Algebra 2 Midterm Review GuideTo prepare for your midterm exam, please follow these suggested steps. The more practice you do, the better prepared you will be for the exam. Be sure to have your calculator ready the day of the exam with WORKING batteries, a straightedge, and more than one sharpened pencil. Do not expect to borrow materials.

1. Review key vocabulary terms at the beginning of each chapter or use the list at the end of the chapter in the review.

2. Read the chapter summary at the end of each chapter several times. Write down any ideas that are unclear.

3. Review the quizzes and tests you have already taken and be sure that you would get 100% if you took the same test today.

4. Complete the lesson-by-lesson review in the Study Guide and Review section at the end of each chapter.

5. Complete the practice test at the end of each chapter.

6. Use pages 947-960, 965 for extra practice problems for each section of each chapter. This is the EXTRA PRACTICE section of the back of your book.

7. Use pages 979-984 for extra practice word problems for each section of each chapter. This is the MIXED PROBLEM SOLVING section of the back of your book.

8. For additional practice on areas you may use previous homework assignments. Your homework should be a solution key to check your work.

9. Use the guiding questions in the remainder of this packet for a general review. However, do not rely solely on these questions.

*REMINDER: Bring all quizzes and tests to the exam for extra credit on the midterm!! You must have all of them or no credit.Algebra 1 Review (Chapters 1-3)

EQUATIONS AND INEQUALITIESA. Apply Properties of Real NumbersB. Evaluate and Simplify Algebraic ExpressionsC. Solve Linear EquationsD. Rewrite Formulas and Equations (Literal Equations)E. Use Problem Solving Strategies and ModelsF. Solve Linear InequalitiesG. Solve Absolute Value Equations and Inequalities

Simplify:

1) 2(-1 + 3) - 428 2) 2(3 + 189) - 7

Evaluate:

3) 2t3 - 4t + 3 when t = 2 4) 43x - 3y + 2 for x=5, y = -3

Solve:

5) 3(5 - a) = -4(a - 4) 6) 15(x - 2) = -13(x + 1) + 11

7) | 5r - 8 | = 2 8) | 3x + 2 | = 13

Solve and graph:

9) 5x - 2 < 13 10) -2x - 1 5

11) | 2x - 1 | < 3 12) | -3x -2 | 4

13) | 3x - 5 | > 9 14) | -2x - 3 | > 7

CH. 2 – LINEAR EQUATIONS AND FUNCTIONS

A. Represent Relations and FunctionsB. Find Slope and Rate of ChangeC. Graph and Write Equations of LinesD. Model Direction, Inverse, and Joint VariationE. Draw Scatter Plots and Best-Fitting LinesF. Use Absolute Value Functions and TransformationsG. Graph Linear Inequalities in Two Variables

PROBLEM SET

Find the x- and y-intercepts for:1) -3x + 4y = -2 2) 2x + 3y – 12 = 0

3) Write the equation of the line with slope of −23 and a y-intercept of 4.

4) Write the equation of the line that goes through the points (-6, -1) and (3, 2).

5) Write the equation of the line that goes through the points (4, 3) and (0, -5).

6) Write the equation of the horizontal line through the point (3, -7).

7) Write the equation of the vertical line through the point (-2, -4).

Graph:

8) 2x + 3y = 6 9) 5x - 2y = -4

10) 5x + 3y < 6 11) 6x – 2y 8

Graph and analyze the following scatter plot.

The manager of a band has kept track of the price of tickets and the attendance at the band’s recent concerts.

Concert Attendance by Ticket SalesPrice ($) 6 5 8.5 8 10 5.5 7 7.5 8Attendance

213 256 155 194 160 267 258 210 235

16) Make a scatter plot of the data on your calculator using price as the independent variable.

17) Find the equation of the line of best fit on your calculator.

18) Using the equation above, predict the attendance at a concert where the price of tickets is $9. Show calculations.

Graph the function.

19) y = −4 | x + 2 |− 3 20) f(x) = |2x + 2 | − 6

22) In 1990 Marc earned $42,360 per year, and he now earns $61,800. What is the rate of change for Marc’s salary per year?

CH. 3 – LINEAR SYSTEMS

A. Solve Linear Systems by GraphingB. Solve Linear Systems AlgebraicallyC. Graph Systems of Linear Inequalities

PROBLEM SET

Solve the system:

1) {−2x+3 y=53 x−2 y=0 2) {2x−5 y=−44 x+3 y=5

3) Draw an example of a system that is inconsistent. Explain how you know that it is inconsistent.

Graph:

4){y≤12 x+4x+2 y>4 5) {6 x−2 y>2x+ y≥3

Solve by writing a system of equations.

6) A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.80 per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for $3.30 per pound. How many pounds of peanuts and how many pounds of cashews should be used to make 100 pounds of the mix?

