Mid-Term Review
Math 2200
Name:________
Chapter 2 Trigonometry
Part 1:
____ 1. What is the reference angle for 200 in standard position?
A 100°
B 70°
C 20°
D 110°
____ 2. If the point P(-3, 4) is on the terminal arm of Ѳ, find Ѳ.
A 53°
B 127°
C 233°
D 307°
____ 3. The point (40, –9) is on the terminal arm of  A. Which is the set of exact primary
trigonometric ratios for the angle?
A
,
C
,
,
B
,
D
,
,
,
,
____ 4. The coordinates of a point P on the terminal arm of an angle are shown.
What are the exact trigonometric ratios for
,
, and
?
y
A
Diagram not drawn to scale.
B

(–8,6)
x
C
D
____ 5. Determine the length of x, to the nearest tenth of a centimetre.
A 26.6
B 36.5
40º
x
C 11.2
D 17.1
70º
25 cm
Diagram not drawn to scale.
____ 6. If
, c = 10.3 cm, and b = 10.5 cm, and  ABC is acute,
what is the measure of
, to the nearest tenth of a degree?
A
c
A 57 
B 123.0 
C 30.5 
D 149.5 
B
b
a
C
Diagram not drawn to scale.
____7.Determine the measure of x, to the nearest tenth of a degree.
40 cm
x
A 25.6 
B 18.1 
C 136.3 
D 71.9 
18 cm
Diagram not drawn to scale.
____ 8. What is the length of x, to the nearest tenth of a metre?
A 27.7 m
B 21.8 m
C 26.1 m
D 37.6 m
25 cm
x
33 m
18 m
52º
Diagram not drawn to scale.
Math 2200 Mid-Term Review
2
____ 9. If
 , r = 20 cm, and p = 23 cm, what is the length
of q, to the nearest centimetre?
q
P
R
r
A 21 cm
B 30 cm
p
C 12 cm
D 11 cm
Q
Diagram not drawn to scale.
____10. Solve the following triangle, rounding side lengths to the
nearest tenth of a unit and angle measures to the nearest degree.
A
B
C
D
,
,
,
, c = 5.0
, c = 5.0
, c = 28.7
, c = 28.2
,
, b = 19, a = 23.5
X

____ 11. If Y  22 , WY  4.5 , and WY  WX ,
what is the length of XY in WXY ?
A 2.4
C 4.5
B 8.3
22 °
D 11.1
Y
4.5
W
Part 2:
12. The point ( – 3 , 4 ) lies on the terminal arm of an angle θ in standard position.
Determine the exact trigonometric ratios of sin θ, cos θ, tan θ.
13. Solve each of the following trigonometric equations for 0° ≤ θ < 360°.
(a)
sin θ =
1
2
(b)

cos θ =
3
2
G
14. George (G) and Henry (H) are getting ready
to walk to the store (S) and George is 7.3 km
away from the store. If  G = 62° and  H = 68°
H
then how far apart are George and Henry before
traveling to the store?
S
15. In ΔABC,  A = 36°, a = 20 cm and b = 27 cm. Solve the triangle by finding all the
missing sides and missing angles (to the nearest degree).
16. The point ( 2 , – 3 ) lies on the terminal arm of an angle θ in standard position.
Determine the exact trigonometric ratios of sin θ, cos θ, tan θ.
17. Solve the following trigonometric equation for 0° ≤ θ < 360°.
(a)
sin θ =

3
(b)
2
cos θ =
1
2
18. Determine the value of x in the following diagram.
D
11
C
36°
x
9
75°
A
30°
B
Math 2200 Mid-Term Review
3
19. Two ships leave a drilling platform at the same time traveling in different directions.
Both ships are traveling at a constant speed of 2 km/h and 3 km/h, respectively.
If after 4 hours the ships are 16 km apart, determine the angle formed by the
courses of the ships, to the nearest degree.
Answers: 1.C 2 B 3.D 4. C 5. B 6. A 7. B 8. C 9. C 10. A 11 B
4
3
4
12. sin θ =
cos θ =
tan θ =
13. (a) θ = 30° , 150° (b) θ = 150° , 210°
5
5
3
14. 6.03 km 15. Acute Triangle:  B = 53° ,  C = 91° , c = 34.02
Obtuse Triangle:  B = 127° ,  C = 17° , c = 9.95
3
16 sin θ =  3 cos θ = 2
tan θ =
17(a) θ = 240° , 300° (b) θ = 60° , 300°
2
13
13
18. x = 10.67
19. 104°
Chapter 3: Quadratic Functions
____ 1. What is the axis of symmetry of
A x=2
B x = –3
?
