Download 1st Semester Final Exam Review

Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
To which sets of numbers does the number belong?
____
____
____
1.
a. irrational numbers, real numbers
b. integers, rational numbers, real numbers
c. rational numbers, irrational numbers
d. whole numbers, integers, rational numbers, real numbers
2. –17
a. integers, rational numbers, real numbers
b. whole numbers, integers, rational numbers, real numbers
c. whole numbers, integers, real numbers
d. rational numbers, real numbers
3. An irrational number can ________ be expressed as a quotient of integers.
a. always
b. sometimes
c. never
Insert <, >, or = to make the sentence true.
____
4.
a. <
b. >
c. =
Name the property of real numbers illustrated by the equation.
____
____
____
5.
a. Distributive Property
b. Associative Property of Multiplication
c. Commutative Property of Multiplication
d. Associative Property of Addition
6. –6 + 6 = 0
a. Identity Property of Multiplication
b. Inverse Property of Multiplication
c. Associative Property of Addition
d. Inverse Property of Addition
7. –2.5 + 0 = –2.5
a. Inverse Property of Multiplication
b. Identity Property of Addition
c. Inverse Property of Addition
d. Identity Property of Multiplication
Evaluate the expression for the given value of the variable(s).
____
8.
;b=2
a. 19
b. 17
c. –11
d. 21
Algebra 2 ---- 1st Semester Final Exam Review
____
9.
; x = –3
a. 3
b. –1
c. 11
d. –17
c.
d.
Simplify by combining like terms.
____ 10.
a.
b.
____ 11. Find the perimeter of the figure. Simplify the answer.
x+y
2x
4x
y
2x
x
a. 9x + 2y
b. 10x + y
c. 10x + 2y
d. 9x + 3y
b.
c.
d.
Solve the equation.
____ 12.
a.
____ 13.
a.
c.
8
2
or x = −
9
9
b.
2
x = 0 or x = −2
3
8
2
or x = −2
9
3
d.
8
x = or x = 0
9
x=
x=
Solve the equation or formula for the indicated variable.
____ 14.
, for t
a.
b.
c.
____ 15. The formula for the time a traffic light remains yellow is
d.
, where t is the time in seconds and s is
the speed limit in miles per hour.
a. Solve the equation for s.
b. What is the speed limit at a traffic light that remains yellow for 4.5 seconds?
a.
b.
; s = 28 mi/h
; s = 36 mi/h
c.
d.
; s = 35
; s = 28 mi/h
Algebra 2 ---- 1st Semester Final Exam Review
Solve for x. State any restrictions on the variables.
____ 16.
a.
c.
;
b.
;
d.
;
;
____ 17. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle.
Round to the nearest tenth if necessary.
a. 7.5 cm by 22.5 cm
c. 20 cm by 60 cm
b. 7.5 cm by 52.5 cm
d. 15 cm by 22.5 cm
____ 18. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle
is 90 cm?
a. 10.5 cm, 11.5 cm, and 12.5 cm
c. 7.5 cm, 11.5 cm, and 32.1 cm
b. 22.5 cm, 30 cm, and 37.5 cm
d. 19.3 cm, 25.7 cm, and 32.1 cm
____ 19. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than
the other car. The cars are 500 mi apart in 5 h. How fast is each car traveling?
a. 35 mi/h and 45 mi/h
c. 45 mi/h and 55 mi/h
b. 55 mi/h and 35 mi/h
d. 55 mi/h and 65 mi/h
Solve the inequality. Graph the solution set.
____ 20. –4k + 5 ≤ 21
a. k ≥ –4
–8 –6 –4 –2
b.
k ≥ −6
c. k ≤ –4
0
2
4
6
8
d.
1
2
–8 –6 –4 –2
0
2
4
6
8
____ 21. 26 + 6b ≥ 2(3b + 4)
a. all real numbers
–8 –6 –4 –2
–8 –6 –4 –2
2
4
6
b≥1
b≤1
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
8
d. no solutions
1
2
–8 –6 –4 –2
–8 –6 –4 –2
4
1
2
–8 –6 –4 –2
b.
2
1
2
–8 –6 –4 –2
c.
0
k ≤ −6
0
0
2
4
6
8
Algebra 2 ---- 1st Semester Final Exam Review
Solve the compound inequality. Graph the solution set.
____ 22. 4x – 5 < –17 or 5x + 6 > 31
a. x < –3 or x > 5
–8 –6 –4 –2
0
c.
2
4
6
x < –3 or x > 7
2
5
8
–8 –6 –4 –2
b.
d.
1
2
x < −5 or x > 7
2
5
–8 –6 –4 –2
0
2
4
6
0
2
4
6
8
0
2
4
6
8
1
x < −5 or x > 5
2
8
–8 –6 –4 –2
____ 23.
a.
c.
–8 –6 –4 –2
0
2
4
6
8
b.