7) Graph the system of inequalities{ x≥0y≥0

x+4 y≤4x+ y≤2

CH. 5 – QUADRATIC FUNCTIONS AND FACTORING

A. Graph Quadratic Functions in Standard FormB. Graph Quadratic Functions in Vertex or Intercept FormC. Perform Operations with Complex NumbersD. Solve x2 + bx + c = 0 by FactoringE. Solve ax2 + bx + c = 0 by FactoringF. Solve Quadratic Equations by Finding Square RootsG. Complete the SquareH. Use the Quadratic Formula and the Discriminant

PROBLEM SET

Factor:

1) x2 - 7x + 6 2) x2 - 81

3) 4x2 + 12x + 9 4) 3x3 - 24x2 + 21x

5) 15x3 + 10x2 + 6x + 4 6) k3 + 4k2 – 9k – 36

Simplify:

7) √−144 8) √−28 + √−63

9) i15 10) (3i)(2i)11) (2 + 3i) + (5 - 4i) 11) (2 + 3i) - (5 - 4i)

12) (2 + 3i)(5 - 4i) 13) (4 -5i)2

Solve:

14) 3x2 - 24 = 0 15) 5x2 + 19x = 125 + 19x

16) x2 - 10x - 4 = 0 17) -2x2 + 3x -7 = -9

18) x2 + 5x + 7 = 0 19) 2x2 - 2x = -3

For each of the following, find: the vertex, axis of symmetry, y-intercept, and x-intercepts. Then graph the function.

20) y = x2 - 4x + 3 21) y = 2x2 - x – 6(Complete the square to put into Vertex form for this one)

Applications: 22) Marcus is shooting of a rocket from a 160 foot cliff at a velocity of 48 ft/sec.

a) Find the time it takes the rocket to hit the ground? b) What is the maximum height the rocket reaches? c) How long does it take for it to reach the height in problem b?

23) If the discriminant of a quadratic equation is -40 what does that tell you about the roots of the equation?

24) The length of a rectangle is 16 cm longer than its width. The area of the rectangle is 65 m2. Find the dimensions of the rectangle, rounding to the nearest hundredth of a meter.

CHAPTER 6 – POLYNOMIALS AND POLYNOMIAL FUNCTIONS

Polynomial division Remainder & Factor Theorems Rational Zero Test Connection between zeros/factors/solutions Fundamental Theorem of Algebra Writing polynomial equations/functions

1) Perform the operation for each of the problems given.

a) (12x4 - 4x2 - 3) (x – 5) b) (8x3 + 2x2 - 5) (x + 1)

c) (6x3 + 11x2 - 4x - 9) + (3x - 2) d) (3x4- 5x3 + 15x2 – 4x + 3) - (x2 - x + 4)

2) What is the remainder when (x3 - 2x2 - 9) (x + 5)?

3) Is (x + 4) a factor of (x3 - 12x + 16)?

4) Find the missing factors for each of the following.a)x3 - 5x2 - 12x + 36 = (x + 3)( )( ) b)2x3 - 13x2 - 13x + 42 = (x - 7)( )( )

5) List the possible rational zeros given by the Rational Zero Test for the function:

f(x) = 4x3 + 15x2 – 8x – 3

6) How many solutions does the equation 2x3 – 4x2 + 6x = 7 have?

7) Two of the zeros of f(x) = x3 + 3x2 – 10x – 24 are 3 and – 4. The third zero must be what kind of a number? Why?

8) Write a polynomial function that has the given zeros and a leading coefficient of 1.

a) -6, 4, 2 b) 4, 3i

9) One zero of f(x) = x3 – 2x2 – 9x + 18 is x = 2. Find the other zeros.

10) Factor f(x) = 2x3 + 11x2 + 18x + 9 given that f(-3) = 0.

11) List the possible roots for each of the following polynomials and describe the end behaviors of the graphs.

a) f(x) = 3x4 - 6x2 + 14 b) g(x) = -6x3 - x + 12

c) f(x) = 9x5 + 3x4 – 10 d) g(x) = x3 – 4x2 + 6x - 3

12) Find all the zeros of the polynomial function f(x) = x4 + x3 + 2x2 + 4x – 8.

13) State the degree, type, and leading coefficient of the polynomial function: g ( x )=6 x3+9 x2−7. Then use direct substitution or synthetic substitution to evaluate the polynomial function for x = 3.

14) A storage container is a rectangular prism with a volume of 392 cubic inches. The height of the container is 3 inches less than its length and its width is twice the length. What are the dimensions of the container?

15) Graph the function f ( x )=12(x+2)¿

CHAPTER 9 – RATIONAL EXPRESSIONS

Simplifying expressions and restrictions Adding, subtracting, multiplying, and dividing expressions Complex fractions Solving equations with fractions

1) Perform the indicated operations.

a) b)

c) 2x+54 x2−25

÷ 2 x3+6 x2+18 x2 x2−x−10

d)6 a+185a+310