Exam and CAT Review
Unit 1: Introduction and Review
MBF3C1-Foundations for College Mathematics
1. Solve each proportion for the unknown value.
a. x:7 ___=___ 3:21
b. y:10 ___=___ 6:8
c. 5:k ___=___ 4:2
d. 15:8 ___=___ 12:m
2. A fertilizer contains nitrogen, phosphorus, and potassium in the ratio 10:6:4. Calculate the mass of each ingredient
in a 50-kg bag of the fertilizer.
3. Express the following as a unit rate, rounded to two decimal places, if necessary.
a. $5.50 for 8 L of gasoline
b. 1200 km driven in 20 h
c. 12 mm of rain in 36 h
4. A local drugstore sells tissues at 3 boxes for $2.50. A super discount warehouse sells the same tissues at 50 boxes
for $35.00. Under what circumstances would a family buy tissues from each store?
5. Solve and Check the following Equations.
a) 15 = 23 – 4x
b) 3( x – 4) = 12
d) 3(1-x) = -2(1– x)
e)
x
6
5 
c) 2 – 5x = -1 – 4x
1
1
x  x 4
2
3
6. Find the value of x in the similar triangles
7. Determine if the triangles are similar, and if they are state how you know this, and find the value of x.
a)
b)
Answers
1. a. 1 b. 7.5 c. 2.5 d.6.4
2. 25 kg nitrogen, 15 kg phosphorus, 10 kg potassium
3. a. $0.69/L b. 60 km/h c. 0.33 mm/h
4. Answers will vary.
5. a) x = 2 b) x = 8 c) x = 3 d) x = 1 e) x= 6
6. One such naming is Triangle PQR (remember it doesn’t matter which way you name it as long as you are consistent), sides p, q, and r and angles
P, Q, and R
7. x = 10 3a) x = 9
3b) x = 2.29
Exam and CAT Review
Unit 2: Trigonometry
MBF3C1-Foundations for College Mathematics
1. Based on the following diagram use the values given to find the missing/indicated side:
(a)
 A = 75°, b = 52 m  find a
(b)
 A = 64°, a = 23 cm  find b
(c)
 B = 18°, a = 24 m  find b
(d)
 B = 31°, b = 58 cm  find a
2. Given the following diagram solve for the lengths of the missing sides.
3. A 1.8-m tall botanist is standing 8.0 m away from a tall tree. The angle of elevation to the top of the tree is 57o.
How tall is the tree?
4. For a safe angle of between 70o and 80o with the ground, how far from the base of a wall can the foot of a 10-m
ladder be placed?
5. For each of the following diagrams solve for the indicated variable:
(a)
(b)
(c)
6. For each of the following diagrams solve for the indicated variable:
(a)
(b)
(c)
7. A smokestack, AB, is 205m high. From two points C and D on the same side of the smokestack’s base B, the
angles of elevation to the top of the smokestack are 40o and 36o respectively. Find the distance between C and D.
(Diagram included.)
8. Trina and Mazaheer are standing on the same side of a Red Maple tree. The angle of elevation from Mazaheer to
the tree top is 67° and the angle of elevation from Trina to the tree top is 53°. If Mazaheer and Trina are 9.3 feet
apart and Mazaheer is closer to the tree than Trina, how tall is the tree?
9. A radar tracking station locates an oil tanker at a distance of 7.8 km, and a sailboat at a distance of 5.6 km. At the
station, the angle between the two ships is 95°. How far apart are the ships?
Answers
1. (a) a = 194.1m (b) b = 11.2cm (c) b = 7.8m (d) a = 96.5cm
2. b = 116.6m c = 275.8m
3. 14.1 m
4. between 1.7 m and 3.4 m away
5. (a) 29.1 cm (b) 38.7 cm (c) 52.5 m
6. (a) 29.1 cm (b) 57° (c) 23.2 m
7. 37.8 m
8. 28.3 feet
9. 10.0 km
Exam and CAT Review
Unit 3: Quadratics I-Vertex and Factored Form
MBF3C1-Foundations for College Mathematics
1.
Complete the following table.
Equation
Vertex
Step Pattern From
Vertex
Direction of Opening
Max/Min
And Value
y = (x – 2)2 + 1
y = -(x + 4)2 + 6
y = 4(x – 4)2 – 1
Min with a
value of -1
(-3, -3)
2, 6, 10
Up
(20, -10)
-1, -3, -5
Down
y = 4(x+2)(x + 8)
Equation=______________
Equation=______________
2. Sketch the graph of the following quadratics.
y = 4(x – 4)2 – 1
y = -(x + 4)2 + 6
Exam and CAT Review
Unit 4: Quadratics II-Standard Form
MBF3C1-Foundations for College Mathematics
1.
Expand the following:
a) (x + 3)(x + 4)
2.
Expand to express y = 2(x – 3)2 – 2 in standard form
3.
Factor each expression.