–8 –6 –4 –2
0
2
4
6
8
–8 –6 –4 –2
0
2
4
6
8
d.
–8 –6 –4 –2
0
2
4
6
8
Solve the inequality. Graph the solution.
____ 24.
a.
c.
–40 –30 –20 –10 0
10 20 30 40
b.
–20 –15 –10 –5
0
5
10 15 20
–20 –15 –10 –5
0
5
10 15 20
d.
–20 –15 –10 –5
0
5
10 15 20
____ 25.
a. –18 > x > 8
–20 –15 –10 –5
c. –36 < x < 16
0
5
10 15 20
b. –18 < x < 8
–20 –15 –10 –5
–40 –30 –20 –10 0
10 20 30 40
–20 –15 –10 –5
5
d.
0
5
10 15 20
Short Answer
26. Name the property used in each step of simplification.
0
10 15 20
Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the domain and range of the relation and determine whether it is a function.
y
4
2
–4
O
–2
2
4
x
–2
–4
____
a. Domain: all real numbers; range: all real numbers; yes, it is a function
b. Domain: x > 0; range: y > 0; yes, it is a function.
c. Domain: positive integers; range: positive integers; no, it is not a function.
d. Domain: x ≥ 0; range: y ≤ 0; no, it is not a function.
2. Use the vertical-line test to determine which graph represents a function.
y
y
a.
c.
–4
–2
4
4
2
2
O
x
–2
,
–4
–2
O
–2
–4
–4
d.
y
–4
3. For
4
–2
b.
____
2
4
2
2
2
4
x
–4
–2
O
–2
–2
–4
–4
.
4
x
2
4
x
y
4
O
2
Algebra 2 ---- 1st Semester Final Exam Review
____
a. –19
4. Suppose
b. 1
and
Find the value of
.
a.
b.
1
5
9
2
c. –21
d. 21
c. −2
d. 2
.
4
7
Find the slope of the line through the pair of points.
____
1
1 1
5. (− , 0) and (− , − )
3
2 2
a. −3
b.
c.
1
3
−
1
3
d. 3
Write in standard form an equation of the line passing through the given point with the given slope.
____
____
6. slope = –8; (–2, –2)
a. 8x + y = –18
b. –8x + y = –18
c. 8x – y = –18
d. 8x + y = 18
7. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).
a.
c.
1
1
y + 4 = (x – 2)
y + 5 = − (x + 6)
8
8
b.
d.
1
1
y + 4 = − (x + 6)
y + 4 = (x + 6)
8
8
Find the slope of the line.
____
8.
a.
−
b.
5
3
c.
5
3
−
3
5
d.
3
5
Find the slope of the line.
____
9.
y
4
2
–4
–2
O
2
4
x
–2
–4
a. undefined
____ 10. x = a
a. a
b. 2
c. 1
d. 0
b. 0
c. undefined
d. 1
Algebra 2 ---- 1st Semester Final Exam Review
Find an equation for the line:
5
____ 11. through (2, 6) and perpendicular to y = − x + 1.
4
a.
b.
c.
5
7
4
38
y= x+
y=− x+
y=
4
2
5
5
____ 12. through (–4, 6) and parallel to y = −3x + 4.
a. y = −3x − 6
b. y = 3x + 18
c.
y=
4
22
x+
5
5
d.
5
17
y=− x+
4
2
1
22
x+
3
3
d.
1
14
y=− x+
3
3
Determine whether y varies directly with x. If so, find the constant of variation k and write the
equation.
____ 13.
x
y
6
24
18
72
54
216
162
648
a. yes; k = 4; y =4x
b. yes; k = 3; y =3x
c. yes; k = 6; y =6x
d. no
Determine whether y varies directly with x. If so, find the constant of variation k.
____ 14. –6y = –5x
a.
5
yes;
6
b.
yes;
6
5
c. yes; –5
d. no
____ 15. A leaky valve on the water meter overcharges the residents for one gallon of water in every
months. The
overcharged amount w varies directly with time t.
a. Find the equation that models this direct variation.
b. How many months it will take for the residents to be overcharged for 8 gallons of water?
a.
b.
; 20 months
; 20 months
c.
d.
;
months
;
months
____ 16. A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a
function of distance d.
a. c = 0.80d + 1.20
c. d = 0.60c + 1.80
b. c = 1.00d + 1.80
d. c = 0.60d + 1.20
____ 17. What is the vertex of the function
?
a.
b. 2
c. 2
d.
2
2
(− , –4)
( , –4)
( , 4)
(− , 4)
3
3
3
3
Algebra 2 ---- 1st Semester Final Exam Review
____ 18. Write two linear equations you can use to graph
a.
c.
b.
.
d.
____ 19. Write an equation for the horizontal translation of
.
y
8
4
–8
–4
O
4
8
x
–4
–8
a.
b.
c.
____ 20. Write the equation that is the translation of
a.
b.
d.
left 1 unit and up 2 units.
c.
d.
