Alg. 2 Final Exam Review Packet and Answers

ALG. 2 FINAL EXAM REVIEW PACKET AND ANSWERS

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____1.An irrational number can ______be expressed as a quotient of integers.

a. / always / b. / sometimes / c. / never

____2.Use the vertical-line test to determine which graph represents a function.

a. / / c. /
b. / / d. /

____3.A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake’s population of waterfowl on each of the next six weeks.

Week / 0 / 1 / 2 / 3 / 4 / 5 / 6
Population / 585 / 582 / 629 / 726 / 873 / 1,070 / 1,317
a. / Find a quadratic function that models the data as a function of x, the number of weeks.
b. / Use the model to estimate the number of waterfowl at the lake on week 8.
a. / ; 1,614 waterfowl
b. / ; 2,679 waterfowl
c. / ; 1,961 waterfowl
d. / ; 2,201 waterfowl

____4.Identify the graph of the complex number .

a. / / c. /
b. / / d. /

To which sets of numbers does the number belong?

____5.

a. / integers, rational numbers, real numbers
b. / rational numbers, real numbers
c. / irrational numbers, real numbers
d. / rational numbers, irrational numbers, real numbers

Name the property of real numbers illustrated by the equation.

____6.

a. / Associative Property of Multiplication
b. / Distributive Property
c. / Commutative Property of Addition
d. / Associative Property of Addition

____7.

a. / Distributive Property
b. / Associative Property of Multiplication
c. / Commutative Property of Multiplication
d. / Associative Property of Addition

Short Answer

8.Write the ordered pairs for the relation. Find the domain and range.

Solve the system by graphing.

10.

Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

11.

12.

Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.

13.

14.Use a graphing calculator to solve the equation . If necessary, round to the nearest hundredth.

15.Simplify using the imaginary number i.

Write the number in the form a + bi.

16.

17.Find .

Simplify the expression.

18.

19.

20.Find the missing value to complete the square.

Solve the quadratic equation by completing the square.

21.

22.

Rewrite the equation in vertex form.

23.

Use the Quadratic Formula to solve the equation.

24.

25.

26.Classify –3x5 – 2x3 by degree and by number of terms.

27.Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.

28.Write the polynomial in standard form.

29.Use a graphing calculator to find a polynomial function to model the data.

x / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
f(x) / 12 / 4 / 5 / 13 / 9 / 16 / 19 / 16 / 24 / 43

30.Write the expression (x + 6)(x – 4) as a polynomial in standard form.

31.Write 4x3 + 8x2 – 96x in factored form.

32.Divide by x + 3.

Divide using synthetic division.

33.

34.

35.In XYZ, Y is a right angle and . Find cos X in fraction and in decimal form. Round to the nearest hundredth, if necessary.

36.In XYZ, Y is a right angle and . Find sin Z in fraction and in decimal form. Round to the nearest hundredth, if necessary.

Find the length x. Round to the nearest tenth.

37.

38.

Find the angle measure to the nearest tenth of a degree.

39.

40.

41.

In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.

42.a = 3.4, c = 5.8

43.Use the Law of Sines. Find b to the nearest tenth.

44.Use the Law of Sines. Find to the nearest tenth.

45.Use the Law of Cosines. Find b to the nearest tenth.

46.Use the Law of Cosines. Find to the nearest tenth of a degree.

47.In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

a. / Find a quadratic model for the data in the table.
b. / Use the model to estimate the population of bacteria at 9 hours.
Time (hours) / 0 / 1 / 2 / 3 / 4 / 5 / 6
Population (1000s) / 5.1 / 3.03 / 1.72 / 1.17 / 1.38 / 2.35 / 4.08

Graph the number on a number line.

48.

49.

Simplify by combining like terms.

50.

51.Find the perimeter of the figure. Simplify the answer.

Solve the equation.

52.

53.

54.

Solve the equation or formula for the indicated variable.

