graphing, factoring, taking square roots and using the quadratic formula.

Extra practice: pg. 947, sections 10.3 – 10.6

Practice problems:

37) Where are the zeros on the graph of a quadratic equation?

38) Solve [pic]

39) Solve [pic]

40) Find the zeros of [pic]

41) What are the solutions of [pic]?

42) Solve [pic]

43) Solve using the quadratic formula: [pic].

44) On pg. 655 complete problems 7, 8, and 10.

45) On pg. 674, complete problem 13.

Radicals (Chapter 11; sections 11.2, 11.4)

Important skills: Evaluate squares and square roots; write an expression in simple radical form; apply Pythagorean Theorem, solve radical equations

Extra practice: pg. 948, sections 11.2, 11.4,

Practice problems:

46) Simplify [pic]

47) Simplify [pic]

48) Simplify [pic]

49) Simplify [pic]

50) Solve [pic]

51) Solve [pic]

52) On pg. 756, complete problem #29.

Chapter 12; sections 12.1, 12.3:

Important skills: Dividing polynomials; inverse variation

Extra practice: pg. 949, sections 12.1 and 12.3

Practice problems:

53) Find the quotient: [pic] ?

54) Find the quotient: [pic].

55) Given that [pic] varies inversely with [pic], and [pic] when [pic]. What is the constant of variation ?

56) On pg. 769, complete problems 3, 5, 7, 29 and 31.

Statistics:

Important skills: Using the bell curve and z-score formula to interpret data.

Z-score: [pic]

57) Draw and label a bell curve: If a set of data is normally distributed with a mean of 82 and a standard deviation of 2.5, how many standard deviations away from the mean is the element 87?

58). Use the z-score formula: If the class mean on a test was 91 with a standard deviation of 2.3, what

was the test score (to the nearest integer) of a student whose z-score was -1.3 ?

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#19-20 Graph your solutions on a number line.

#17-18 Use graph paper and

don’t forget to shade!

[pic]

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