Practice Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which of the following numbers occurs in the sequence 50, 40, 30, 20, 10, . . .?
A –80
C –60
B –50
D –70
____
2. The common difference in the arithmetic sequence –6, –13, –20, –27, . . . is
A –7
C –14
B 13
D 7
6
____
3. The common difference in the arithmetic sequence
A 4
B 13
81
2 13 11 31 20
,
,
,
,
, . . . is
9 18 9 18 9
C 2
D
____
4. In the formula for the general term of an arithmetic sequence tn = –5 + (n – 1)  (–7.75), the common difference
is
A 2.75
C 38.75
B –7.75
D –5
____
5. What is the 8th term of the sequence –26, –19.2, –12.4, –5.6, 1.2, …?
A 21.6
C 35.2
B 6.8
D –73.6
____
6. The sum of the series (1) + (–1) + (–3) +
A –63
B 16
____
7. What is the reference angle for 260in standard position?
A 170
C 80
B 10
D 130
____
8. What are the three other angles in standard position that have a reference angle of 44?
A 88132176
C 136224316
B 134224314
D 89134224
____
9. Determine the length of x, to the nearest tenth of a centimetre.
+ (–15) is
C –270
D –126
x
80º
85º
29 cm
Diagram not drawn to scale.
A 28.7
B 29.1
C 14.6
D 29.3
____ 10. Which strategy would be best to use to solve for x?
x
13 cm
25 cm
18º
Diagram not drawn to scale.
A primary trigonometric ratios
B cosine law
____ 11. What is the axis of symmetry of
A x=4
B x=2
C sine law
D none of the above
?
C x = –5
D x = –2
____ 12. What is the quadratic function in vertex form for the parabola shown below?
y
11
10
9
8
7
6
5
4
3
2
1
–11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
A
B
____ 13. What is the vertex of
C
D
?
A (4, –3)
B (3, –4)
____ 14. What are the domain and range of
A Domain:
Range:
B Domain:
Range:
____ 15. Identify the characteristics of this graph.
C (–3, –4)
D (5, 4)
?
C Domain:
Range:
D Domain:
Range:
2
3
4
5
6
7
8
9
10
11
x
y
22
20
18
16
14
12
10
8
6
4
2
–22 –20 –18 –16 –14 –12 –10 –8
–6
–4
–2
–2
2
4
6
8
10
12
14
16
–4
–6
–8
–10
–12
–14
–16
–18
–20
–22
A vertex: (1, 10)
axis of symmetry:
y-intercept: 9.6
x-intercepts: –6 and 4
opens upward
B vertex: (10, 1)
axis of symmetry:
y-intercept: 9.6
x-intercepts: 6 and –4
opens downward
C vertex: (10, 1)
axis of symmetry:
y-intercept: 9.6
x-intercepts: 6 and –4
opens upward
D vertex: (1, 10)
axis of symmetry:
y-intercept: 9.6
x-intercepts: 6 and –4
opens downward
____ 16. What are the coordinates of the vertex of the quadratic function
A (–4, 2)
B (2, –4)
C (–8, 4)
D (8, –4)
____ 17. What are the x-intercepts of the quadratic function graphed here?
?
18
20
22
x
y
12
10
8
6
4
2
–6
–5
–4
–3
–2
–1
–2
1
2
3
4
5
6
x
–4
–6
–8
–10
–12
A –3 and 4
B 3 and –4
C 6.125
D 6
____ 18. What are the roots of the quadratic function
C 5 and –3
D 18
A 19.2
B –5 and 3
____ 19. Factor
completely.
A
B
C
D
____ 20. Factor
completely.
A
B
____ 21. Solve
C
D
.
A –6 + 29 and –6 29
B 6 + 29 and 6  29
____ 22. Determine the value of the expression
A 3 155
B 7
____ 23. Simplify
A 51
B 15 + 5 3
?
C
D
23
35
when
and
C 88 11
D
19
.
C 15 +
D
7
.
____ 24. Simplify
A 2+ 3
B
.
