Foundations of Math 11 Exam Review
1. Which law could you use to determine the unknown angle in
this triangle?
2. In ΔABC, ∠A = 45°, a = 6.0 cm, and b = 7.5 cm. Determine
the number of triangles (zero, one, or two) that are possible
for these measurements. Draw the triangle(s) to support
your answer.
3. Why would you use a dashed boundary line when graphing the solution set
of the linear inequality
1.6x – 3y < 50?
4. A publisher makes romance and adventure novels. Romance novels sell for
$9.95 and adventure novels for $8.95. The publishers noticed that each
month they sell between 500 and 800 romance novels and that the number
of adventure novels sold is never more than double the number of romance
novels sold.
Let r represent the number of romance novels sold.
Let a represent the number of adventure novels sold.
Write a system of linear inequalities to describe the constraints. Then, write
an objective function that represents the profit made from the sale of novels.
y
5. Rewrite x2 = – 3x + 4 in standard form and solve for x.
1
6. Use the graph to determine the equation of the parabola.
–3
7. Solve 9x2 – 30x = –25 by factoring. Verify your solution.
8. Determine two angles between 0° and 180° that have the
sine ratio 0.8480.
–2
–1
1
–1
–2
–3
9. Solve
. State solution as exact values.
10. The base and height of a trapezoid with an area of 35 cm2 will be enlarged by
a scale factor of 4.
Determine the area of the enlarged trapezoid.
11. An airplane is flying directly toward two forest fires. From the airplane, the
angle of depression to one fire is 43° and 20° to the other fire. The airplane is
flying at an altitude of 2500 ft. What is the distance between the two fires to
the nearest foot? Show your work.
12. The stylists in a hair salon cut hair for women and men.
x
• The salon books at least 5 women’s appointments for every man’s
appointment.
• Usually there are 90 or more appointments, in total, during a week.
• The salon is trying to reduce the number of hours the stylists work.
• A woman’s cut takes about 45 min, and a man’s cut takes about 20 min.
What combination of women’s and men’s appointments would minimize the
number of hours the stylists work? How many hours would this be?
13. This graph represents the path of a snowboarder sliding
down a mountain.
a) Calculate the slopes of segments AB, BC, CD, and DE.
Show your work.
b) What do these slopes represent?
14. Lamar jogs at 11 km/h. When Lamar jogs at this rate for
15 min, he burns 276 Cal. Angela jogs at a slower rate, 9
km/h, burning 641 Cal in 60 min. If Angela jogs for 2.5 h,
how long will Lamar have to jog in order to burn the same amount of Calories
as Angela?
15. This scale diagram, drawn on 0.5 cm grid paper, shows the plan of a
swimming pool, drawn using a scale factor of 1:250.
a) Determine the perimeter of the pool.
b) Determine the area of the bottom of the pool.
ANSWERS
1. Cosine Law then Sine Law
2. Two triangles
3. To indicate that the points on the
boundary line are not part of the
solution set.
4. Constraints:
𝑟≥0
𝑎≥0
500 ≤ 𝑟 ≤ 800
2𝑟 ≥ 𝑎
Objective function:
P = 9.95r + 8.95a
5. x = 1, x = 4
6. y=-2(x+1.5)(x+0.5)
7. x=5/3
8. 58o, 122o
9.
,
10. 560cm2
11. 4188ft
12. The minimum is at point (75, 15) and
represents 75 women’s appointments
and 15 men’s appointments.
E = 75(45) + 20(15)
E = 3675
The minimum amount of time is 3675
h.
13. a) AB = -10
BC = -4
CD = -10
DE = -3.33…
b) The slopes represent the
snowboarder's speed in metres per
second (m/s).
14. 1.45h or 87 min
15. a) 57.5m
b) 93.75m2