MATH 2201 MIDTERM REVIEW WORKSHEET
FORMULAE
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐵 𝑠𝑖𝑛𝐶
=
=
𝑎
𝑏
𝑐
𝑎2 = 𝑏 2 + 𝑐 2 − 2𝑏𝑐𝑐𝑜𝑠𝐴
∑(𝑥 − 𝑥̅ )2
𝜎=√
𝑛
𝑐𝑜𝑠𝐴 =
𝑧=
𝑏 2 + 𝑐 2 − 𝑎2
2𝑏𝑐
𝑥−𝜇
𝜎
Chapter 3 – Acute Triangle Trigonometry
1.
Which represents the correct trigonometric equation for the diagram below?
17
x
sin 25 
(A)
25º
17
x
cos 25 
(B)
17
x
x
tan 25 
(C)
17
2.
Which triangle would require you to use the Law of Sines to determine the value of x?
(A)
(B)
35º
x
x
35º
40º
105º
7
105º
(C)
(D)
x
10
10
105º
3.
20
x
7
7
Determine the measure of  V to the nearest tenth of a degree.
V
15.1
8.9
T
4.
U
A ladder which is 6 m in length is resting against a house. The ladder makes an angle
of 20 with the ground. How far from the base of the house is the ladder touching
the ground?
1
5.
(A)
6.
6.95
(B)
59.09
(C) 1.74
(D) 57.59
x2 = 22 + 52 – 20cos 60º
Solve for x:
(A)
7.
x
20

sin 30 sin 10
Solve for x:
6.24
(B)
4.36
(C)
3.42
(D) 4.50
Which represents the appropriate equation to solve for x?
20 cm
55 cm
x
(A)
34 cm
552 = 202 + 342 – 2( 20 )( 34 )( cos x )
(B)
x2 = 202 + 342 – 2( 20 )( 34 )( cos 55° )
(C)
202 = 552 + 342 – 2( 55 )( 34 )( cos x )
(D)
342 = 552 + 202 – 2( 55 )( 20 )( cos x )
Chapter 4 - Radicals
8.
Evaluate:
(A)
–2
16  3  8
–4
(B)
(C) 2
(D)
(A)
4
9.
Express 2 3 3 as an entire radical.
10.
What is the perimeter of the given diagram in simplest radical form?
12
(B)
3
(C)
12
3
24
(D)
7
(A) 10 7 (C) 14 7
28
28
(B) 18 7 (D) 8 7
63
11.

Simplify:
(A) 5 – 2 6
12.
3 3
2

2
(B) 1 – 2 6
Rationalize the denominator:
(A)
13.
3 
(B)
6 3
(C) 5 + 2 6
(D) 1 + 2 6
6
3
(C)
2 3
(D)
3
Determine the width, w, of the given rectangle.
w
(A) 3 10
(B) 6 10
(C) 12 10
(D) 18 10
Area = 27 80
l= 9 2
2
24
14.
2
Simplify:
(A) 2 x 6  8 x
15.
16.
9x 2
Solve for x:
Solve for x:
(A) x = 1
18.
19.
(B)
3

(C) 2 x3  8x
(D) 2 x6  8x 2
(C)
3x 2
(D)
3x 4
4x   2
(B)
3
9x 4
x=2
(C) x = – 4
(D) x = 4
3x  6  3
(B)
x=2
2x  8   6
(A) x = 14
(B)
(A) x = 20
x
3x 2
Solve for x:
Solve for x:
x5  4
27 x 6
(A) x = – 2
17.