Short Answer
21. An electronics store makes a profit of $20 for every portable DVD player sold and $45 for every DVD
recorder sold. The manager’s target is to make at least $180 a day on sales of the portable DVD players and
DVD recorders. Write and graph an inequality that represents the number of both kinds of DVD players that
can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r
represent the number of DVD recorders.
22. Graph the equation
.
23. Graph the absolute value inequality y < |x + 2| – 2
24. Graph the absolute value equation
25. Graph the absolute value equation
26. Graph the inequality 4x – 2y < –3
27. Graph the function
.
28. A new candle is 8 inches tall and burns at a rate of 2 inches per hour.
a. Write an equation that models the height h after t hours.
b. Sketch the graph of the equation.
29. Graph the equation
by finding the intercepts.
Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 3
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
A
Month
Jan
Feb
Mar
Apr
May
1
2
3
4
5
6
a.
b.
B
Revenue
4000
9000
13,000
16,000
21,000
C
Expenses
22,000
24,000
25,000
27,000
30,000
The spreadsheet shows the monthly revenue and expenses for a new business. Use your
graphing calculator to find a linear model for monthly revenue and a linear model for
monthly expenses.
Use the models to predict the month in which revenue will equal expenses.
a.
c.
a.
a.
b. October
b. August
b.
d.
a.
a.
b. September
b. September
Without graphing, classify each system as independent, dependent, or inconsistent.
____
____
____
2.
a. dependent
b. inconsistent
c. independent
a. independent
b. inconsistent
c. dependent
a. independent
b. inconsistent
c. dependent
3.
4.
Solve the system by the method of substitution.
____
5.
a. (0, –5)
b. (–5, 0)
c. (5, 1)
d. (1, 5)
Algebra 2 ---- 1st Semester Final Exam Review
Solve the system by the method of substitution.
____
____
6.
a. (–1, –6, –1)
b. (1, –6, 1)
c. (–1, –6, 1)
d. (–1, 6, 1)
7. A group of 52 people attended a ball game. There were three times as many children as adults in the group.
Set up a system of equations that represents the numbers of adults and children who attended the game and
solve the system to find the number of children who were in the group.
a.
c.
; 39 adults; 25 children
; 25 adults; 39 children
b.
d.
; 39 adults, 13 children
; 13 adults, 39 children
Use the elimination method to solve the system.
____
8.
a. (0, –2)
____
b. (–2, 0)
c. (–2, 2)
d. (2, –2)
9.
a. (1, –3, 1)
b. (1, 3, 1)
c. (–1, 3, 1)
d. (1, 3, –1)
____ 10. Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the
maximum value?
a. maximum value at (5, 4); 32
b. maximum value at (0, 8); 16
c. maximum value at (9, 0); 27
d. maximum value at (0, 0); 0
Algebra 2 ---- 1st Semester Final Exam Review
____ 11. Given the system of constraints, name all vertices. Then find the maximum value of the given objective
function.
Maximum for
a. (0, 2), (2, 0), (4, 6); maximum value of –6
b. (0, 2), (2, 0), (6, 4); maximum value of 12
c. (0, 2), (2, 0), (4, 2); maximum value of 10
d. (0, 2), (2, 0), (4, 6); maximum value of 8
Solve the system using either method of substitution or elimination.
____ 12.
a. (–3, 6, –2)
b. (–3, 8, 0)
c. (–3, 6, –8)
d. no solution
____ 13.
a. no solution
b. (2, –5, –2)
Short Answer
Solve the system by graphing.
14.
15.
Solve the system of inequalities by graphing.
16.
17.
18.
c. (–2, –5, 2)
d. (2, 5, 2)
Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. State the dimensions of the matrix. Identify the indicated element.
a. 3 × 2, 0
b. 2 × 3, –7
2. How many elements are in an m × n matrix?
a. m + n
b.
c. 2 × 3, 4
d. 3 × 2, –7
c.
d. mn
Find the sum or difference.
____
____
____
3.
a.
c.
b.
d.
a.
c.
b.
d.
4.
5. Suppose A and B are 2 × 5 matrices. Which of the following are the dimensions of the matrix A + B?
a. 2 × 5
b. 10 × 10
c. 7 × 1
d. 7 × 7
Find the values of the variables.
____
6.
a. f = 4, k = 4, w = 11
b. f = 4, k = 4, w = 11 or –11
c. f = 4, k = –4, w = 11 or –11
d. f = 4, k = 4, w = 121 or –121
Algebra 2 ---- 1st Semester Final Exam Review
Solve the matrix equation.
____
____
7.
a.
c.
b.
d.
8.
a.
b.
c.
Find the product.
____
9.
a.
c.
b.
d. [12]
a.
c.
b.
d.
____ 10.
d.
Algebra 2 ---- 1st Semester Final Exam Review
____
11.Which of the following is the multiplicative inverse of the given matrix?
a.
b.
c.
d.