C x = –6
D x=6
y
____ 2. What is the quadratic function in vertex form for the
parabola shown to the right?
5
4
3
2
1
-3
A
B
-2
-1
C
D
____ 3. What is the vertex of
A (5, 4)
?
B (–4, 5)
C (–5, 4)
D (7, –4)
____ 4. Which graph represents the quadratic function
A
-1
-2
-3
-4
-5
-6
-7
-8
-9
- 10
?
C
y
y
12
12
10
10
8
8
6
6
4
4
2
2
–12 –10 –8 –6 –4 –2–2
2
4
6
8 10 12
–12 –10 –8 –6 –4 –2–2
x
2
4
6
8 10 12
x
–4
–4
–6
–6
–8
–8
–10
–10
–12
–12
B
D
y
y
12
12
10
10
8
8
6
6
4
4
2
2
–12 –10 –8 –6 –4 –2–2
–4
–6
–8
–10
–12
2
4
6
8 10 12
x
–12 –10 –8 –6 –4 –2–2
–4
–6
–8
–10
–12
2
4
6
8 10 12
x
1
2
3
4
x
Math 2200 Mid-Term Review
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____ 5. What are the domain and range of
?
A Domain:
Range:
C
B
D Domain:
Range:
Domain:
Range:
Domain:
Range:
____ 6. The vertex of a parabola is located at
. If the parabola has a y-intercept of 231, which
quadratic function represents the parabola?
A
C
B
D
____ 7. What information can be determined from the quadratic function
A
B
C
D
?
the vertex is at (–2, –9) and the graph opens upward
the vertex is at (–9, –2) and the graph opens downward
the vertex is at (–2, –9) and the graph opens downward
the vertex is at (–9, –2) and the graph opens upward
y
22
____ 8. Identify the characteristics of this graph.
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
18
20
22
x
–4
–6
–8
–10
–12
–14
–16
–18
–20
–22
A vertex: (–2, –5)
axis of symmetry:
y-intercept: 10.5
x-intercepts: –3 and –7
opens downward
C
B
D vertex: (–5, –2)
axis of symmetry:
y-intercept: 10.5
x-intercepts: 3 and 7
opens downward
vertex: (–5, –2)
axis of symmetry:
y-intercept: 10.5
x-intercepts: –3 and –7
opens upward
vertex: (–2, –5)
axis of symmetry:
y-intercept: 10.5
x-intercepts: –3 and –7
opens upward
____ 9. What are the coordinates of the vertex of the quadratic function
A (–6, –1)
B (8, –2)
C (–1, –6)
____10. What is the equation of the quadratic function
A
B
____11. State whether the function
coordinates of the vertex.
A maximum at
B maximum at
?
D (8, –6)
in vertex form?
C
D
has a maximum or minimum value and identify the
C minimum at
D minimum at
Math 2200 Mid-Term Review
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12. Determine the following information and sketch the graph of the given function.
1 2
x + 4x – 6
2
Direction of Opening, Vertex, Equation of the Axis of Symmetry,
Maximum or Minimum Value, X–intercepts, Y–Intercept, Domain, and Range
(a) y = 3( x + 2 )2 – 3
(b) y =
y
13. A ball is kicked from an initial height of
1 foot and follows a parabolic path as shown.
After 4 seconds the ball reaches a maximum
height of 33 feet.
(a) Determine the quadratic function that
models the path traveled by the ball.
(b)
Determine the height of the ball at 2 seconds.
1 ft
x
14. A farmers has a rectangular field that is divided into three regions of equal area.
The farmer decides to enclose the entire field, and regions, using 160 m of fencing.
(a) Determine the function which gives
the area of the entire region as a function
of its width, x, and use this function
to calculate the maximum possible area.
x
x
x
x
(b) What is the length and width
of the entire rectangular field?
(c) State the domain and the range of the
variables in the function.
fencing
15. A theatre seats 200 people per show and is currently sold out with a ticket price of $6. A survey
shows that for every $1 per ticket price increase, 20 fewer people will attend the show.
