1st Semester Exam Review

Multiple Choice

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

What inequality represents the sentence?

____ 1. 14 fewer than a number is at least –18

a. c. b. d.

Solve the inequality. Graph the solution set.

____ 2. 4 + 5k 29

a. k 6

3

5

0 2 4 6 80–2–4–6–8

c. k 5

0 2 4 6 80–2–4–6–8

b. k 6

3

5

0 2 4 6 80–2–4–6–8

d. k 5

0 2 4 6 80–2–4–6–8

Solve the compound inequality. Graph the solution.

____ 3. 8x – 14 < –6 or 2x + 2 > 6

a. x < 1 or x > 2

0 2 4 6 80–2–4–6–8

c. x < 1 or x > 4

0 2 4 6 80–2–4–6–8

b. x < 2

1

2 or x > 2

0 2 4 6 80–2–4–6–8

d. x < 2

1

2 or x > 4

0 2 4 6 80–2–4–6–8

Solve the absolute value equation. Graph the solution.

____ 4.

a. x = 1 or x = 1

0 1 2 3 4 50–1–2–3–4–5

c. x = 1 or x = 2

0 1 2 3 4 50–1–2–3–4–5

b. x = 2 or x = 1

0 2 40–2–4

d. x = 1 or x = 4

0 1 2 3 4 50–1–2–3–4–5

____ 5. You start with $20 and save $3 each week. What algebraic expression models the total amount you save?

a. c. b. d.

Evaluate the expression for the given value of the variable(s).

____ 6. ; b = –3

a. 82 b. 68 c. –26 d. 46

Combine like terms. What is a simpler form of each expression?

____ 7.

a. b. c. d.

____ 8. Use the vertical-line test to determine which graph represents a function.

a.

O 4 8–4–8 x

4

8

–4

–8

y

c.

O 4 8–4–8 x

4

8

–4

–8

y

b.

O 4 8–4–8 x

4

8

–4

–8

y

d.

4 8–4–8 x

4

8

–4

–8

y

____ 9. Tickets to a concert are available online for $15 each, plus a one-time handling fee of $1.25. The total cost is

a function of the number of tickets bought. What function rule models the cost of the concert tickets ( )?

Evaluate the function for 6 tickets.

a. ; $22.50 c. ; $91.25

b. ; $91.25 d. ; $22.50

What is the graph of each direct variation equation?

____ 10.

a.

4 8–4–8 x

4

8

–4

–8

y

c.

4 8–4–8 x

4

8

–4

–8

y

b.

4 8–4–8 x

4

8

–4

–8

y

d.

4 8–4–8 x

4

8

–4

–8

y

What is the slope of the line that passes through the given points?

____ 11. (10, 4) and (–11, 1)

a.

1

7

c. 7

b. 7 d. 1

7

Write the equation in slope-intercept form. What are the slope and y-intercept?

____ 12. 4

3x +

1

2y = 4

a. 8

38;

slope: 8; y-intercept: 8

3

c. 8

38

slope: 8

3; y-intercept: 8

b. 8

38

slope: 8

3; y-intercept: 8

d. 8

38;

slope: 8

3; y-intercept: 8

What is the graph of the equation?

____ 13.

a.

4 8–4–8 x

4

8

–4

–8

y

c.

4 8–4–8 x

4

8

–4

–8

y

b.

4 8–4–8 x

4

8

–4

–8

y

d.

4 8–4–8 x

4

8

–4

–8

y

What is an equation of the line, in point-slope form, that passes through the given point and has the

given slope?

____ 14. point: ; slope: 7

a. c.

b. d.

What is the equation of the given line in standard form? Use integer coefficients.

____ 15. 3

7

a. c.

b. d.

What are the intercepts of the equation? Graph the equation.

____ 16.

a. x-intercept: (4, 0)

y-intercept: (0, –4)

4 8–4–8 x

4

8

–4

–8

y

c. x-intercept: (4, 0)

y-intercept: (0, –4)

4 8–4–8 x

4

8

–4

–8

y

b. x-intercept: (–4, 0)

y-intercept: (0, 4)

d. x-intercept: (–4, 0)

y-intercept: (0, 4)

4 8–4–8 x

4

8

–4

–8

y

4 8–4–8 x

4

8

–4

–8

y

What is the equation of the line in slope-intercept form?