C 2 + 3 21
D –124
____ 25. Solve
A
144
x= 
5
B
12
x=
25
____ 26. Solve
A
1
x = 3
2
B
1
x = 12
4
C
144
25
D
12
x= 
5
x=
.
C
2
7
D
4
x=
49
x= 
____ 27. The non-permissible value(s) for the rational expressions
A x   x 
B x  5
is (are)
C x 
D x 
____ 28. When fully simplified, ignoring non-permissible values,
A
C
1
6
B 6
1
6
D 6
____ 29. Express the product
in simplest form.
A
C
B
D
____ 30. When fully simplified,
is equal to
A 24x
C
B
D
1
x
7
____ 31. Evaluate the expression
A 6.2
B 1.6
63
x
25
24
x
5
.
C 1.1
D –1.1
____ 32. Determine the value of the absolute value expression
A 27
is equal to
C –27
.
B –99
D 99
____ 33. Identify where on the number line
B
–14 –13 –12 –11 –10 –9
–8
is located.
C
–7
–6
–5
–4
D
–3
–2
–1
A D
B C
0
A
1
2
3
4
6
.
A
B
C
D
or
or
____ 35. The equation of the vertical asymptote for the reciprocal of y =
C
24
5
B
24
x=
5
x= 
D
x=
5
x + 3 is
8
5
24
x= 
5
24
____ 36. The approximate solutions to the system of equations shown below are
y
9
8
7
6
5
4
3
2
1
–9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
x
–2
–3
–4
–5
–6
–7
–8
–9
A
B
7
C A
D B
____ 34. Solve
A
5
and
and
C
D
and
and
8
9
10
11
12
13
14
x
____ 37. Find the coordinates of the point(s) of intersection of the line y = 4
and the quadratic function
.
A
C (2 , 34)
9
(0 , 8 ) and ( , 17)
4
B (0, 0)
D
9
( , 1 ) and (0 , 8 )
4
____ 38. What are the solutions for the following system of equations?
A
B
and
and
C
D
____ 39. The graph of
is
y
A
–5
–4
–3
–2
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–3
–2
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
y
–4
y
C
5
B
–5
and
and
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
2
3
4
5
x
1
2
3
4
5
x
y
D
5
–1
–1
1
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
____ 40. Which number line represents the solution set to the inequality
A
?
C
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
B
D
–5
–4
–3
–2
–1
0
1
2
3
4
–5
5
____ 41. The solution set to the inequality
A
–4
–3
–2
–1
0
1
2
3
4
5
is
C
B
D
____ 42. The solution to the inequality
is
y
A
–5
–4
–3
–2
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–3
–2
–4
–3
–2
–1
–1
–2
–3
–3
–4
–4
–5
–5
y
–4
–5
–2
B
–5
y
C
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
____ 43. Which point does not satisfy the inequality
2
3
4
5
x
1
2
3
4
5
x
y
D
5
–1
–1
1
?
y
11
10
9
8
7
6
5
4
3
2
1
–11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
11
x
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
A
B
C
D
____ 44. While flying, a helicopter pilot spots a water tower that is 7.4 km to the north. At the same time, he sees a
monument that is 8.5 km to the south. The tower and the monument are separated by a distance of 11.4 km
along the flat ground. What is the angle made by the water tower, helicopter, and monument?
7.4 km
11.4 km
8.5 km
Diagram not drawn to scale.
A 91°
C 40°
B 11°
D 48°
Short Answer
1. The starting wage at a bookstore is $8.50 per hour with a yearly increase of $0.75 per hour.
a) Write the general term of the sequence representing the hourly rate earned in each year.
b) Use your expression from part a) to determine the hourly rate after 6 years.
c) How many years will someone need to work at the store to earn $15.25 per hour?
For each arithmetic series, determine
a) an explicit formula for the general term
b) a formula for the general sum
c)
d)
2.
= 2, d = 3, n = 4
Determine the sum of each arithmetic series.
3.
4. The point A(–3, –5) is on the terminal arm of an angle . Determine exact expressions for the primary
trigonometric ratios for the angle.