____ 12. Which of the following is the multiplicative inverse of the given matrix?
a.
c.
b.
d.
Evaluate the determinant of the matrix.
____ 13.
a. 17
b. 1
c. –1
d. –17
a. –24
b. 40
c. –32
d. –40
____ 14.
Determine whether the matrix has an inverse. If an inverse exists, find it.
____ 15.
a.
c. does not exist
b.
d.
Algebra 2 ---- 1st Semester Final Exam Review
Determine whether the matrix has an inverse. If an inverse exists, find it.
____ 16.
a.
c. does not exist
b.
d.
____ 17. Write an augmented matrix to represent the system.
a.
c.
b.
d.
____ 18. Use an augmented matrix to solve the system
a.
____
19.
b. no solution
.
c.
d.
Use Cramer’s Rule to solve the system.
a.
b. no solution
____ 20. Use Cramer’s Rule to solve the system.
a. (3, 5, 4)
b. (3, –5, –4)
c.
d.
.
c. (–2, –25, 10)
d. (–3, –5, –4)
Algebra 2 ---- 1st Semester Final Exam Review
Solve the system.
____ 21. Use an augmented matrix:
a. (7, 13, –13)
b. (–4, –1, 3)
c. (–4, 1, –3)
d. (4, 1, –3)
____ 22. Use an augmented matrix:
a. no unique solution
b. (2, 0, –5)
c. (2, 1, 5)
d. (–2, 0, –5)
Algebra 2 ---- 1st Semester Final Exam Review
Chapter 5 Review Questions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Consider the quadratic function
of symmetry.
a. The y-intercept is –2.
. Find the y-intercept and the equation of the axis
1
2
The equation of the axis of symmetry is x = − .
b.
1
2
The y-intercept is .
The equation of the axis of symmetry is x = 2.
c. The y-intercept is + 2.
1
2
The equation of the axis of symmetry is x = .
d.
1
2
The y-intercept is − .
The equation of the axis of symmetry is x = –2.
____ 2. Graph the quadratic function
f( x)
a.
–5
–4
–3
–2
.
f( x)
c.
6
6
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
6
7
8
9
10
11 x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
1
2
3
4
5
6
7
8
9
10
11 x
Algebra 2 ---- 1st Semester Final Exam Review
f( x)
b.
–5
–4
–3
–2
f( x)
d.
6
6
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
6
7
8
9
10
11 x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
1
2
3
4
5
6
7
8
9
10
11 x
Determine whether the given function has a maximum or a minimum value. Then, find the maximum
or minimum value of the function.
____
3.
a.
b.
c.
d.
The function has a maximum value. The maximum value of the function is 1.
The function has a maximum value. The maximum value of the function is 5.
The function has a minimum value. The minimum value of the function is 1.
The function has a minimum value. The minimum value of the function is 5.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers
between which the roots are located.
____
a.
4.
One c.
f( x)
–4
f( x)
6
6
4
4
2
2
–2
2
4
6
8
10
x
–4
–2
2
–2
–2
–4
–4
–6
–6
solution is between 3 and 4, while the other solution is
between 0 and 1.
4
6
8
10
solution is between –3 and 0, while the other solution
between –4 and –1.
Algebra 2 ---- 1st Semester Final Exam Review
b.
One d.
f( x)
–4
6
6
4
4
2
2
–2
2
4
6
8
10
x
–4
–6
–6
5.
c.
d.
6.
a.
{–4, − }
b.
{− , 2}
7
2
7
2
c. {–4, 7}
d. {2, 7}
Simplify.
____
____
2
–4
a.
b.
____
–2
–2
Solve the equation by factoring.
____
–4
–2
solution is between –3 and –1, while the other solution is
between 0 and –4.
____
f( x)
7.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
a.
c.
8.
9.
____ 10.
____ 11.
4
6
8
10
solution is between –3 and –4, while the other solutio
between 0 and –1.
Algebra 2 ---- 1st Semester Final Exam Review
b.
d.
Solve the equation by completing the square.
____ 12.
a.
b.
c.
d.
a.
b.
c.
d.
____ 13.
Find the exact solution of the following quadratic equation by using the Quadratic Formula.
____ 14.
a.
c.
b.
d.
Find the value of the discriminant. Then describe the number and type of roots for the equation.
____ 15.
a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect
square, the two roots are real and rational.
b. The discriminant is –204. Because the discriminant is less than 0, the two roots are
complex.
c. The discriminant is 204. Because the discriminant is greater than 0 and is not a
perfect square, the two roots are real and irrational.
d. The discriminant is –188. Because the discriminant is less than 0, the two roots are
complex.
____ 16.
a. The discriminant is –29.
Because the discriminant is less than 0, the two roots are complex.
b. The discriminant is 1.
Because the discriminant is greater than 0 and is a perfect square, the two roots are
real and rational.
c. The discriminant is –27.
Because the discriminant is less than 0, the two roots are complex.
d. The discriminant is 27.