(a) Write a function to model the revenue generated from the show and use this
function to determine the maximum revenue the show can make.
(b) Determine the new ticket price that will result in the greatest revenue.
16. An orange grower has 400 crates of oranges ready for market and will have 20 more
crates available each day that shipment is delayed. The present price is $ 60 per
crate, however, for each day that shipment is delayed the price per crate
decreases by $ 2.
(a) Write a function to model the revenue generated from the sale of oranges
and determine the maximum revenue that can be generated.
(b) What will be the new price that will generate the maximum revenue?
29.ANS: Answers 1. C 2. B 3. C 4. B 5. B 6. B 7. A 8. B 9. C 10.D 11. D
12. (a) Up, ( – 2 , – 3 ), x = – 2 , Min. of – 3, x-int: -3 and -1, y-int: 9, Dom: xR, Range: y ≥ -3
(b) Down, ( 4 , 2 ), x = 4 , Max. of 2, x-int: 2 and 6, y-int: -6, Dom: xR, Range: y ≤ 2
13. (a) h(t) = –2( t - 4 )2 + 33 (b) 25 feet
14. (a) A(x) = –2x2 + 80x , Max. Area = 800 m2 (b) L = 40 m , W = 20 m
(c) Domain: 0 < x ≤ 40 , Range: 0 < y ≤ 800
15. (a) R = –20x2 + 80x + 1200 Max Revenue of $ 1280 when x = 2 (b) $ 8
16. (a) R = –40x2 + 400x + 24 000 Max Revenue of $ 25 000 when x = 5 (b) $ 50
Math 2200 Mid-Term Review
6
y
Chapter 4 Quadratic Equations
12
10
8
____ 1. How many x-intercepts does the graph of the quadratic
function
have?
6
4
2
–6
–5
–4
–3
–2
–1
–2
1
2
3
4
5
x
6
–4
–6
A unknown
B 2
C 1
D 0
–8
–10
–12
y
12
10
8
6
____ 2. What are the x-intercepts of the quadratic function shown?
A 2 and –4
C 11.2
B –2 and 4
D 12.6
4
2
–6
–5
–4
–3
–2
–1
–2
1
2
3
4
5
4
5
6
x
–4
–6
–8
–10
–12
y
12
____ 3. What are the x-intercepts of the quadratic function
graphed here?
10
8
6
4
2
A 4.6
C
B
D 9.0
there are none
–6
–2.2
–5
–4
–3
–2
–1
–2
–4
–6
–8
–10
–12
____ 4. What are the roots of the quadratic function
A –0.125
B 4 and 3
____ 5. Factor
?
C –4 and –3
D 6
completely.
A
B
C
D
____ 6. Factor −4𝑥 2 + 52𝑥 − 120 completely.
A
B
C
D
____ 7. Solve
.
A x = 18 and x = –3
B
C
x = –18 and x = 3
x=
9
3
and x = 
4
8
D x = –144 and x = 24
____ 8. Determine the roots of the quadratic equation
A x = –10 and x = –1
B
x = –50 and x = –5
____ 9. Solve
A
B
C
.
x = 10 and x = 1
D x = 2 and x = 1
5
.
and
and
C
D
and
and
1
2
3
6
x
Math 2200 Mid-Term Review
7
____10. A rectangle has dimensions
and
, where x is in centimetres. If the area of the
2
rectangle is 72 cm , what is the value of x, to the nearest tenth of a centimetre?
A x = 2.0
B x = –4.6
____11. The vertex form of
C x = 11.2
D x = -11.2
is
A
B
C
D
____12. Which is the vertex form of
necessary.
? Round coefficients to the nearest hundredth if
A
C
B
D
____13. Solve
.
A 1 + 43 and 1- 43
B –1 + 43 and –1 - 43
C
D
2 11
42
____14. A rectangle with an area of
is x centimetres wide and (x + 8) centimetres long. To
the nearest tenth of a centimetre, the width and length are
A 50.0 cm and 50.0 cm
C
B
D –14.0 cm and 114.0 cm
–46.2 cm and –54.2 cm
46.2 cm and 54.2 cm
____15. When Alex rides his dirt bike off a ramp, his path can be modelled by
, where d is the horizontal distance from the ramp and h is the height, both in metres. How
far away from the ramp does he land, to the nearest tenth of a metre?