5. Sketch the graph of the function
. Label the vertex.
y
18
16
14
12
10
8
6
4
2
–18 –16 –14 –12 –10 –8
–6
–4
–2
–2
2
4
6
8
10
12
14
16
18
x
–4
–6
–8
–10
–12
–14
–16
–18
6. A tennis ball follows a path described by the function h(d) =
(d – 12)2 + 2, where h is the height of the ball
above the court and d is the horizontal distance of the ball from the tennis player, both in metres. How high
above court level did the tennis player hit the ball?
7. Sketch the graph of the quadratic relation
. Label the x-intercepts and the vertex.
y
24
20
16
12
8
4
–24
–20
–16
–12
–8
–4
4
8
12
16
20
24
x
–4
–8
–12
–16
–20
–24
8. Express the quadratic function
9. Factor the quadratic
10. Solve the quadratic function
hundredth, if necessary.
in vertex form.
completely.
by completing the square. Round roots to the nearest
11. Use the quadratic formula to find the roots of the equation x2 + 4x – 21 = 0. Express your answers as exact roots.
12. Simplify each expression.
a)
b)
c)
d)
13. Rationalize the denominator in each expression. Express each answer in simplest form.
a)
b)
c)
Simplify each expression and state any non-permissible values.
14.
15.
Simplify each expression and state any non-permissible values.
16.
17. Solve the absolute value equation
graphically.
y
50
40
30
20
10
–9
–8
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
8
9 x
18. Graph each reciprocal function. For each graph, state the non-permissible values and the equation of the vertical
asymptote(s).
a)
b)
19. Solve the system graphically.
y
18
16
14
12
10
8
6
4
2
–9
–8
–7
–6
–5
–4
–3
–2
–1
–2
1
2
3
4
5
6
7
8
9
x
–4
–6
–8
–10
–12
–14
–16
–18
20. Solve the system of equations by elimination.
and
21. Solve the system of equations using substitution. State your answers to two decimal places.
and
22. Graph the quadratic inequality
.
y
9
8
7
6
5
4
3
2
1
–9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
x
–2
–3
–4
–5
–6
–7
–8
–9
23. Graph the inequality
.
y
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
1
–1
–2
–3
–4
–5
–6
–7
24. Solve and check.
2
3
4
5
6
7
x
Problem
1. A store can increase its profit by increasing the price of the sweaters it sells. The relation between the income, R,
and the dollar increase in the price per sweater, d, can be modelled by the equation
.
a) What is the maximum possible income?
b) What would the income be if the price per sweater were increased by $10?
2. A ball that is hit or thrown horizontally with a velocity of v metres per second will travel a distance d metres
before hitting the ground, where
and h is the height, in metres, from which the ball is hit or thrown.
a) Use the properties of radicals to rewrite the formula with a rational denominator.
b) How far will a ball that is hit with a velocity of 45 m/s at a height of 0.8 m above the ground travel before
hitting the ground, to the nearest tenth of a metre?
3. Gwen wants to buy some used CDs that cost $10 each and some used DVDs that cost $13. She has $40 to spend.
a) Write an inequality to represent the situation, where c is the number of CDs she buys and d is the number of
DVDs.
b) Graph the inequality.
c) Can she buy two CDs and three DVDs? Explain.
c
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
d
4. At the end of the second week after opening, a new fitness club has 870 members. At the end of the seventh
week, there are 1110 members. Suppose the increase is arithmetic.
a) How many members joined the club each week?
b) How many members were there in the first week?
5. In
, c = 11 cm, b = 7 cm, and
.
a) Sketch possible diagrams for this situation.
b) Determine the measure of C in each diagram.
c) Find the measure of A in each diagram.
d) Calculate the length of BC in each diagram.
6. When an object is dropped from the top of a building that is 50 ft tall, the object will be h feet above the ground
after t seconds, where
. How far above the ground will the object be after 1 s?