Because the discriminant is greater than 0 and is a perfect square, the two roots are
real and rational.
Write the following quadratic function in vertex form. Then, identify the axis of symmetry.
____ 17.
Algebra 2 ---- 1st Semester Final Exam Review
a. The vertex form of the function is
The equation of the axis of symmetry is
b. The vertex form of the function is
The equation of the axis of symmetry is
c. The vertex form of the function is
The equation of the axis of symmetry is
d. The vertex form of the function is
The equation of the axis of symmetry is
.
.
.
.
____ 18.
a. The vertex form of the function is
.
The equation of the axis of symmetry is
.
b. The vertex form of the function is
.
The equation of the axis of symmetry is
.
c. The vertex form of the function is
.
The equation of the axis of symmetry is
.
d. The vertex form of the function is
.
The equation of the axis of symmetry is
.
____ 19. Write an equation for the parabola whose vertex is at
and which passes through
a.
c.
b.
d.
.
Short Answer
where
25. The path of the water from a sprinkler is modeled by a quadratic function
h(d) is the height of water, in feet, at a distance of d feet from the jet. Find how far from the sprinkler
the water hits the ground.
26. The height of a pebble dropped from a cliff 604 feet high is described by the formula
. How long will the pebble take to reach a height of 348 feet?
27. A rectangular frame has length
is the value of ?
units and width
units. If the area is 7 square units, what
28. The volume of a box is 400 cubic meters. If the width of the box is 2 meters and its length is 10
meters more than its height, find the length and height of the box.
29. The window of a building is in the shape of a parabola that can be modeled by the equation
where h(w) is the height of the window and w is the width in feet. Find the width of
the window at a height of 8 feet.
30. The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation.
The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff.
The rocket touches the ground at a horizontal distance of 9 feet from the cliff. Determine a quadratic
function that models the height h(d) of the rocket at any given distance d feet from the cliff.
31. The figure below shows the trajectory followed by a tennis ball on the first volley. Assuming that the
ball was served at the origin, write an equation of the parabola that models the trajectory of the ball.
Algebra 2 ---- 1st Semester Final Exam Review
Algebra 2 ---- 1st Semester Final Exam Review
Algebra 2 ---- 1st Semester Final Exam Review
Chapter 1
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
A
A
C
B
B
D
B
D
B
B
C
C
B
D
A
D
A
B
C
A
A
A
B
C
B
SHORT ANSWER
26.
Distributive Property
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Definition of Addition
Commutative Property of Multiplication
Commutative Property of Addition
Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 2
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B
C
A
B
D
A
B
C
D
C
C
A
A
A
A
D
B
C
B
B
SHORT ANSWER
20p + 45r ≥ 180
21.
22.
y
r
4
6
2
4
–4
–2
O
2
4
–2
2
–4
0
2
4
23.
6
p
24.
y
y
16
6
12
3
8
–6
–3
O
3
6
x
4
–3
–6
–8
–4
O
–4
4
8
x
x
Algebra 2 ---- 1st Semester Final Exam Review
25.
26.
4
y
y
6
–8
O
–4
4
8
x
4
–4
2
–8
–6
–4
–2 O
–2
2
4
6
x
–12
–4
–16
–6
27.
y
6
3
–6
–3
O
3
6
x
–3
–6
28.
29.
t
16
15
y
12
10
8
4
5
–4
0
5
10
15 h
O
–4
4
8
12
16 x
Algebra 2 ---- 1st Semester Final Exam Review
1st Semester Final Exam Review Chapter 3
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
SHORT ANSWER
14.
B
C
C
B
A
C
D
A
B
C
D
A
A
–4
15.
y
–2
y
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
(3, 1)
16.
x
No solutions
17.
18.
y
y
y
6
4
4
4
2
2
2
–4
–2
O
2
4
x
–6
–4
–2
O
2
–2
–2
1st Semester Final Exam Review Chapter 4
Answer Section
MULTIPLE CHOICE
D
D
B
A
A
B
B
B
D
10.
11.
12.
13.
14.
15.
16.
17.
18.
B
B
B
C
D
D
C
B
A
19.
20.
21.
22.
x
–4
–2
O
–4
–6
1.
2.
3.
4.
5.
6.
7.
8.
9.
6
–2
–4
–4
4
D
B
C
A
2
4
x
Algebra 2 ---- 1st Semester Final Exam Review
Chapter 5 Review Questions
Answer Section
MULTIPLE CHOICE
1. ANS: C
For the quadratic equation
symmetry is
, the y-intercept is c and the equation of axis of
.
Feedback
A
B
C
D
Did you check the signs?
Did you interchange the y-intercept and the x-coordinate of the vertex?
Correct!
Did you use the correct formulas for the y-intercept and the x-coordinate of the
vertex?
PTS: 1
DIF: Average
REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA: IL J 8B.2 | IL J 8B
TOP: Graph quadratic functions.
