IMSA – Intermediate Math Skills Assessment (Algonquin College) — Questions and Answers

Question 1: What does the graph of y = x² look like?

A straight line
A parabola opening downward
A parabola opening upward (Correct answer)
A circle

Correct answer: A parabola opening upward

y = x² is a quadratic equation whose graph is a U-shaped parabola opening upward.

Question 2: Which of the following represents a function?

One input can have multiple outputs
Inputs and outputs are always equal
Each input has exactly one output (Correct answer)
Each output must equal its input

Correct answer: Each input has exactly one output

A function requires that every input (x-value) maps to exactly one output (y-value).

Question 3: A bar chart shows sales of 50, 70, 60, and 80 units over 4 months. What is the mean?

65 (Correct answer)
60
70
55

Correct answer: 65

Mean = (50 + 70 + 60 + 80)/4 = 260/4 = 65.

Question 4: The ratio of A to B is 3:5 and the ratio of B to C is 4:7. What is the ratio of A to C?

7:12
4:15
12:35 (Correct answer)
3:7

Correct answer: 12:35

Making B common: A:B = 12:20 and B:C = 20:35, so A:C = 12:35.

Question 5: Which value of x satisfies |2x - 6| = 8?

x = 7 or x = 1
x = -7 or x = 1
x = 7 only
x = 7 or x = -1 (Correct answer)

Correct answer: x = 7 or x = -1

2x - 6 = 8 gives x = 7, and 2x - 6 = -8 gives x = -1.

Question 6: Which of the following is the slope-intercept form of a linear equation?

y - y1 = m(x - x1)
ax + by = c
x/a + y/b = 1
y = mx + b (Correct answer)

Correct answer: y = mx + b

y = mx + b is the slope-intercept form where m is the slope and b is the y-intercept.

Question 7: A cylinder has radius 3 and height 5. What is its volume? (Use π ≈ 3.14)

188.4
94.2
141.3 (Correct answer)
47.1

Correct answer: 141.3

Volume = πr²h = 3.14 × 9 × 5 = 141.3.

Question 8: The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many boys are there?

21 (Correct answer)
18
24
12

Correct answer: 21

Using the proportion 3/4 = x/28, cross-multiplying gives x = 21 boys.

Question 9: What is 40% of 250?

40
150
10
100 (Correct answer)

Correct answer: 100

40% of 250 = 0.40 × 250 = 100.

Question 10: A bag has 4 red and 6 blue marbles. What is the probability of picking a red marble?

4/6
2/5 (Correct answer)
1/4
3/5

Correct answer: 2/5

P(red) = 4/(4+6) = 4/10 = 2/5.

Question 11: Which graph passes through the origin and has a slope of 3?

y = x + 3
y = x/3
y = 3x + 3
y = 3x (Correct answer)

Correct answer: y = 3x

A line through the origin with slope 3 has equation y = 3x (b = 0).

Question 12: Two dice are rolled. What is the probability that both show a 6?

1/36 (Correct answer)
1/12
1/6
2/36

Correct answer: 1/36

P(6) × P(6) = (1/6) × (1/6) = 1/36.

Question 13: What is the surface area of a cube with side length 4?

96 (Correct answer)
64
24
48

Correct answer: 96

A cube has 6 faces, each with area 4² = 16, so surface area = 6 × 16 = 96.

Question 14: A store sold 120 items last month. This month sales decreased by 15%. How many items were sold this month?

102 (Correct answer)
18
105
108

Correct answer: 102

Decrease = 15% of 120 = 18; items sold = 120 − 18 = 102.

Question 15: What is the value of 5! (5 factorial)?

24
60
120 (Correct answer)
20

Correct answer: 120

5! = 5 × 4 × 3 × 2 × 1 = 120.

Question 16: If a number is divisible by 6, it must also be divisible by:

4 and 6
2 and 3 (Correct answer)
3 and 4
2 and 4

Correct answer: 2 and 3

Since 6 = 2 × 3, any multiple of 6 must be divisible by both 2 and 3.

Question 17: Which of the following is a linear function?

f(x) = 1/x
f(x) = 2x + 5 (Correct answer)
f(x) = x²
f(x) = √x

Correct answer: f(x) = 2x + 5

f(x) = 2x + 5 is linear because the variable x has an exponent of 1.

Question 18: A tank is 40% full. After adding 30 liters, it becomes 70% full. What is the total capacity of the tank?

100 liters (Correct answer)
90 liters
75 liters
80 liters

Correct answer: 100 liters

The 30 liters added represents 70% − 40% = 30% of the capacity, so capacity = 30 ÷ 0.30 = 100 liters.

Question 19: Two consecutive integers have a sum of 53. What is the larger integer?

27 (Correct answer)
28
25
26

Correct answer: 27

If n and n+1 are consecutive integers, then 2n + 1 = 53, giving n = 26 and n+1 = 27.

Question 20: What is the area of a triangle with a base of 8 cm and a height of 5 cm?

20 cm^2 (Correct answer)
50 cm^2
40 cm^2
30 cm^2

Correct answer: 20 cm^2

The area of a triangle is calculated using the formula (base * height) / 2. So, (8 cm * 5 cm) / 2 = 20 cm^2.

Question 21: Two workers together can finish a task in 6 hours. Worker A alone takes 10 hours. How long does Worker B alone take?

15 hours (Correct answer)
18 hours
12 hours
4 hours

Correct answer: 15 hours

Combined rate = 1/6; A's rate = 1/10; B's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so B takes 15 hours.

Question 22: What is the mean of the following set of numbers: 4, 8, 15, 16, 23, 42?

18
20
19 (Correct answer)
21

Correct answer: 19

The mean is calculated by adding all the numbers and dividing by the count: (4 + 8 + 15 + 16 + 23 + 42) / 6 = 19.

Question 23: If f(x) = 3x - 2, what is f(4)?

10 (Correct answer)
14
12
8

Correct answer: 10

f(4) = 3(4) - 2 = 12 - 2 = 10.

Question 24: What is the slope of a line perpendicular to y = (1/4)x + 3?

4
1/4
−4 (Correct answer)
−1/4

Correct answer: −4

A perpendicular slope is the negative reciprocal of 1/4, which is -4.

Question 25: What is the prime factorization of 60?

2 × 3 × 5²
2 × 3² × 5
2² × 3 × 5 (Correct answer)
2³ × 3 × 5

Correct answer: 2² × 3 × 5

60 = 4 × 15 = 2² × 3 × 5.

Question 26: What is the interquartile range (IQR) of the following dataset: 1, 3, 7, 9, 12, 15, 18, 20?

9
7
6
8 (Correct answer)

Correct answer: 8

IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Here, Q1 is 6 and Q3 is 14. So, IQR = 14 - 6 = 8.

IMSA – Intermediate Math Skills Assessment (Algonquin College)

The Intermediate Math Skills Assessment (IMSA) is Algonquin College's Accuplacer-based admission test covering arithmetic and quantitative reasoning, algebra, and statistics. It determines eligibility for programs requiring intermediate mathematics proficiency.

Questions

75 min

Time Limit

70%

To Pass

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