7. Sarah and Simone are walking in a walk-a-thon down a straight street that leads to the finish line. At the same
time, they both notice a tethered hot-air balloon directly over the finish line. Sarah sees that the angle from the
ground to the balloon as 30°, and Simone (who is 0.25 km closer to the finish line than Sarah) sees the angle
from the ground to the balloon as 45°.
a) Draw a diagram to represent this situation.
b) Let x represent the distance that Simone is from the finish line, and write an expression for the distance from
Sarah to the finish line.
c) Write a trigonometric ratio for each girl’s position that involves the height, h, of the balloon, the distance each
girl is away from the finish line, and the angle from the girl to the balloon.
d) Rearrange each equation from part c) to isolate h.
e) Set the two expressions for h equal to each other and solve for x, to the nearest hundredth of a kilometre.
f) Determine the height of the balloon, to the nearest hundredth of a kilometre.
8. A baseball batter hits an infield fly ball. The height, h, in metres, of the baseball after t seconds is approximately
modelled by the function h(t) = –5t2 + 4t + 1.
a) State the domain and range of the function.
b) What is the initial height of the ball?
c) How long does it take for the ball to hit the ground?
Practice Final Exam
Answer Section
MULTIPLE CHOICE
1. ANS:
NAT:
2. ANS:
NAT:
3. ANS:
NAT:
4. ANS:
NAT:
5. ANS:
NAT:
6. ANS:
NAT:
KEY:
7. ANS:
NAT:
8. ANS:
NAT:
9. ANS:
NAT:
10. ANS:
NAT:
11. ANS:
NAT:
KEY:
12. ANS:
NAT:
KEY:
13. ANS:
NAT:
KEY:
14. ANS:
NAT:
KEY:
15. ANS:
NAT:
KEY:
16. ANS:
NAT:
KEY:
17. ANS:
NAT:
KEY:
B
PTS: 1
DIF: Easy
OBJ: Section 1.1
RF 9
TOP: Arithmetic Sequences
KEY: nth term
A
PTS: 1
DIF: Easy
OBJ: Section 1.1
RF 9
TOP: Arithmetic Sequences
KEY: common difference
D
PTS: 1
DIF: Average
OBJ: Section 1.1
RF 9
TOP: Arithmetic Sequences
KEY: common difference | fraction
B
PTS: 1
DIF: Easy
OBJ: Section 1.1
RF 9
TOP: Arithmetic Sequences
KEY: common difference | general term
A
PTS: 1
DIF: Average
OBJ: Section 1.1
RF 9
TOP: Arithmetic Sequences
KEY: terms | arithmetic sequence
A
PTS: 1
DIF: Average
OBJ: Section 1.2
RF 9
TOP: Arithmetic Series
sum | number of terms | arithmetic series
C
PTS: 1
DIF: Easy
OBJ: Section 2.1
T1
TOP: Angles in Standard Position
KEY: reference angle | > 180°
C
PTS: 1
DIF: Average
OBJ: Section 2.1
T1
TOP: Angles in Standard Position
KEY: reference angle
D
PTS: 1
DIF: Easy
OBJ: Section 2.3
T3
TOP: The Sine Law
KEY: sine law | side length
B
PTS: 1
DIF: Easy
OBJ: Section 2.4
T3
TOP: The Cosine Law
KEY: cosine law | solution method
B
PTS: 1
DIF: Easy
OBJ: Section 3.1
RF 3
TOP: Investigating Quadratic Functions in Vertex Form
axis of symmetry
A
PTS: 1
DIF: Average
OBJ: Section 3.1
RF 3
TOP: Investigating Quadratic Functions in Vertex Form
vertex form
B
PTS: 1
DIF: Average
OBJ: Section 3.1
RF 3
TOP: Investigating Quadratic Functions in Vertex Form
vertex
B
PTS: 1
DIF: Average
OBJ: Section 3.1
RF 3
TOP: Investigating Quadratic Functions in Vertex Form
domain | range
D
PTS: 1
DIF: Average
OBJ: Section 3.2
RF 4
TOP: Investigating Quadratic Functions in Standard Form
vertex | axis of symmetry | y-intercept | x-intercept | direction of opening
B
PTS: 1
DIF: Average
OBJ: Section 3.2
RF 4
TOP: Investigating Quadratic Functions in Standard Form
vertex
B
PTS: 1
DIF: Average
OBJ: Section 4.1
RF 5
TOP: Graphical Solutions of Quadratic Equations
x-intercepts | two real roots
18. ANS:
NAT:
KEY:
19. ANS:
NAT:
20. ANS:
NAT:
21. ANS:
NAT:
KEY:
22. ANS:
NAT:
23. ANS:
NAT:
24. ANS:
NAT:
25. ANS:
NAT:
26. ANS:
NAT:
27. ANS:
NAT:
28. ANS:
NAT:
KEY:
29. ANS:
NAT:
KEY:
30. ANS:
NAT:
KEY:
31. ANS:
NAT:
32. ANS:
NAT:
33. ANS:
NAT:
34. ANS:
NAT:
35. ANS:
NAT:
36. ANS:
NAT:
KEY:
37. ANS:
NAT:
KEY:
38. ANS:
NAT:
B
PTS: 1
DIF: Average
OBJ: Section 4.1
RF 5
TOP: Graphical Solutions of Quadratic Equations
two real roots
C
PTS: 1
DIF: Easy
OBJ: Section 4.2
RF 5
TOP: Factoring Quadratic Equations
KEY: factor trinomial
B
PTS: 1
DIF: Average
OBJ: Section 4.2
RF 5
TOP: Factoring Quadratic Equations
KEY: factor trinomial
B
PTS: 1
DIF: Easy
OBJ: Section 4.3
RF 5
TOP: Solving Quadratic Equations by Completing the Square
square root
A
PTS: 1
DIF: Easy
OBJ: Section 5.1
AN 2
TOP: Working With Radicals
KEY: simplify radicals | substitution
D
PTS: 1
DIF: Average
OBJ: Section 5.1
AN 2
TOP: Working With Radicals
KEY: simplify radicals
B
PTS: 1
DIF: Average
OBJ: Section 5.1
AN 2
TOP: Working With Radicals
KEY: simplify radicals
A
PTS: 1
DIF: Easy
OBJ: Section 5.3
AN 3
TOP: Radical Equations
KEY: evaluate radical equation
A
PTS: 1
DIF: Average
OBJ: Section 5.3
AN 3
TOP: Radical Equations
KEY: two radicals
A
PTS: 1
DIF: Easy
OBJ: Section 6.1
AN 4
TOP: Rational Expressions
KEY: non-permissible values
A
PTS: 1
DIF: Easy
OBJ: Section 6.2
AN 5
TOP: Multiplying and Dividing Rational Expressions
multiplying rational expressions
C
PTS: 1
DIF: Average
OBJ: Section 6.2
AN 5
TOP: Multiplying and Dividing Rational Expressions
multiplying rational expressions
D
PTS: 1
DIF: Easy
OBJ: Section 6.3
AN 5
TOP: Adding and Subtracting Rational Expressions
adding rational expressions
C
PTS: 1
DIF: Easy
OBJ: Section 7.1
RF 2
TOP: Absolute Value
KEY: evaluating expressions
B
PTS: 1
DIF: Average
OBJ: Section 7.1
RF 2
TOP: Absolute Value
KEY: evaluating expressions
C
PTS: 1
DIF: Easy
OBJ: Section 7.1
RF 2
TOP: Absolute Value
KEY: number line
B
PTS: 1
DIF: Average
OBJ: Section 7.3
RF 2
TOP: Absolute Value Equations
KEY: linear | algebraic solution
A
PTS: 1
DIF: Easy
OBJ: Section 7.4
RF 11
TOP: Reciprocal Functions
KEY: vertical asymptote
D
PTS: 1
DIF: Easy
OBJ: Section 8.1
RF 6
TOP: Solving Systems of Equations Graphically
linear-quadratic systems | interpreting graphs
D
PTS: 1
DIF: Difficult
OBJ: Section 8.2
RF 6
TOP: Solving Systems of Equations Algebraically
linear-quadratic systems | points of intersection | algebraic solution
B
PTS: 1
DIF: Average
OBJ: Section 8.2
RF 6
TOP: Solving Systems of Equations Algebraically
KEY:
39. ANS:
NAT:
KEY:
40. ANS:
NAT:
KEY:
41. ANS:
NAT:
KEY:
42. ANS:
NAT:
KEY:
43. ANS:
NAT:
KEY:
44. ANS:
NAT:
linear-quadratic systems | algebraic solution
D
PTS: 1
DIF: Average
OBJ:
RF 7
TOP: Linear Inequalities in Two Variables
linear inequality | graphing
B
PTS: 1
DIF: Average
OBJ:
RF 7
TOP: Quadratic Inequalities in One Variable
quadratic inequality | one variable
A
PTS: 1
DIF: Average
OBJ:
RF 7
TOP: Quadratic Inequalities in One Variable
quadratic inequality | one variable | solution set
B
PTS: 1
DIF: Easy
OBJ:
RF 7
TOP: Quadratic Inequalities in Two Variables
quadratic inequality | two variables | graphing | a < 0
D
PTS: 1
DIF: Average
OBJ:
RF 7
TOP: Quadratic Inequalities in Two Variables
quadratic inequality | two variables | test point
A
PTS: 1
DIF: Average
OBJ:
T3
TOP: The Cosine Law
KEY:
Section 9.1
Section 9.2
Section 9.2
Section 9.3
Section 9.3
Section 2.4
cosine law | angle measure
SHORT ANSWER
1. ANS:
a)
b)
The hourly rate after 6 years is $12.25.
c)
You would need to work at the bookstore for 10 years to earn $15.25 per hour.
PTS: 1
DIF: Average
TOP: Arithmetic Sequences
2. ANS:
a)
OBJ: Section 1.1
NAT: RF 9
KEY: explicit formula | terms
b)
c)
d)
PTS: 1
DIF: Easy
TOP: Arithmetic Series
3. ANS:
OBJ: Section 1.2
NAT: RF 9
KEY: explicit formula | sum | terms | arithmetic series
PTS: 1
DIF: Easy
OBJ: Section 1.2
NAT: RF 9
TOP: Arithmetic Series
KEY: sum | arithmetic series
4. ANS:
The angle is in the third quadrant, so only the tangent ratio will be positive.
From the given point, x = –3 and y = –5.
Therefore,
.
PTS: 1
DIF: Average
OBJ: Section 2.2
TOP: Trigonometric Ratios of Any Angle
KEY: primary trigonometric ratios | point on terminal arm
5. ANS:
NAT: T 2
y
18
16
14
12
10
8 (–1, 8)
6
4
2
–18 –16 –14 –12 –10 –8
–6
–4
–2
–2
2
4
6
8
10
12
14
16
18
x
–4
–6
–8
–10
–12
–14
–16
–18
PTS: 1
DIF: Average
OBJ: Section 3.1
TOP: Investigating Quadratic Functions in Vertex Form
6. ANS:
The tennis player hit the ball when d = 0.
NAT: RF 3
KEY: vertex form | graph
The tennis player hit the ball 1 m above court level.
PTS: 1
DIF: Difficult
OBJ: Section 3.1
TOP: Investigating Quadratic Functions in Vertex Form
7. ANS:
NAT: RF 4
KEY: vertex form | intercept
y
24
20
16
12
8
4
(–4, 0)
–24
–20
–16
–12
–8
(1, 0)
–4
4
8
12
16
20
24
x
–4
(–1.5, –6.25)
–8
–12
–16
–20
–24
PTS: 1
DIF: Average
OBJ: Section 3.2
TOP: Investigating Quadratic Functions in Standard Form
KEY: standard form | graph | vertex | x-intercepts
8. ANS:
NAT: RF 4
PTS: 1
DIF: Average
OBJ: Section 3.3
NAT: RF 4
TOP: Completing the Square
KEY: standard to vertex form
9. ANS:
Let P =
so that the quadratic becomes
.