55., for t

56., for U

Solve the inequality. Graph the solution set.

57.2 + 2k 8

58.

2(4y – 5)  –10

Solve the compound inequality. Graph the solution set.

59.4x – 5 < –17 or 5x + 6 > 31

60.Suppose and .

Find the value of .

61.Graph the equation .

Find the slope of the line through the pair of points.

62.

63.(6, 12) and (–6, –2)

Write in standard form an equation of the line passing through the given point with the given slope.

64.slope = –8; (–2, –2)

65.Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).

Find the slope of the line.

66.

67.

Find an equation for the line:

68.through (–7, –4) and vertical.

69.Graph the equation of y = |x| translated 4 units up.

Find the value of y for a given value of x, if y varies directly with x.

70.If y = 166 when x = 83, what is y when x = 23?

71.If y = 4.8 when x = 2.4, what is y when x = 2.05?

72.A balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model the balloon’s elevation h as a function of time t.

Graph the absolute value equation.

73.

Without graphing, classify each system as independent, dependent, or inconsistent.

74.

Solve the system by the method of substitution.

75.

Use the elimination method to solve the system.

76.

77.

Solve the system of inequalities by graphing.

78.

79.

Find a quadratic model for the set of values.

80.(–2, 8), (0, –4), (4, 68)

81.

x / –2 / 0 / 4
f(x) / 1 / –3 / 85

82.Write in vertex form.

Factor the expression.

83.

84.

85.

86.

87.

Solve the equation by finding square roots.

88.

ALG. 2 FINAL EXAM REVIEW PACKET - 1

Answer Section

MULTIPLE CHOICE

1.ANS:C 1-1 Properties of Real Numbers

2.ANS:C 2-1 Relations and Functions

3.ANS:C 5-1 Modeling Data With Quadratic Functions

4.ANS:B 5-6 Complex Numbers

5.ANS:B 1-1 Properties of Real Numbers

6.ANS:B 1-1 Properties of Real Numbers

7.ANS:B 1-1 Properties of Real Numbers

SHORT ANSWER

8.ANS:

{(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}

2-1 Relations and Functions

9.ANS:

(–5, –4)

3-1 Graphing Systems of Equations

10.ANS:

no solutions

3-1 Graphing Systems of Equations

11.ANS:

linear function

linear term:

constant term: –6

5-1 Modeling Data With Quadratic Functions

12.ANS:

quadratic function

quadratic term:

linear term:

constant term: –6

5-1 Modeling Data With Quadratic Functions

13.ANS:

(–1, –2), x = –1

P'(0, –1), Q'(–3, 2)

5-1 Modeling Data With Quadratic Functions

14.ANS:

0.87, –2.07

5-5 Quadratic Equations

15.ANS:

5-6 Complex Numbers

16.ANS:

5-6 Complex Numbers

17.ANS:

5-6 Complex Numbers

18.ANS:

5-6 Complex Numbers

19.ANS:

5-6 Complex Numbers

20.ANS:

5-7 Completing the Square

21.ANS:

5-7 Completing the Square

22.ANS:

5-7 Completing the Square

23.ANS:

5-7 Completing the Square

24.ANS:

5-8 The Quadratic Formula

25.ANS:

5-8 The Quadratic Formula

26.ANS:

quintic binomial

6-1 Polynomial Functions

27.ANS:

quintic trinomial

6-1 Polynomial Functions

28.ANS:

6-1 Polynomial Functions

29.ANS:

f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58

6-1 Polynomial Functions

30.ANS:

x2 + 2x – 24

6-2 Polynomials and Linear Factors

31.ANS:

4x(x – 4)(x + 6)

6-2 Polynomials and Linear Factors

32.ANS:

, R –93

6-3 Dividing Polynomials

33.ANS:

6-3 Dividing Polynomials

34.ANS:

, R –38

6-3 Dividing Polynomials

35.ANS: