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

Question 1: How many degrees are in the interior angles of a hexagon?

900°
540°
720° (Correct answer)
1080°

Correct answer: 720°

The sum of interior angles of an n-gon is (n-2) × 180°; for a hexagon: (6-2) × 180° = 720°.

Question 2: What is the volume of a rectangular prism with length 5, width 4, and height 3?

47
120
24
60 (Correct answer)

Correct answer: 60

Volume = length × width × height = 5 × 4 × 3 = 60.

Question 3: A car travels 240 miles using 8 gallons of gas. At the same rate, how many gallons are needed to travel 360 miles?

16
12 (Correct answer)
14
10

Correct answer: 12

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

Question 4: If 8 workers can complete a job in 6 days, how many days would 12 workers take?

4 (Correct answer)
2
3
9

Correct answer: 4

Total work = 8 × 6 = 48 worker-days; 48 ÷ 12 = 4 days.

Question 5: Solve the inequality: 4x - 3 > 13

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

Correct answer: x > 4

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

Question 6: A line passes through (2, 5) and (4, 9). What is its slope?

2 (Correct answer)
1/2
3
4

Correct answer: 2

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

Question 7: Which of the following is the slope-intercept form of a linear equation?

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

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 8: 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?

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

Correct answer: 12:35

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

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

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

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

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

Correct answer: x = 7 or x = -1

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

Question 11: What is the length of the diagonal of a rectangle with sides of length 3 cm and 4 cm?

8 cm
7 cm
5 cm (Correct answer)
6 cm

Correct answer: 5 cm

The diagonal can be found using the Pythagorean theorem: √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm.

Question 12: Two consecutive integers have a sum of 53. What is the larger integer?

27 (Correct answer)
26
28
25

Correct answer: 27

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

Question 13: What is the value of f(g(x)) if f(x) = x + 3 and g(x) = 2x?

2x + 3 (Correct answer)
2x + 6
x + 6
2(x + 3)

Correct answer: 2x + 3

f(g(x)) = f(2x) = 2x + 3.

Question 14: A school's enrollment increased from 800 to 920 students. What is the percent increase?

15% (Correct answer)
18%
12%
10%

Correct answer: 15%

Percent increase = (920 − 800) / 800 × 100 = 120/800 × 100 = 15%.

Question 15: Which of the following represents the number 45 written as a product of prime factors?

3² × 5 (Correct answer)
3 × 5²
3 × 15
5 × 9

Correct answer: 3² × 5

45 = 9 × 5 = 3² × 5; this is the complete prime factorization.

Question 16: A store's sales were $12,000 in January and $15,000 in February. What was the percent increase?

25% (Correct answer)
20%
3%
15%

Correct answer: 25%

Percent increase = (15000 − 12000)/12000 × 100 = 3000/12000 × 100 = 25%.

Question 17: A salesperson earns a 6% commission on sales. How much commission does she earn on $4,500 in sales?

$270 (Correct answer)
$225
$300
$240

Correct answer: $270

Commission = 0.06 × 4,500 = $270.

Question 18: For the function y = 3x − 1, what is the output when the input is 4?

3
13
9
11 (Correct answer)

Correct answer: 11

y = 3(4) − 1 = 12 − 1 = 11.

Question 19: Which number is divisible by both 3 and 4?

26
36 (Correct answer)
14
22

Correct answer: 36

36 ÷ 3 = 12 and 36 ÷ 4 = 9, so 36 is divisible by both.

Question 20: A family has 3 children. What is the probability that all 3 are girls (assuming equal probability)?

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

Correct answer: 1/8

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

Question 21: Simplify: 4(2x - 3) + 2(x + 5)

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

Correct answer: 10x - 2

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

Question 22: What is the y-value when x = −1 on the graph of y = x³?

−1 (Correct answer)
−3
3
1

Correct answer: −1

y = (−1)³ = −1.

Question 23: How many ways can you arrange 4 books on a shelf?

16
8
12
24 (Correct answer)

Correct answer: 24

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

Question 24: If a number is divisible by 6, it must also be divisible by:

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

Correct answer: 2 and 3

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

Question 25: What is the value of 5! (5 factorial)?

20
24
120 (Correct answer)
60

Correct answer: 120

5! = 5 × 4 × 3 × 2 × 1 = 120.

Question 26: In a right triangle, what is the length of the hypotenuse if the legs are 6 cm and 8 cm?

12 cm
10 cm (Correct answer)
14 cm
16 cm

Correct answer: 10 cm

The hypotenuse can be found using the Pythagorean theorem: √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.

Question 27: What is the slope of a line perpendicular to y = (1/4)x + 3?

1/4
−1/4
−4 (Correct answer)
4

Correct answer: −4

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

Question 28: A scatterplot shows a positive correlation. This means:

x and y are not related
As x increases, y tends to increase (Correct answer)
As x increases, y tends to decrease
y is always greater than x

Correct answer: As x increases, y tends to increase

A positive correlation means both variables tend to move in the same direction.

Question 29: What is the interquartile range (IQR) of the following dataset: 1, 3, 7, 9, 12, 15, 18, 20?

9
6
7
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.

Question 30: What is the median of the following set of numbers: 7, 3, 9, 12, 15?

15
9 (Correct answer)
12
7

Correct answer: 9

The median is the middle number when the data set is ordered: 3, 7, 9, 12, 15. The middle number is 9.

Question 31: A box contains 20 items: 8 defective and 12 good. If 2 are randomly tested, what is the probability both are good (without replacement)?

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

Correct answer: 66/190

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

Question 32: What does a negative slope indicate about a line?

The line is horizontal
The line falls from left to right (Correct answer)
The line is vertical
The line rises from left to right

Correct answer: The line falls from left to right

A negative slope means that as x increases, y decreases, so the line falls from left to right.

Question 33: A function f(x) is even if:

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

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 34: What is the value of −2 + (−5) − (−3)?

−7
−4 (Correct answer)
4
−10

Correct answer: −4

−2 + (−5) − (−3) = −2 − 5 + 3 = −4.

Question 35: What is the formula for the surface area of a cylinder?

2πrh
πr^2h
2πr^2
2πr(r + h) (Correct answer)

Correct answer: 2πr(r + h)

The surface area of a cylinder is given by the formula 2πr(r + h), where r is the radius and h is the height.

Question 36: What is the mode of the following set of numbers: 2, 4, 4, 4, 6, 7, 8, 9?

2
4 (Correct answer)
7
6

Correct answer: 4

The mode is the number that appears most frequently in the data set, which is 4 in this case.

Question 37: What is the absolute value of −15?

−15
15 (Correct answer)
0
1/15

Correct answer: 15

Absolute value measures distance from zero, so |−15| = 15.

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

35 min

Time Limit

70%

To Pass

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