____ 17. the line parallel to through (–7, –5)

a.

1

3

c.

b. d.

The function f(x) is represented by the given table. What are the corresponding values of the given

g(x)?

____ 18. Write an equation for the following transformation of :

a vertical stretch by a factor of 4

a. 1

4x

c. 4x

b. 1

4x

d. 4x

What is the graph of the absolute value equation?

____ 19.

a.

O 4 8–4–8 x

4

8

12

16

–4

y

c.

O 4 8–4–8 x

4

8

12

16

–4

y

b.

O 4 8–4–8 x

4

8

–4

–8

–12

y

d.

O 4 8–4–8 x

4

8

12

16

–4

y

Write an inequality for the graph.

____ 20.

O 6 12–6–12 x

6

12

–6

–12

y

a. y |x – 2| – 5 c. y |x + 2| + 5

b. y |x – 2| + 5 d. y |x – 2| + 5

Solve the system of inequalities by graphing.

____ 21.

a.

O 2 4–2–4 x

2

4

–2

–4

y

c.

O 2 4–2–4 x

2

4

–2

–4

y

b.

O 2 4–2–4 x

2

4

–2

–4

y

d.

O 2 4–2–4 x

2

4

–2

–4

y

How can you represent the system of equations with a matrix?

____ 22.

a.

c.

b.

d.

What is the solution of the system?

____ 23.

a. (–2, –4) c. (2, 4)

b. (4, 2) d. (–2, 4)

What is the graph of the equation?

____ 24.

a.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

____ 25. You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled

with the function where x and y are in feet. How high above the river is the bridge

(the top of the arch)? How long is the section of bridge above the arch?

a. The bridge is about 1767.98 ft above the river and the length of the bridge above the arch

is about 336.8 ft

b. The bridge is about 336.8 ft above the river and the length of the bridge above the arch is

about 1767.98 ft

c. The bridge is about 1767.98 ft above the river and the length of the bridge above the arch

is about 883.99 ft

d. The bridge is about 336.8 ft above the river and the length of the bridge above the arch is

about 883.99 ft

What are the solutions of the quadratic equation?

____ 26.

a. 5, –3 c. 5, 3

b. –5, –3 d. –5, 3

What is the solution of the quadratic system of equations?

____ 27.

a. (–5, –3)

(–21, –5)

c. (3, –5)

(5, –21)

b. (–3, 91)

(–5, 139)

d. (–3, –5)

(–5, –21)

Consider the leading term of each polynomial function. What is the end behavior of the graph?

____ 28.

a. As , and As ,

b. As , and As ,

c. As , and As ,

d. As , and As ,

What are the zeros of the function? What are their multiplicities?

____ 29.

a. the number 0 is a zero of multiplicity 2; the numbers –4 and –1 are zeros of multiplicity 1

b. the number 0 is a zero of multiplicity 2; the numbers 4 and 1 are zeros of multiplicity 1

c. the numbers –4 and –1 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1

d. the numbers 0 and 4 are zeros of multiplicity 2; the number 1 is a zero of multiplicity 1

____ 30. Divide by x – 3.

a. , R 59 c. , R –55

b. d.

Graph each function. How is each graph a translation of ?

____ 31.

a. c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

translated down 2 unit(s) and translated to

the right 3 unit(s)

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

translated up 2 unit(s) and translated to the

right 3 unit(s).

b.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

translated up 2 unit(s) and translated to the

left 3 unit(s)

d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

translated down 2 unit(s) and translated to

the left 3 unit(s)

What is the expression in factored form?

____ 32.

a. c.

b. d.

What value completes the square for the expression?

____ 33.

a. c. 64

b. d. 8

Use the Quadratic Formula to solve the equation.

____ 34.

a. 2, 6 c. 3, 1

b. 1, 3 d. 2, 6

Simplify the expression.

____ 35.

a. c. b. d.

____ 36.

a. 20 c. 20i

b. –20i d. –20

Find all the zeros of the equation.

____ 37.

a. , c. 4, , ,

b. 4, , , 0 d. 4,

____ 38. Find .

a.

c.

b.

d.

Solve the matrix equation.

____ 39.

a.

c.

b.

d.

Find the product.

