Algebra 2 Midterm Review Guide To prepare for your midterm exam, please follow these suggested steps. The more practice you do, the better prepared you will be for the exam.

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 chapte. Write down any ideas that are unclear and ask about them during class review. 3. Review the quizzes and tests (including group comps) you have already taken and be sure that you would get 100% if you took the same test today. 4. Complete the chapter review and chapter test practice at the end of each chapter. 5. Use Khan Academy to review topics on the midterm exam. Direct links to specific topics can be found on my website: https://sites.google.com/a/aaps.k12.mi.us/algebra-2-2017-2018/

6. Complete all review packets given (including this one) and use math support for questions that you need help with.

PRE REQUISITE MATERIAL AND CHAPTERS 1-3 EQUATIONS AND INEQUALITIES A. Apply Properties of Real Numbers B. Evaluate and Simplify Algebraic Expressions C. Solve Linear Equations D. Rewrite Formulas and Equations (Literal Equations) E. Use Problem Solving Strategies and Models F. Solve Linear Inequalities G. Solve Absolute Value Equations and Inequalities Simplify: 1)

2(-1 + 3) - 42÷8

2)

2(3 + 18÷9) - 7

4)

43x - 3y + 2 for x=5, y = -3

Evaluate: 3)

2t3 - 4t + 3 when t = 2

Solve: 5)

3(5 - a) = -4(a - 4)

6)

15(x - 2) = -13(x + 1) + 11

7)

A = P + Prt for t

8)

S = L - rL for L

9)

V = πr2h for h

10) | 5r - 8 | = 2

11) | 3x + 2 | = 13

Solve and graph: 12) 5x - 2 < 13

13) -2x - 1 ≥ 5

14) | 2x - 1 | < 3

15) | -3x -2 | ≤ 4

16) | 3x - 5 | > 9

17) | -2x - 3 | > 7

CH. 2 – LINEAR EQUATIONS AND FUNCTIONS A. B. C. D. E. F. G.

Represent Relations and Functions Find Slope and Rate of Change Graph and Write Equations of Lines Model Direction, Inverse, and Joint Variation Draw Scatter Plots and Best-Fitting Lines Use Absolute Value Functions and Transformations Graph Linear Inequalities in Two Variables

PROBLEM SET Find the x- and y-intercepts for: 1) -3x + 4y = -2

2)

2x + 3y – 12 = 0

−2 and a y-intercept of 4. 3

3)

Write the equation of the line with slope of

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

10) 5x + 3y < 6

12)

y= − 4 x + 2 − 3

9) 5x - 2y = -4

11) 6x – 2y ≥ 8

13)

f(x) = 2x + 2 − 6

14) 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 (assume a constant rate of change)?

CH. 3 – LINEAR SYSTEMS A. Solve Linear Systems by Graphing B. Solve Linear Systems Algebraically C. Graph Systems of Linear Inequalities PROBLEM SET Solve the system: 1)

#− 2x + 3y = 5 " ! 3x − 2y = 0

2)

#2x − 5y = −4 " ! 4x + 3y = 5

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

Graph: 4)

1 $ !y ≤ x + 4 # 2 !" x + 2y > 4

#6x − 2y > 2 5) " ! x+y≥3

Solve by writing a system of equations. 6)

7)

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?

Graph the system of inequalities

⎧ x≥0 ⎪ y≥0 ⎪ ⎨ ⎪x + 4 y ≤ 4 ⎪⎩ x + y ≤ 2

CH. 4 – QUADRATIC FUNCTIONS AND FACTORING A. B. C. D. E. F. G. H.

Graph Quadratic Functions in Standard Form Graph Quadratic Functions in Vertex or Intercept Form Perform Operations with Complex Numbers Solve x2 + bx + c = 0 by Factoring Solve ax2 + bx + c = 0 by Factoring Solve Quadratic Equations by Finding Square Roots Complete the Square Use the Quadratic Formula and the Discriminant

PROBLEM SET Factor: 1)

x2 - 7x + 6

2)

x3 – 8

3)

4y3 + 108

4)

3x3 - 24x2 + 21x

5)

8x3 + 27

6)

4x2 + 12x + 9

7)

x2 - 81

8)

64x3 – 27

9)

15x3 + 10x2 + 6x + 4

10) k3 + 4k2 – 9k – 36

Simplify: 22)

− 144

23)

− 28 +

− 63

24) i15

25) (3i)(2i)

26) (2 + 3i) + (5 - 4i)

27) (2 + 3i) - (5 - 4i)

28) (2 + 3i)(5 - 4i)

29)

30) (3i)5

31) (4 -5i)2

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

Solve: 11) 3x2 - 24 = 0

12) 5x2 + 19x = 125 + 19x

13) x2 - 10x - 4 = 0

14) -2x2 + 3x -7 = -9

15) x2 + 5x + 7 = 0

16) 2x2 - 2x = -3

For each of the following, find: the vertex, axis of symmetry, y-intercept, and x-intercepts. Then graph the function. 17) y = x2 - 4x + 3 (Complete the square to put into Vertex form for this one)

18) y = 2x2 - x – 6

Applications: 19) The length of a rectangle is 16 cm longer than its width. The area of the rectangle is 65 meters squared. Find the dimensions of the rectangle, rounding to the nearest hundredth of a meter.

20) 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?

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

CHAPTER 5 – POLYNOMIALS AND POLYNOMIAL FUNCTIONS A. B. C. D. E. F. 1)

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

Perform the division 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)

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

5)

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?

6)

Write a polynomial function that has the given zeros and a leading coefficient of 1. a) -6, 4, 2 b) 4, 3i

7)

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

8)

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

9)

Find all the real zeros of f(x) = 10x4 – 3x3 – 29x2 + 5x + 12.

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

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