A 2.0m
B 0.6m
C 7.9m
D 3.9m
____16. For a science experiment, a projectile is launched. Its path is given by
, where h is the height of the projectile above the ground and d is
the horizontal distance of the projectile from the launch pad, both in metres. How far away
from the launch pad is the projectile when it begins to fall, to the nearest tenth of a metre?
A 255.8 m
B 7.7 m
C 0.3 m
D 15.7 m
17. The trajectory of a rocket is represented by the function h(t) = –3t2 + 18t + 48,
where h is height in m and t is time in seconds.
(a) What is the initial height of the rocket before it takes off?
(b) What is the height of the rocket after 2 seconds?
(c) At what time does the rocket reach its maximum height?
(d) What is the maximum height reached by the rocket?
(e) When will the rocket land back on the ground?
18. A toy rocket is launched in the air from a launcher. The rocket’s path is described by
h(t) = -6t2 + 26t + 30 where h(t) is the height of the rocket above the ground t seconds
after its launch. Determine when the rocket reaches a height of 10 m.
Math 2200 Mid-Term Review
8
19. A rectangular rug 8 feet by 6 feet is placed in a room
with floor area 120 ft2 such that a strip of bare floor
x
Rug
of uniform width surrounds the rug. Determine the width
x
x
of the strip of bare floor.
x
x
12 m
20. A rectangular garden, measuring 20 m by 12 m,
has a uniform strip removed from the edge of
one length and the edge of one width to make
a concrete walkway. If the area of the remaining
garden is 128 m2, what is the width of the strip
that has been removed?
x
20 m
21. Use any method to determine the roots of the following quadratic equations.
(a)
1 2
x = 3x + 16
4
(b) 4( 3x + 1 )2 = 64
(c) 2( 4x + 8 )2 – 8( 4x + 8 ) = 0
(d) 3x2 – 6x – 6 = 0
Answers: 1. B 2. B 3. B 4. C 5. D 6. A 7. A 8. C 9. C 10. A 11. C 12. D
13. B 14. C 15. D 16. B 17. (a) 48 m (b) 72 m (c) 3 sec (d) 75 m (e) 8 18. 5 sec
5
19. w = 2 m 20. w = 4 m 21(a) -4 , 16 (b)
, 1 (c) -2 , -1 (d) 1  3
3
Chapter 5 Radical Equations
Not to scale.
____ 1. Find a simplified expression for the perimeter of this shape.
4
5
8
7
A
B
C
D
____ 2. Simplify
A 9+
B
.
____ 3. Simplify
A 4+ 2
B 4 + 2 15
____ 4. Express
A
B 252
C
9+ 2 2
D 114
238
.
C
–36
D
in simplest form.
C
D
5
2
6
Math 2200 Mid-Term Review
9
Not to scale.
____ 5. Find a simplified expression for the area of this shape.
3
7
4
2
3
A
B
2
in simplest form.
C 12
D
2 3
____ 7. Solve
A x = 25
49
B x = 25
7
.
C
5
7
D x= 5
49
____ 8. Solve
x=
.
A x = –6
B x = 24
C x=6
D x = 12
____ 9. Solve
.
A x = 25
B
4
C 95
D 31
____ 6. Express
A
B
7
C
1
25
D x = 1
5
x = 5
____ 10. What is 2 xy 2

3
x=

3 x written as an entire radical?
A
3
6x 2 y 2
C
3
18 x 4 y 6
B
3
12 x 3 y 4
D
3
24 x 4 y 6
11. Simplify:
2
1
12  4 200 
48  6 50
3
2
12. Simplify:
2 3 6
3 62 3
13. A square shaped play ground has an area of 72m2. Determine an exact value for the perimeter
of the playground.
14. Solve for x:
15.
3x  13  x  3  2 and identify any restrictions
The areas of congruent squares A and B are represented by
3 x  1 square units and ( x  1)
square units, respectively. Algebraically determine the area of each square.
B
A
Area =
3x + 1
Area =
(x – 1 )
Answers 1. B 2. B 3. D 4. C 5. D 6. C 7. B 8. C
12.
4√2−5
7
13. 24√2 14. x=-3,1 ;𝑥 ≥ −3 15. 25square units
2
9. B 10 D 11.− 3 √3 − 10√2