1st Semester Exam Review - PC\|MAC
Transcript of 1st Semester Exam Review - PC\|MAC
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