(B) 2 x3  8x 2
Simplify:
(A)
x
x = 22
(C) x = 3
(D)
x=7
(C) x = – 14
(D)
No solution
4 x  10  20
(B)
x = 10
(C) x = 35
(D) x = 15
Chapter 5 – Statistical Reasoning
20.
The heights of all students in a class were measured. It was later discovered that the tape
measure used was inaccurate and 5 mm had to be added to each person’s height. Which
calculation would stay the same based on the new height measures?
(A)
(B)
(C)
(D)
21.
Which set of data has the lowest standard deviation?
(A)
(B)
(C)
(D)
22.
central tendency
mean
median
standard deviation
{0.1 , 0.2 , 0.3 , 0.4 , 0.5}
{3.5 , 3.6 , 3.7 , 3.8 , 3.9}
{4 , 4 , 5 , 5 , 6}
{9 , 9 , 9 , 9 , 9}
A random survey of 100 teens reported that 28% of those surveyed exercise at least three
times per week. The results are considered accurate within ±4 percent, 19 times out of
20. If the sample size is increased, which statement is most accurate?
A) The margin of error will decrease
B) The margin of error will increase
C) The mean will decrease
D) The mean will increase
3
23.
The number of goals by all hockey players in the NHL is normally distributed. The mean
number of goals is 18 with a standard deviation of 4 goals. In what goal range would
68% of the players score?
A) 10 to 22
B) 10 to 26
C) 14 to 22
D) 14 to 26
24.
A study of income in a large city states the mean family income is $29 500. The study
states the results are accurate 9 times out of 10. What is the confidence level in this
situation?
A) 90%
B)
95%
C)
99%
D)
100%
Chapter 6 – Quadratic Functions
25.
For the graph, what are the x-intercepts of the
quadratic function?
1
A) 𝑥 = −3, 𝑥 = − 2
1
B) 𝑥 = −3, 𝑥 = 2
1
C) 𝑥 = 3, 𝑥 = − 2
1
D) 𝑥 = 3, 𝑥 = 2
26.
What is the 𝑦-intercept of 𝑦 = 3𝑥 2 + 4𝑥 + 5?
A)
27.
2
B)
3
C)
4
D)
5
What is the vertex of 𝑦 = 2𝑥 2 − 12𝑥 + 14?
A) (−3, 38)
B) (−3, 68)
C) (3, −10)
D) (3, −4)
28.
A quadratic function has an x-intercept at (−7, 0) and an axis of symmetry at
𝑥 = −1. What is the other x-intercept?
A) (−13, 0)
B) (−4, 0)
C) (5, 0)
D) (9, 0)
29.
Which of the following quadratic functions would have the widest graph?
A) 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 1
B) 𝑓(𝑥) = −3𝑥 2 + 5𝑥 + 3
C) 𝑓(𝑥) =
2
3
𝑥 2 − 5𝑥 − 6
D) 𝑓(𝑥) = −2𝑥 2 − 2𝑥 + 7
4
30.
The function 𝑦 = 𝑥 2 + 6𝑥 + 1 has an axis of symmetry at 𝑥 = −3. Which graph
best models this function?
y
x
(A)
(-3, -8)
y
x
(B)
(-3, -26)
y
x
(C)
(-3, -8)
y
x
(-3, -26)
(D)
Questions
Chapter 3 – Acute Triangle Trigonometry
31.
Find the distance between the two police officers.
32.
A pulley is suspended from the ceiling by two chains. One chain 7 m in length forms an angle
of 62° with the ceiling. Determine the angle the second chain makes with the ceiling if it has a
length of 9 m. Include a diagram. (Hint: See page 135 in text if you need help with a diagram.)
5
33. Determine the measure of x.
34.
A ship passing an island establishes, by sonar, a distance of 7 km from the ship to one
end of the island and 9 km to the other end of the island. The angle formed at the ship,
from the sonar, is 84°. Determine the length of the island.
Chapter 4 - Radicals
35.
Perform the operations indicated and express the answer in simplest radical form.
1
48  4 28  75
(A) 2 63 
(B)
3 3  2 2 3 3  2 12
2

(C)
36.
2


20  3 45
4
Solve for x:
2
3x  9  5  11
(Verify your solution and state restrictions.)
6
37.
Tom installs lawn watering systems. The radius of sprayed water, r, in meters, can be
expressed as 𝑟 = √0.64𝐴 where A represents the area watered, in square meters. Tom
has set each sprayer to spray at a radius of 1.4 m. Determine the area of grass watered by
one sprayer, to the nearest tenth of a square meter.
Chapter 5 – Statistical Reasoning
38.
Determine the range, mean and median of the following test scores.
Chapter 1 Test Scores (out of 100)
90
84
77
66
89
84
77
65
86
82
75
65
86
81
72
61
84
79
70
56
39.
A)
The results of a math unit test are normally distributed with a mean score of
76 and a standard deviation of 7.
Draw and label the normal curve to represent this data.
B)
What percent of the students scored between 62 and 83?
40.
A)
The mean life of Brand A batteries is 160 hours with a standard deviation of
20 hours.
Determine the z-score of a battery that lasted 170 hours.
B)
Using z-scores, what percent of the batteries will last less than 170 hours?
7
41.
In a pre-election survey in St. John’s, 32% of those surveyed were undecided about their
choice for mayor. The survey is considered accurate within 8 percentage points, 99 times
out of 100. If there are 102 000 eligible voters in St. John’s, state the range of the
number of people who are undecided and the confidence level.
Range
Confidence Level
42.
Janine has 20 minutes to get to her after-school job. Despite her best efforts, she is
frequently late. Her employer says that unless she arrives to work on time
consistently, she will lose her job. She has recorded her travel times (in minutes) for
the past 7 shifts: 18, 20, 22, 27, 19, 23, 25. Over the next 7 shifts, she continues to
record her travel times: 20, 22, 19, 20, 23, 16, 25. Do you think Janine will lose her
job? Use standard deviation to justify your answer.
Chapter 6 – Quadratic Functions
43.
Given the function 𝑦 = −𝑥 2 − 4𝑥 + 5 , determine each of the following:
A) the axis of symmetry
B) the vertex
C) the y-intercept
D) sketch the graph (with at least 2 points other than the vertex)
E) domain and range
y
x
8