KEY: Quadratic Functions | Graph Quadratic Functions
2. ANS: B
First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting
coordinate pairs and connect the points with a smooth curve.
Feedback
A
B
C
D
Graph ordered pairs that satisfy the function.
Correct!
Did you plot the graph correctly?
When the coefficient of x2 is less than 0, the graphs opens down.
PTS: 1
DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA: IL J 8B.2 | IL J 8B
TOP: Graph quadratic functions.
KEY: Quadratic Functions | Graph Quadratic Functions
3. ANS: C
The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained
by the function.
Feedback
A
B
C
D
The coefficient of x2 is greater than zero.
The graph of this function opens up.
Correct!
What is the value of the y-coordinate of the vertex?
PTS:
OBJ:
NAT:
TOP:
KEY:
4. ANS:
1
DIF: Average
REF: Lesson 5-1
5-1.2 Find and interpret the maximum and minimum values of a quadratic function.
NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA: IL J 8B.4 | IL J 8B
Find and interpret the maximum and minimum values of a quadratic function.
Maximum Values | Minimum Values | Quadratic Functions
D
Algebra 2 ---- 1st Semester Final Exam Review
When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive
integers between which the roots are located.
Feedback
A
B
C
D
Is the coefficient of x2 less than zero?
Did you graph the function correctly?
When the coefficient of x2 is greater than 0, the graph opens up.
Correct!
PTS: 1
DIF: Advanced REF: Lesson 5-2
OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: IL J 8B.4 | IL J 8B
TOP: Estimate solutions of quadratic equations by graphing.
KEY: Quadratic Equations | Solve Quadratic Equations
5. ANS: B
, then either
,
, or both a and b are equal to zero.
For any real numbers a and b, if
Feedback
A
B
C
D
Did you use the Zero Product Property correctly?
Correct!
Did you verify the answer by substituting the values?
Did you factor the binomial correctly?
PTS: 1
DIF: Average
REF: Lesson 5-3
OBJ: 5-3.2 Solve quadratic equations by factoring.
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA
2
STA: IL J 8D
TOP: Solve quadratic equations by factoring.
KEY: Quadratic Equations | Solve Quadratic Equations | Factoring
6. ANS: B
For any real numbers a and b, if
, then either
,
, or both a and b are equal to zero.
Feedback
A
B
C
D
Did you use the Zero Product Property correctly?
Correct!
Did you factor the binomial correctly?
Did you verify the answer by substituting the values?
PTS: 1
DIF: Average
REF: Lesson 5-3
OBJ: 5-3.2 Solve quadratic equations by factoring.
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA
2
STA: IL J 8D
TOP: Solve quadratic equations by factoring.
KEY: Quadratic Equations | Solve Quadratic Equations | Factoring
7. ANS: C
Multiply the real numbers and imaginary numbers separately.
Feedback
A
B
C
D
Check your calculation.
Check the sign.
Correct!
Multiply the imaginary numbers again.
Algebra 2 ---- 1st Semester Final Exam Review
PTS: 1
DIF: Average
REF: Lesson 5-4
OBJ: 5-4.2 Perform operations with pure imaginary numbers.
NAT: NA 1 | NA 3 | NA 7 | NA
10 | NA 2
STA: IL J 6B.1 | IL J 6B
TOP: Perform operations with pure imaginary numbers.
KEY: Imaginary Numbers
8. ANS: A
Multiply the real numbers and imaginary numbers separately.
Feedback
A
B
C
D
Check your calculation.
Check the sign.
Correct!
Compute again.
PTS: 1
DIF: Average
REF: Lesson 5-4
OBJ: 5-4.2 Perform operations with pure imaginary numbers.
NAT: NA 1 | NA 3 | NA 7 | NA
10 | NA 2
STA: IL J 6B.1 | IL J 6B
TOP: Perform operations with pure imaginary numbers.
KEY: Imaginary Numbers
9. ANS: A
Combine the real and imaginary parts of the complex numbers to add them.
Feedback
A
B
C
D
Correct!
Combine the real parts and then combine the imaginary parts.
Add the real and imaginary parts of the two numbers separately.
Did you combine the similar terms correctly?
PTS: 1
DIF: Average
REF: Lesson 5-4
OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: IL J 6B.3 | IL J 6B.7 | IL J
6B
TOP: Perform addition and subtraction operations with complex numbers.
KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers
10. ANS: B
. Combine the
Use the FOIL method to multiply the complex numbers and use the formula
real parts and then the imaginary parts of the two numbers.
Feedback
A
B
C
D
Did you combine the real parts?
Correct!
Use the value of i2.
Did you use the FOIL method to find the product?
PTS: 1
DIF: Average
REF: Lesson 5-4
OBJ: 5-4.4 Perform multiplication operations with complex numbers.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: IL J 6B.3 | IL J 6B.7 | IL J
6B
Algebra 2 ---- 1st Semester Final Exam Review
TOP: Perform multiplication operations with complex numbers.