____ 40.

a.

c.

b.

d.

Are matrices A and B inverses?

____ 41. and

a. yes b. no

Evaluate the determinant of the matrix.

____ 42.

a. –42 b. 42 c. 20 d. –2

____ 43.

a. –53 b. –123 c. 123 d. 53

Does the given matrix, A, have an inverse? If it does, what is A ?

____ 44. A =

a.

c.

b.

d. does not exist

____ 45. Find all the real fourth roots of .

a. and

c. , , , and

b. and

d.

What is the simplest form of the expression?

____ 46.

a. c.

b. d. none of these

What is the simplest form of the expression?

____ 47.

a. c. b. d.

What is the product of the radical expression?

____ 48.

a. c. b. d.

Simplify.

____ 49.

a. c.

b. 4 d. 16

What is the simplest form of the number?

____ 50.

a. 1024 c.

b.

d.

1st Semester Exam

Answer Section

MULTIPLE CHOICE

1. ANS: B REF: 1-5 Solving Inequalities

2. ANS: C REF: 1-5 Solving Inequalities

3. ANS: A REF: 1-5 Solving Inequalities

4. ANS: B REF: 1-6 Absolute Value Equations and Inequalities

5. ANS: A REF: 1-3 Algebraic Expressions

6. ANS: A REF: 1-3 Algebraic Expressions

7. ANS: C REF: 1-3 Algebraic Expressions

8. ANS: D REF: 2-1 Relations and Functions

9. ANS: B REF: 2-1 Relations and Functions

10. ANS: D REF: 2-2 Direct Variation

11. ANS: D REF: 2-3 Linear Functions and Slope-Intercept Form

12. ANS: B REF: 2-3 Linear Functions and Slope-Intercept Form

13. ANS: D REF: 2-3 Linear Functions and Slope-Intercept Form

14. ANS: C REF: 2-4 More About Linear Equations

15. ANS: B REF: 2-4 More About Linear Equations

16. ANS: A REF: 2-4 More About Linear Equations

17. ANS: D REF: 2-4 More About Linear Equations

18. ANS: C REF: 2-6 Families of Functions

19. ANS: C REF: 2-7 Absolute Value Functions and Graphs

20. ANS: B REF: 2-8 Two-Variable Inequalities

21. ANS: D REF: 3-3 Systems of Inequalities

22. ANS: B REF: 3-6 Solving Systems Using Matrices

23. ANS: C REF: 3-6 Solving Systems Using Matrices

24. ANS: D REF: 4-2 Standard Form of a Quadratic Function

25. ANS: B REF: 4-2 Standard Form of a Quadratic Function

26. ANS: C REF: 4-5 Quadratic Equations

27. ANS: D REF: 4-9 Quadratic Systems

28. ANS: D REF: 5-1 Polynomial Functions

29. ANS: B REF: 5-2 Polynomials, Linear Factors, and Zeros

30. ANS: C REF: 5-4 Dividing Polynomials

31. ANS: C REF: 4-1 Quadratic Functions and Transformations

32. ANS: D REF: 4-4 Factoring Quadratic Expressions

33. ANS: C REF: 4-6 Completing the Square

34. ANS: B REF: 4-7 The Quadratic Formula

35. ANS: B REF: 4-8 Complex Numbers

36. ANS: A REF: 4-8 Complex Numbers

37. ANS: C REF: 5-6 The Fundamental Theorem of Algebra

38. ANS: C REF: 12-2 Matrix Multiplication

39. ANS: D REF: 12-2 Matrix Multiplication

40. ANS: A REF: 12-2 Matrix Multiplication

41. ANS: A REF: 12-3 Determinants and Inverses

42. ANS: B REF: 12-3 Determinants and Inverses

43. ANS: A REF: 12-3 Determinants and Inverses

44. ANS: D REF: 12-3 Determinants and Inverses

45. ANS: B REF: 6-1 Roots and Radical Expressions

46. ANS: A REF: 6-2 Multiplying and Dividing Radical Expressions

47. ANS: A REF: 6-3 Binomial Radical Expressions

48. ANS: A REF: 6-3 Binomial Radical Expressions

49. ANS: B REF: 6-4 Rational Exponents

50. ANS: B REF: 6-4 Rational Exponents