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

Question 1: Tom is 3 times as old as his sister. In 4 years, he will be twice her age. How old is Tom now?

12 (Correct answer)
9
15
6

Correct answer: 12

If sister is s, Tom is 3s; in 4 years: 3s+4 = 2(s+4), giving s = 4, so Tom is 12.

Question 2: A spinner has 8 equal sections numbered 1−8. What is the probability of landing on an odd number?

5/8
1/4
1/2 (Correct answer)
3/8

Correct answer: 1/2

The odd numbers are 1, 3, 5, 7 (four values), so P = 4/8 = 1/2.

Question 3: Which of the following statements is true about similar triangles?

They have the same shape but not necessarily the same size. (Correct answer)
They have the same angles and sides.
They have the same area.
They have the same perimeter.

Correct answer: They have the same shape but not necessarily the same size.

Similar triangles have the same shape and angles but their side lengths are proportional.

Question 4: A dataset is: 3, 7, 7, 9, 12. What is the median?

9
3
7.6
7 (Correct answer)

Correct answer: 7

The dataset is already ordered; the middle value (3rd of 5) is 7.

Question 5: How many ways can you arrange 4 books on a shelf?

8
24 (Correct answer)
16
12

Correct answer: 24

The number of arrangements of 4 items is 4! = 4 × 3 × 2 × 1 = 24.

Question 6: If a dataset has a mean of 50 and a standard deviation of 5, what is the z-score of a data point that is 60?

1
2 (Correct answer)
3
4

Correct answer: 2

The z-score is calculated as (X - mean) / standard deviation. (60 - 50) / 5 = 2.

Question 7: What is the range of f(x) = |x|?

y ≤ 0
y ≥ 0 (Correct answer)
y > 0
All real numbers

Correct answer: y ≥ 0

The absolute value function always produces non-negative results, so the range is y ≥ 0.

Question 8: What is the value of 5! (5 factorial)?

20
120 (Correct answer)
24
60

Correct answer: 120

5! = 5 × 4 × 3 × 2 × 1 = 120.

Question 9: What is the inverse of f(x) = 2x + 6?

f⁻¹(x) = 2x − 6
f⁻¹(x) = x/2 + 6
f⁻¹(x) = (x − 6)/2 (Correct answer)
f⁻¹(x) = (x + 6)/2

Correct answer: f⁻¹(x) = (x − 6)/2

Swap x and y: x = 2y + 6, then solve for y: y = (x − 6)/2.

Question 10: How many 2-digit codes can be formed using digits 1-5 if repetition is allowed?

10
15
20
25 (Correct answer)

Correct answer: 25

Each digit can be any of 5 values, so total codes = 5 × 5 = 25.

Question 11: A family has 3 children. What is the probability that all 3 are girls (assuming equal probability)?

3/8
1/2
1/4
1/8 (Correct answer)

Correct answer: 1/8

P(GGG) = (1/2)³ = 1/8, since each birth is independent.

Question 12: A die is rolled. What is the probability of rolling a number greater than 4?

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

Correct answer: 1/3

Numbers greater than 4 on a standard die are 5 and 6, giving P = 2/6 = 1/3.

Question 13: What is the probability of NOT rolling a 3 on a standard die?

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

Correct answer: 5/6

P(not 3) = 1 − P(3) = 1 − 1/6 = 5/6.

Question 14: What is the y-value when x = −1 on the graph of y = x³?

3
1
−3
−1 (Correct answer)

Correct answer: −1

y = (−1)³ = −1.

Question 15: A rectangle has a perimeter of 36 cm and a width of 6 cm. What is its length?

18 cm
12 cm (Correct answer)
9 cm
24 cm

Correct answer: 12 cm

Perimeter = 2(l + w), so 36 = 2(l + 6), giving l = 12 cm.

Question 16: A car rental costs $25 per day plus $0.10 per mile. Which equation represents the total cost C for d days and m miles?

C = 25 + 0.10(d + m)
C = 25d + 0.10m (Correct answer)
C = 25m + 0.10d
C = (25 + 0.10)dm

Correct answer: C = 25d + 0.10m

The total cost is the daily rate times days plus the per-mile rate times miles: C = 25d + 0.10m.

Question 17: If f(x) = x² − 4, what is f(−2)?

4
8
−8
0 (Correct answer)

Correct answer: 0

f(−2) = (−2)² − 4 = 4 − 4 = 0.

Question 18: If 5 workers can complete a job in 12 days, how many days will 10 workers take to complete the same job?