KEY: Complex Numbers | Multiply Complex Numbers
11. ANS: D
Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the
FOIL method and the difference of squares to simplify the given expression.
Feedback
A
B
C
D
Multiply the numerator with the conjugate of the denominator.
Have you multiplied the constant in the numerator with its conjugate of the
denominator?
Did you multiply the conjugates correctly in the denominator?
Correct!
PTS: 1
DIF: Average
REF: Lesson 5-4
OBJ: 5-4.5 Perform division operations with complex numbers.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
6B
TOP: Perform division operations with complex numbers.
KEY: Complex Numbers | Divide Complex Numbers
12. ANS: A
To complete the square for any quadratic expression of the form
.
the result. Then, add the result to
STA: IL J 6B.3 | IL J 6B.7 | IL J
, find half of b, and square
Feedback
A
B
C
D
Correct!
Did you make the quadratic expression a perfect square?
Did you verify the answer by substituting the values?
Did you check the signs of the roots?
PTS: 1
DIF: Average
REF: Lesson 5-5
OBJ: 5-5.2 Solve quadratic equations by completing the square.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: IL J 8D
TOP: Solve quadratic equations by completing the square.
KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square
13. ANS: D
To complete the square for any quadratic expression of the form
, find half of b, and square
the result. Then, add the result to
.
Feedback
A
B
C
D
Did you make the quadratic expression a perfect square?
Did you check the signs of the roots?
Find both the solutions.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
REF: Lesson 5-5
5-5.2 Solve quadratic equations by completing the square.
NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: IL J 8D
Solve quadratic equations by completing the square.
Quadratic Equations | Solve Quadratic Equations | Completing the Square
Algebra 2 ---- 1st Semester Final Exam Review
14. ANS: D
The solution of a quadratic equation of the form
the formula
, where
, is obtained by using
.
Feedback
A
B
C
D
Did you substitute the values of a, b, and c correctly in the formula?
Did you evaluate the discriminant correctly?
Did you use the correct formula?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
15. ANS:
If
If
1
DIF: Average
REF: Lesson 5-6
5-6.1 Solve quadratic equations by using the Quadratic Formula.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA:
IL J 8D
Solve quadratic equations by using the Quadratic Formula.
Quadratic Equations | Solve Quadratic Equations | Quadratic Formula
C
and
is a perfect square, then the roots are rational.
and
is not a perfect square, then the roots are real and irrational.
Feedback
A
B
C
D
Did you use the correct formula for the discriminant?
Did you check the sign of the answer?
Correct!
Did you use the correct order of operations while evaluating the discriminant?
PTS:
OBJ:
NAT:
TOP:
KEY:
16. ANS:
If
1
DIF: Basic
REF: Lesson 5-6
5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA:
IL J 8D
Use the discriminant to determine the number and types of roots of a quadratic equation.
Quadratic Equations | Roots of Quadratic Equations | Discriminates
C
, then the roots are complex.
Feedback
A
B
C
D
Did you use the correct order of operations while evaluating the discriminant?
Did you use the correct formula for the discriminant?
Correct!
Did you check the sign of the answer?
PTS: 1
DIF: Basic
REF: Lesson 5-6
OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
STA:
IL J 8D
TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.
KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates
17. ANS: A
The vertex form of a quadratic function is
.
.
The equation of the axis of symmetry of a parabola is
Algebra 2 ---- 1st Semester Final Exam Review
Feedback
A
B
C
D
Correct!
Did you check the x-coordinate of the vertex?
Did you identify the coordinates of the vertex correctly?
Did you use the correct equation of the axis of symmetry of a parabola?
PTS: 1
DIF: Basic
REF: Lesson 5-7
OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.
NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6
STA: IL J 8B.4 | IL J 8B
TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.
KEY: Quadratic Functions | Axis of Symmetry
18. ANS: C
The vertex form of a quadratic function is
.
The equation of the axis of symmetry of a parabola is
.
Feedback
A
B
C
D
Did you use the correct equation of the axis of symmetry?
Did you check the x-coordinate of the vertex?
Correct!
Did you identify the coordinates of the vertex correctly?
PTS: 1
DIF: Basic
REF: Lesson 5-7
OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.
NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6
STA: IL J 8B.4 | IL J 8B
TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.
KEY: Quadratic Functions | Axis of Symmetry
19. ANS: C
If the vertex and another point on the graph of a parabola are known, the equation of the parabola
can be written in vertex form.
Feedback
A
B
C
D
Did you substitute correctly in the vertex form of the equation?
Did you find the correct coefficient values?
Correct!
Did you check the signs of the coefficients?
PTS:
OBJ:
NAT:
TOP:
KEY:
20. ANS:
If
1
DIF: Average
REF: Lesson 5-7
5-7.2 Write a quadratic function in the form y = a(x - h)^2 + k.
