ACP ALGEBRA II MIDTERM REVIEW PACKET 2015-16

Name _____________________________ Per__ Date______

This review packet includes new problems and a list of problems from the textbook. The answers to the problems from

the textbook can be found in the back of the textbook and a detailed solution on www.hotmath.com.

Section 1-4 Solving Absolute Value Equations

Vocabulary: Absolute value, empty set, equation, solution, variable

p.30-31 #5-13odd,17-43odd,47,49,53

1. Solve each equation. Remember to check your solutions!

a. 7 4 1p b. 4 1 5 37w w

Section 2-1 Relations and Functions

Vocabulary: Dependent and independent variable, domain/range, relation/function, function notation, vertical line test

p.60-61 #3-31odd,35,36,37,47-53odd

2. Find the value of each of the following for the functions: 4 8f x x and 26 25g x x x .

a. 9f b. (3 )g a c. 𝑔(𝑥 + 1)

3. Determine whether each relation is a function. Also, identify the domain and range.

a. 2,1 , 2,1 , 3,4 , 8,0 b. 6 7y x

c. d.

Section 2-6 Special Functions (graphing absolute value functions and piecewise functions)

x y

-5 6

4 7

-3 8

0.5 9

4 5

Vocabulary: Absolute value function, constant function, identity function, parent graph, piecewise function

p.93-94 #8-11all,15,16,19,20,32-41all,44

4. Graph each function. Identify the x-intercepts, y-intercepts, vertex, domain, and range

a. ( ) 3 9g x x b. ( ) 2 1 6g x x

5. Graph each function. Identify the domain and range. Be sure to use proper notation.

a.

4 , 0

5 , 0

x xf x

x x

b.

, 03

2 6 , 0 2

1 , 2

xx

g x x x

x

6. Write the definition (the equations) of the function shown in the graph below. Identify the range of the

graph also.

Section 5-1 Monomials

Vocabulary: Coefficient, constant, degree, monomial, power, scientific notation, simplify, standard notation,

p.226-7 #3-41odd,45-57odd

7. Simplify the expression. Assume that no variable equals zero. Remember: leave no negative exponents.

a.

23 4 23 2x y x y

b.

218 10

9 20

32

16

x y

x y

Section 5-2 Polynomials

Vocabulary: Binomial, FOIL method, like terms, polynomial, terms, trinomial

p.231-2 #5-33odd,37-51odd,57

8. Find 5p for the polynomial: 5 4 25 5 10 6 1p x x x x x

9. Simplify.

a. 4 3 4 23 4 9 6 5 1x x x x b. 2 2 213 6 12 9 4x xy y x xy

c. 3 2 2 2 33 2 9 3a ab a b a b d. 4 8x x

e. 2 5 3 7x x f. 4 5 4 5x x

g. 2

5 6x h. 24 3 2x x x

Section 5-3 Dividing Polynomials

Vocabulary: Long division, synthetic division

p.236-7 #3,5,7,11-43odd,49

10. Simplify.

a.

3 218 30

3

a a

a

b. 6 2 3 2 324 40 4mn m n m n

11. Simplify by synthetic or long division.

a. 3 23 7 4 3 3w w w w b.

4 36 15 28 6

2

y y y

y

Section 5-4 Factoring Polynomials

Vocabulary: Difference of cubes, difference of squares, greatest common factor, grouping, perfect square trinomial, sum

of cubes

p.242-3 #5-37odd,47,49

12. Factor completely.

a. 27 5 18x x b.

220 12 11x x

c. 38 125x d.

225 20 4p p

e. 22 18 40x x f.

249 81n

g.4 16c

Section 5-5 Roots of Real Numbers

Vocabulary: cube root, nth root, principal root, square root

p.248 #5-55odd

13. Simplify.

a. 8144x b.

6 6 42729m n

c. 9 123 27x y

d. 196

e.

8625

49

x

f.

28x

Section 5-6 Radical Expressions

Vocabulary: Conjugates, like radical expressions, rationalizing the denominator

p.254-5 #5-45odd,49

14. Simplify

a. 23 12288x y b. 200 300

c. 9 143 128x y

d.

20

10

64

11

y

y

e.

2

3

25

5

x

x f.

2

8 7

g. 5 5 2 80 3 45 h. 20 125 169 45

i. 3 3 32 4 12

j. 2 3 4 5

k.

7

3 l.

2 5

6

m.

2 7

3 7

Section 5-7 Rational Exponents

Vocabulary: Rational exponents

p.261 #5-15odd,21-47odd

15. Write

2

310 in radical form.

16. Write each expression using rational exponents.

a. 647d b.

3 5 23a b

17. Evaluate each expression.

a.

2

327 b.

2 3

3 28 4

18. Simplify each expression.

a.

4 6

5 5x x b.

32 43y

c.