6 (Correct answer)
4
10
8

Correct answer: 6

This is an inverse proportion: 5 × 12 = 10 × x, so x = 6 days.

Question 19: What is the value of y in the equation 2y + 5 = 3y - 7?

y = -2
y = -12
y = 12 (Correct answer)
y = 2

Correct answer: y = 12

Subtracting 2y from both sides gives 5 = y - 7, so y = 12.

Question 20: A line passes through (2, 5) and (4, 9). What is its slope?

2 (Correct answer)
1/2
4
3

Correct answer: 2

Slope = (9 - 5)/(4 - 2) = 4/2 = 2.

Question 21: What is the interquartile range (IQR) of the following dataset: 1, 3, 7, 9, 12, 15, 18, 20?

6
8 (Correct answer)
7
9

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.

Question 22: A bag has 4 red and 6 blue marbles. What is the probability of picking a red marble?

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

Correct answer: 2/5

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

Question 23: Simplify: 4(2x - 3) + 2(x + 5)

8x - 2
10x - 2 (Correct answer)
6x - 2
10x + 2

Correct answer: 10x - 2

Distributing gives 8x - 12 + 2x + 10 = 10x - 2.

Question 24: A function f(x) is even if:

f(x) > 0 for all x
f(−x) = −f(x) for all x
f(0) = 0
f(−x) = f(x) for all x (Correct answer)

Correct answer: f(−x) = f(x) for all x

An even function satisfies f(−x) = f(x), meaning it is symmetric about the y-axis.

Question 25: If h(t) = −16t² + 64t represents the height of an object, what is h(2)?

64 (Correct answer)
128
0
32

Correct answer: 64

h(2) = −16(4) + 64(2) = −64 + 128 = 64.

Question 26: Which of the following is the slope-intercept form of a linear equation?

ax + by = c
y - y1 = m(x - x1)
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 27: Two angles are supplementary. One angle measures 65°. What is the other?

25°
90°
115° (Correct answer)
295°

Correct answer: 115°

Supplementary angles sum to 180°, so the other angle is 180° - 65° = 115°.

Question 28: A price increased from $50 to $65. What is the percent increase?

25%
30% (Correct answer)
15%
20%

Correct answer: 30%

Percent increase = (65 − 50) / 50 × 100 = 15/50 × 100 = 30%.

Question 29: If y = 2x + 1, what is x when y = 15?

x = 31
x = 7 (Correct answer)
x = 6
x = 8

Correct answer: x = 7

Substituting y = 15 gives 15 = 2x + 1, so 2x = 14, meaning x = 7.

Question 30: In a proportion a/b = c/d, which of the following must always be true?

a − b = c − d
a × b = c × d
a × d = b × c (Correct answer)
a + b = c + d

Correct answer: a × d = b × c

The cross-multiplication property of proportions states that a × d = b × c.

Question 31: A car travels 240 miles using 8 gallons of gas. At the same rate, how many gallons are needed to travel 360 miles?

16
14
10
12 (Correct answer)

Correct answer: 12

The rate is 30 miles/gallon, so 360 ÷ 30 = 12 gallons.

Question 32: A box contains 20 items: 8 defective and 12 good. If 2 are randomly tested, what is the probability both are good (without replacement)?

144/400
1/2
12/20
66/190 (Correct answer)

Correct answer: 66/190

P = (12/20) × (11/19) = 132/380 = 66/190.

Question 33: A pie chart shows 30% of a company's budget goes to marketing. If the total budget is $500,000, how much is spent on marketing?

$50,000
$300,000
$30,000
$150,000 (Correct answer)

Correct answer: $150,000

30% of $500,000 = 0.30 × 500,000 = $150,000.

Question 34: A student scored 72 out of 90 on a test. What percentage did the student score?

80% (Correct answer)
82%
75%
78%

Correct answer: 80%

72 ÷ 90 × 100 = 0.80 × 100 = 80%.

Question 35: Solve the inequality: 4x - 3 > 13

x > 4.25
x > 4 (Correct answer)
x ≥ 4
x < 4

Correct answer: x > 4

Adding 3 gives 4x > 16, then dividing by 4 gives x > 4.

Question 36: Which of the following is NOT an integer?

√7 (Correct answer)
0
14
−5

Correct answer: √7

√7 ≈ 2.646, which is irrational and not an integer; the others are all whole numbers or their negatives.

Question 37: In a normal distribution, what percentage of data falls within one standard deviation of the mean?

99%
50%
68% (Correct answer)
95%

Correct answer: 68%

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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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