Factor the resulting expression:
PTS: 1
DIF: Difficult
OBJ: Section 4.2
NAT: RF 5
TOP: Factoring Quadratic Equations
KEY: polynomials of quadratic form
10. ANS:
To solve the equation, set it equal to 0 and solve for x.
PTS: 1
DIF: Average
OBJ: Section 4.3
TOP: Solving Quadratic Equations by Completing the Square
11. ANS:
PTS: 1
DIF: Easy
TOP: The Quadratic Formula
12. ANS:
a)
NAT: RF 5
KEY: completing the square
OBJ: Section 4.4
NAT: RF 5
KEY: quadratic formula
b)
c)
d)
PTS: 1
DIF: Easy
OBJ: Section 5.1 | Section 5.2
NAT: AN 2
TOP: Working With Radicals | Multiplying and Dividing Radical Expressions
KEY: simplify radicals
13. ANS:
a)
b)
c)
PTS: 1
DIF: Average
OBJ: Section 5.2
TOP: Multiplying and Dividing Radical Expressions
KEY: conjugates | rationalize the denominator
14. ANS:
NAT: AN 2
PTS: 1
DIF: Average
OBJ: Section 6.2
NAT: AN 5
TOP: Multiplying and Dividing Rational Expressions
KEY: simplifying rational expressions | non-permissible values | multiplying rational expressions
15. ANS:
PTS: 1
DIF: Difficult
OBJ: Section 6.2
NAT: AN 5
TOP: Multiplying and Dividing Rational Expressions
KEY: simplifying rational expressions | non-permissible values | multiplying rational expressions | dividing
rational expressions
16. ANS:
PTS: 1
DIF: Average
OBJ: Section 6.3
NAT: AN 5
TOP: Adding and Subtracting Rational Expressions
KEY: simplifying rational expressions | non-permissible values | adding rational expressions
17. ANS:
Graph the functions
and
on the same grid.
y
40
30
(–5, 25)
(8, 25)
20
10
–9
–8
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
The points of intersection of the two functions are
6
7
8
9 x
and
. Therefore, the solutions to the equation
are x = 5 and x = 8.
PTS: 1
DIF: Average
TOP: Absolute Value Equations
18. ANS:
OBJ: Section 7.3
NAT: RF 2
KEY: graphical solution | quadratic
a)
y
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
x
7
–1
–2
–3
–4
–5
–6
–7
The non-permissible value occurs when
or when
The equation of the vertical asymptote is
b)
.
.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
The non-permissible values occur when
The equations of the vertical asymptotes are
PTS: 1
DIF: Average
TOP: Reciprocal Functions
19. ANS:
or when
and
.
.
OBJ: Section 7.4
NAT: RF 11
KEY: linear | quadratic | vertical asymptote
y
18
16
14
12
10
8
6
4
2
(–4, 0)
–9
–8
–7
–6
–5
–4
–3
–2
–1
–2
1
2
3
4
5
6
7
8
9
x
–4
–6
–8
–10
–12
–14
–16
(0, –16)
–18
The solutions are (4, 0) and (0, 16).
PTS: 1
DIF: Easy
OBJ: Section 8.1
NAT: RF 6
TOP: Solving Systems of Equations Graphically
KEY: quadratic-quadratic systems | interpreting graphs | graphical solution
20. ANS:
Subtract the equations:
Solve for x:
Substitute x =  into either equation and solve for y:
The single solution is (0, 3).
PTS: 1
DIF: Easy
OBJ: Section 8.2
NAT: RF 6
TOP: Solving Systems of Equations Algebraically
KEY: quadratic-quadratic systems | algebraic solution | elimination
21. ANS:
Substitute
into the first equation:
Solve for x using the quadratic formula
and
Substitute these values into
:
and
The approximate solutions are (2.91, 32.13) and (0.57, 2.74).