NA 2 | NA 7 | NA 8 | NA 10 | NA 6
STA: IL J 8B
Write a quadratic function in the form y = a(x – h)^2 + k.
Quadratic Functions
B
are the coordinates of a point on a circle,
is the center, and r is the radius, then the
equation of this circle is
.
Feedback
A
Did you subtract the y-coordinate of the center from y?
Algebra 2 ---- 1st Semester Final Exam Review
B
C
D
Correct!
Take the square of the radius on the right side of the equation.
Did you subtract the x-coordinate of the center from x?
PTS: 1
DIF: Average
REF: Lesson 10-3 OBJ: 10-3.1 Write equations of
circles.
NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 8B.9 | IL J 8B
TOP: Write equations of circles.
KEY: Circles | Equations of Circles
21. ANS: A
If
is the equation of a circle in standard form, then
circle and r is the radius.
is the center of the
Feedback
A
B
C
D
Correct!
Did you calculate the radius correctly?
The y-coordinate of the center of the circle is incorrect.
How do you determine the coordinates of the center of a circle?
PTS:
NAT:
TOP:
22. ANS:
1
DIF: Advanced REF: Lesson 10-3 OBJ: 10-3.2 Graph circles.
NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 8B.5 | IL J 8B
Graph circles.
KEY:
Circles | Graph Circles
C
If
is the equation of a circle in standard form, then
circle and r is the radius.
is the center of the
Feedback
A
B
C
D
How do you determine the coordinates of the center?
The y-coordinate of the center of the circle is incorrect.
Correct!
Did you calculate the radius correctly?
PTS:
NAT:
TOP:
23. ANS:
1
DIF: Advanced REF: Lesson 10-3 OBJ: 10-3.2 Graph circles.
NA 2 | NA 6 | NA 9 | NA 10 | NA 3
STA: IL J 8B.5 | IL J 8B
Graph circles.
KEY:
Circles | Graph Circles
B
The equation of an ellipse is
, where
is the center of the ellipse, 2a is the
length of the major axis, and 2b is the length of the minor axis.
Feedback
A
B
C
D
Did you use the correct expression for the length of the two axes?
Correct!
The center of the ellipse is not at the origin.
Take the squares of the values of a and b for the ellipse.
PTS: 1
DIF: Advanced REF: Lesson 10-4 OBJ: 10-4.1 Write equations of
ellipses.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA: IL J 8B.9 | IL J 8B
Algebra 2 ---- 1st Semester Final Exam Review
TOP: Write equations of ellipses.
KEY: Ellipses | Equations of Ellipses
24. ANS: C
You can determine the type of conic section represented by the equation
, where
, by checking the relationship between A and C.
Feedback
A
B
C
D
The coefficients of neither x2 nor y2 is zero.
The coefficients of x2 and y2 are equal.
Correct!
The coefficients of x2 and y2 are equal and have the same signs.
PTS:
OBJ:
NA 3
STA:
KEY:
1
DIF: Basic
REF: Lesson 10-6
10-6.2 Identify conic sections from their equations. NAT: NA 2 | NA 6 | NA 9 | NA 10 |
IL J 8B.5 | IL J 8B
TOP: Identify conic sections from their equations.
Conic Sections | Equations of Conic Sections | Identify Conic Sections
SHORT ANSWER
25. ANS:
3.6 ft
When the water hits the ground, its height will be zero. Replace h(d) by 0 in the given quadratic
function and solve for d.
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
26. ANS:
4s
Replace
REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems.
KEY: Solve multi-step problems.
in the given quadratic function and solve for t.
PTS: 1
DIF: Average
TOP: Solve multi-step problems.
27. ANS:
x=5
REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems.
KEY: Solve multi-step problems.
Solve the quadratic equation
PTS: 1
DIF: Average
REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems.
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
28. ANS:
Length is 20 meters and height is 10 meters.
Solve the quadratic equation
PTS: 1
DIF: Average
TOP: Solve multi-step problems.
29. ANS:
REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems.
KEY: Solve multi-step problems.
Algebra 2 ---- 1st Semester Final Exam Review
1.4 ft
Repalce
in the quadratic equation and solve for w.
PTS: 1
DIF: Advanced
TOP: Solve multi-step problems.
30. ANS:
REF: Lesson 5-5 OBJ: 5-5.3 Solve multi-step problems.
KEY: Solve multi-step problems.
Use the vertex form of the quadratic equation
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
31. ANS:
REF: Lesson 5-7 OBJ: 5-7.3 Solve multi-step problems.
KEY: Solve multi-step problems.
Find an equation of the parabola of the form
PTS: 1
DIF: Average
problems.
TOP: Solve multi-step problems.
to model the trajectory of the rocket.
with vertex
and focus
REF: Lesson 10-2 OBJ: 10-2.3 Solve multi-step
KEY: Solve multi-step problems.
Algebra 2 ---- 1st Semester Final Exam Review