3

4

1

6

y

y d.

21

32

1

6

a a

a

Section 5-9 Complex Numbers

Vocabulary: Complex conjugates, complex number, imaginary unit, pure imaginary numbers

p.273-274 #5-41odd,49-61odd

19. Simplify

a. 11 3 15i i b. 11 12 21 8i i

c. 4 4 3 3i i d. 2 7 8i i

e. 2 5

3

i

i

f.

3

6 7i

g. 6 3

8 11

i

i

h.

27i

i. 49 j. 200 300

20. Solve 22 18 0x

21. Find the values of m and n that makes the equation true:8 15 2 3i m ni

Section 6-1 Graphing Quadratic Functions

Vocabulary: Axis of symmetry, constant term, linear term, maximum value, minimum value, parabola, quadratic

function, quadratic term, vertex

p.290-292 #2,3-47odd,51

22. State whether the graph of the quadratic function opens up or down. Then, state whether the function has a

maximum or minimum value. Find the minimum or maximum value.

a. 27 14 11f x x x b. 23 2 10f x x x

23. SOLVE A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for

each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month.

a. Write the function, I x , where x is the number of increases or decreases.

b. How much should the owner charge for each mug in order to maximize the monthly income from their

sales?

c. What is the maximum monthly income the owner can expect to make from these items?

24. Complete the following pieces for each function.

a. Find the y-intercept, the equation of the axis of symmetry, and the vertex.

b. Use this information to graph the function.

i. 2 3 4f x x x

ii. 2 4 1f x x x

Section 6-2 Solving Quadratic Equations by Graphing

Vocabulary: Quadratic equation, roots, solutions, x-intercepts, zeros

p.297-299 #5-43odd,49

25. Use the formula 2

016h t t v t , where h t is the height of an object in feet, 0v is the object’s initial

velocity in feet per second, and t is the time in seconds.

ARCHERY An arrow is shot upward with a velocity of 64 feet per second. Ignoring the height of the archer,

how long after the arrow is released does it hit the ground?

26. Use the related graph of each equation to determine its solution(s). If exact roots cannot be found, state the

consecutive integers between which the roots are located.

a. 22 2 4f x x x b. 2 3 5f x x x

Section 6-3 Solving Quadratic Equations by Factoring

Vocabulary: Zero Product Property

p.303-305 #5-41odd,51

27. Solve the equation by factoring.

a. 2 3 28 0x x b.

2 25 0x

c. 23 5 0x x d.

22 7 9 0x x

28. Write a quadratic equation with the given roots. Write the equation in the form 2 0ax bx c , where a, b, and

c are integers.

a. -5 and 2 b.

2

3

and

4

5

Section 6-5 The Quadratic Formula and the Discriminant

Vocabulary: Discriminant, Quadratic Formula

p.317-319 #5-27odd,40,41,43,47

29. State the discriminant.

30. State the Quadratic Formula.

31. Find the value of the discriminant. Then, describe the number and types of roots for the equation.

a. 2 14 2 0x x b.

2 7 0x x

c. 2 6 9 0x x d.

2 11 10 0x x

32. Find the exact solution(s) of the quadratic equation by using the Quadratic Formula.

a. 2 8 20x x b.

22 4 5 0x x c. 2 4 13x x

***Choose a method p.318 #29-39odd*** If you choose to solve by graphing – please use graph paper.

33. Solve each equation by using the method of your choice. State the method you chose. Find the exact solution(s).

a. 2 4 29 0x x b.

24 3 2 0x x

c. 22 5 9x x d.

2 8 16x x

e. 27 4x x f.

22 6 5 0x x

34. DIVING The distance a diver above the water d t (in feet) t seconds after diving off a platform is modeled by

the equation 216 8 30d t t t .

a. Find the time at which the diver will be at a maximum height.

b. Find the maximum height of the diver.

c. Find the time it will take the diver to hit the water.

35. Graph the quadratic equation.

a. 2

2 4 5y x b. 21

5 102

y x

c. 2 8 18y x x d.

2 6 7y x x

Section 7-7 Operations on Functions

Let ( ) 2 6f x x and 2( ) 3 2g x x x

42. Find:

a. f g x b. f g x

c. f g x d. f

xg

e. ( ( ))f g x f. g f x

g. ( (0))f g h. 1f g

43. For the set of ordered pairs, find f g x and g f x

2,3 , 1,4 , 7, 5

5, 1 , 6,2 , 3,7

f

g

Section 7-8 Inverse Functions and Relations

44. Find the inverse:

a. 3, 2 , 5,7 , 8,9 , 0,12 b. 1

( ) 63

f x x

c. 2 7

( )8

xg x

45. Use function composition to determine if the functions are inverse functions.

a. 11 4

4

xf x

and

9 6

11

xg x

b. 8f x x and 8g x x