PTS: 1
DIF: Difficult
OBJ: Section 8.2
NAT: RF 6
TOP: Solving Systems of Equations Algebraically
KEY: quadratic-quadratic systems | algebraic solution | substitution
22. ANS:
y
9
8
7
6
5
4
3
2
1
–9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
x
–2
–3
–4
–5
–6
–7
–8
–9
PTS: 1
DIF: Easy
OBJ: Section 9.3
TOP: Quadratic Inequalities in Two Variables
KEY: quadratic inequality | two variables | graphing
23. ANS:
Rearrange the inequality to make it easier to graph.
NAT: RF 7
y
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
x
–1
–2
–3
–4
–5
–6
–7
PTS: 1
DIF: Difficult
OBJ: Section 9.1
TOP: Linear Inequalities in Two Variables
KEY: linear inequality | graphing | two variables
24. ANS:
NAT: RF 7
and
Check:
and
L.S. = R.S
PTS: 1
DIF: Average
TOP: Rational Equations
OBJ: Section 6.4
NAT: AN 6
KEY: solving an equation
PROBLEM
1. ANS:
a) The maximum profit occurs at the vertex (3.5, 4500) or $4500.
b) Substitute d = 10 into the equation:
The income would be $2387.50.
PTS: 1
DIF: Average
OBJ: Section 3.1
TOP: Investigating Quadratic Functions in Vertex Form
2. ANS:
a)
NAT: RF 3
KEY: vertex form | vertex
b)
The ball will travel approximately 18.2 m before hitting the ground.
PTS: 1
DIF: Average
OBJ: Section 5.2 | Section 5.3
NAT: AN 2 | AN 3 TOP: Multiplying and Dividing Radical Expressions | Radical Equations
KEY: rationalize the denominator | solve radical equation
3. ANS:
a)
b) Rearrange the inequality:
5
c
4
3
2
(3, 2)
1
1
2
3
4
d
c) The coordinate pair (3, 2) is not within the shaded region of the solution, so she cannot purchase two CDs and
three DVDs
PTS: 1
DIF: Easy
OBJ: Section 9.1
NAT: RF 7
TOP: Linear Inequalities in Two Variables
KEY: linear inequality | two variables | graphing | interpreting graphs
4. ANS:
a)
Each week, 48 members joined the club.
b)
There were 822 members in the first week.
PTS: 1
DIF: Average
OBJ: Section 1.1
NAT: RF 9
TOP: Arithmetic Sequences
KEY: arithmetic sequence | explicit formula | terms
5. ANS:
a) This is the ambiguous case, so there are two triangles.
Triangle 1
Triangle 2
b) For triangle 1,
For triangle 2,
c) For triangle 1,
For triangle 2,
d) For triangle 1,
For triangle 2,
In triangle 1, the length of BC is 10.4 cm. In triangle 2, the length of BC is 6.9 cm.
PTS: 1
DIF: Average
TOP: The Sine Law
6. ANS:
Solve for h in the formula:
OBJ: Section 2.3
NAT: T 3
KEY: sine law | ambiguous case
Substitute t = 1:
After 1 s, the object will be 34 ft above the ground.
PTS: 1
DIF: Easy
TOP: Radical Equations
7. ANS:
a)
OBJ: Section 5.3
NAT: AN 3
KEY: solve radical equation
b) x + 0.25
c) Sarah:
Simone:
d) Sarah:
e)
Simone:
f)
The height of the balloon is 0.34 km.
PTS: 1
DIF: Average
OBJ: Section 2.1 | Section 2.2
NAT: T 1 | T 2
TOP: Angles in Standard Position | Trigonometric Ratios of Any Angle
KEY: primary trigonometric ratios | special angles
8. ANS:
a) Find the t-intercepts to determine the domain.
The t-intercepts are
and 1. Since
, the domain is
.
To find the range, write the equation in vertex form.
The parabola opens downward, so the maximum value is the h-coordinate of the vertex, or 1.8. Thus, the range
is
b) The initial height of the ball is the h-intercept, or 1 m.
c) The time it takes for the ball to hit the ground is the t-intercept that is greater than zero, or 1 s.
PTS: 1
DIF: Easy
OBJ: Section 3.2
TOP: Investigating Quadratic Functions in Standard Form
NAT: RF 4
KEY: domain | range | intercept