(a) x2 – 3x – 4
(b) x2 – 11x + 28
(c) x2 + 7x + 12
(d) x2 – 4x – 32
(e) x2 – 13x + 42
(f) x2 – 4x + 4
4.
c) 5(3x – 1)2
d) y = 2(x – 3)2 + 5
Given the equation: y = x2 – 13x + 42
(a)
(b)
(c)
(d)
(e)
5.
b) (2x + 3)(3x – 1)
state the y – intercept _____________
write the expression in factored form y =______________
the zeros of the parabola are _________ and ___________
the vertex of the parabola is ________________
(hint: the vertex is located halfway between the zeros)
the axis of symmetry of the parabola is ______________
The “Quadratics Cup” is a new coffee shop that sells various coffee-related items, but with a quadratics twist (like
an equation written on your cup, or your caramel drizzle in the shape of parabolas, etc)
The profit of this new coffee shop can be described by the equation
(a)
(b)
(c)
(d)
P = –4n2 + 64n – 112
Where P represents profit in thousands of dollars and n represents the number of customers, in ten thousands.
What is the profit if no customers visit the store?
What are the break-even points of the store? (zero profit)
What is the maximum possible profit of the store?
If a company makes a $80 000 profit they receive a municipal Silver Business Award. How many customers are
needed in order for the Quadratics Cup to receive the award?
Answers
1. (a) x2 + 7x + 12 b) 6x2 + 7x – 3 c) 45x2 – 30x + 5, d) 2x2 – 12x + 23
2.
3.
2
y = 2x -12x + 16
a) (x – 4)(x + 1) b) (x – 7)(x – 4) c) (x + 3)(x + 4) d) (x – 8 )(x + 4) e) (x – 7)(x – 6) f) (x – 2)(x – 2)
Exam and CAT Review
Unit 5: Statistics
MBF3C1-Foundations for College Mathematics
1.
An English class had the following grades on a test (out of 100).
26
63
73
82
32
73
35
63
53
70
43
92
64
75
46
64
67
a) Find the mean, median and the mode
b) find the standard deviation and describe the meaning of it
56
23
87
67
40
52
51
28
55
76
43
56
2.
You earned the following marks (each out of 50) on your first five test: 28, 36, 38, 41, 44. What mark would you
have to get on the next test in order to bring your test average up to 80%?
3.
The machine packaging cookies has been considered defective. The packages are labelled as containing 150g. A
sample of 15 packages was selected and the masses are given.
145, 151, 152, 150, 147, 152, 149, 148, 153, 150, 146, 152, 148, 149, 151
a) Calculate the mean.
b) If any packages are more than 2.2g from the mean, the package is not sold. How many are defective?
c) Should the machine be fixed?
4.
The sales price of the last 10 homes sold in 2005 were: $345 500, $467 800, $289 000,
$675 000, $398 500, $243 000, $899 950, $453 000, $239 000, $256 000.
a) What is the average sales price?
b) What is the standard deviation?
c) Which year was more consistent? How do you know?
Answers
1.
2.
3.
4.
(a) mean=57.07, median=56, mode=63, 64, 67 (b) 18.04
106% or 53 out of 50
a) 149.5 b) 7
a) $426 675 b) 214 078.1 c) 1985; smaller range of values
Exam and CAT Review
Unit 6: Probability
MBF3C1-Foundations for College Mathematics
1.
(a)
(b)
(c)
(d)
2.
(a)
(b)
(c)
(d)
Find the probability of each situation of rolling a six-sided die:
What is the probability of rolling a 5?
What is the probability of rolling a 1 or a 2?
What is the probability of rolling an odd number?
What is the probability of rolling a number greater than 2?
Using the table of possible sums from rolling a pair of dice answer the following questions:
What is the probability of rolling sum that is a multiple of 3?
What is the probability of rolling sum that is a multiple of 5?
What is the probability of rolling sum that is 7 or 11?
Ignoring the sums for this question what would be the probability of rolling doubles? (Doubles occur when
both numbers on the die match – i.e. 1st die shows a 1 and so does the 2nd.)
3.
A coin is flipped 15 times to simulate a family having a boy. Heads were used to represent boys and tails for girls.
Twelve heads were recorded. Is the experimental probability of 4/5 close to the theoretical probability?
4.
Suppose your teacher gave a 3 question multiple choice quiz, each with 3 possible answers of A, B, and C. What is
the probability that someone will pass this quiz if they randomly guess the correct answer for each question?
Answers
1.
2.
(a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
(a) 1/3 (b) 7/36 (c) 2/9 (d) 1/6
3.
No, the theoretical prob. is
1
2
Exam and CAT Review
Unit 8: Exponential Equations
MBF3C1-Foundations for College Mathematics
1. Evaluate the following (1 mark each)
a)
510 =
b)
2. Simplify the following
a)
(b4) (b5) (b4)
3-2 =
b)
c)
a16 ÷ a24
640 =
c)
(c5)4
d) (7m2n-2) (3m4n4)
(7m4n4)
3. Please fill out the table below for each of the relations given:
Property
x
y 2
y  2(3) x
1
4
y  3 
x
Increasing
or
Decreasing
Y-intercept
Ratio
Graph
4. Explain the difference between the graphs of the following exponential equations:
a) y = 2x and y = (1/2)x
b) y = 3x and y = 5(3)x
5. African locusts are known to devastate farm and Pasteur regions affecting millions of people. To control the
population a swarm of 2,234,876 locusts was sprayed with a pesticide. If the population decreases by 20% every
2 hours,
a. Write an equation to represent the population of the locust over time. [3]
b. Use your equation to find the number of locusts after 24 hours. [2]
6. The half-life of Attanasium is 10 hours. If originally there was 1200 mg of Attanasium,
a. Write an equation to determine the amount of Attanasium left after x half lifes [3]
b. How much Attanasium will be left after 1 week (7 days)? [2]