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

Question 1: What is the area of a triangle with base 10 and height 6?

20
15
60
30 (Correct answer)

Correct answer: 30

Area of a triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30.

Question 2: A function f(x) is even if:

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

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 3: What type of correlation exists if an increase in one variable corresponds to an increase in another variable?

Zero correlation
Positive correlation (Correct answer)
No correlation
Negative correlation

Correct answer: Positive correlation

A positive correlation means that as one variable increases, the other variable also increases.

Question 4: How many different 3-letter arrangements can be made from the letters A, B, C, D (no repetition)?

12
64
6
24 (Correct answer)

Correct answer: 24

This is a permutation: P(4,3) = 4 × 3 × 2 = 24.

Question 5: On a graph, a horizontal line y = 4 intersects y = 2x − 2 at what x-value?

3 (Correct answer)
1
6
2

Correct answer: 3

Setting 2x − 2 = 4 gives 2x = 6, so x = 3.

Question 6: Solve for x: 3x + 7 = 22

x = 7
x = 3
x = 4
x = 5 (Correct answer)

Correct answer: x = 5

Subtracting 7 from both sides gives 3x = 15, so x = 5.

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

9 (Correct answer)
15
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 8: If y = 2x + 1, what is x when y = 15?

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

Correct answer: x = 7

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

Question 9: What is the measure of each interior angle of a regular pentagon?

72°
120°
90°
108° (Correct answer)

Correct answer: 108°

Sum of interior angles = (5-2) × 180° = 540°; each angle = 540°/5 = 108°.

Question 10: If h(t) = −16t² + 64t represents the height of an object, what is h(2)?

0
128
64 (Correct answer)
32

Correct answer: 64

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

Question 11: Which number is divisible by both 3 and 4?

26
14
36 (Correct answer)
22

Correct answer: 36

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

Question 12: A spinner has 8 equal sections numbered 1−8. What is the probability of landing on an odd number?

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

Correct answer: 1/2

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

Question 13: In a right triangle, what is the length of the hypotenuse if the legs are 6 cm and 8 cm?

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

Correct answer: 10 cm

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

Question 14: If f(x) = x² − 4, what is f(−2)?

0 (Correct answer)
8
4
−8

Correct answer: 0

f(−2) = (−2)² − 4 = 4 − 4 = 0.

Question 15: Which graph passes through the origin and has a slope of 3?

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

Correct answer: y = 3x

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

Question 16: If f(x) = 3x - 2, what is f(4)?

14
8
12
10 (Correct answer)

Correct answer: 10

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

Question 17: What is the y-intercept of the line 5x - 2y = 10?

(2, 0)
(0, 5)
(0, -5) (Correct answer)
(0, 10)

Correct answer: (0, -5)

Setting x = 0 gives -2y = 10, so y = -5, making the y-intercept (0, -5).

Question 18: Which of the following is a prime number?

37 (Correct answer)
49
39
51

Correct answer: 37

37 is only divisible by 1 and itself, making it prime; the others have additional factors.

Question 19: Which of the following equals C(5,2)?

5
10 (Correct answer)
20
15

Correct answer: 10

C(5,2) = 5!/(2! × 3!) = (5 × 4)/(2 × 1) = 10.

Question 20: In a proportion a/b = c/d, which of the following must always be true?

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

Correct answer: a × d = b × c

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

Question 21: Solve: 2(x − 4) = 3x + 6

x = 2
x = 14
x = −14 (Correct answer)
x = −2

Correct answer: x = −14

Expanding gives 2x - 8 = 3x + 6, so -x = 14, meaning x = -14.

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

21
19 (Correct answer)
18
20

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

102 (Correct answer)
108
18
105

Correct answer: 102

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

Question 24: What does a negative slope indicate about a line?

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

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 25: An item costs $45 after a 25% discount. What was the original price?

$54
$56.25
$60 (Correct answer)
$57

Correct answer: $60

$45 is 75% of the original price, so original = 45 ÷ 0.75 = $60.

Question 26: What is the mode of the following set of numbers: 2, 4, 4, 4, 6, 7, 8, 9?

7
6
4 (Correct answer)
2

Correct answer: 4

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

Question 27: What is the formula for the surface area of a cylinder?

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

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 28: What is the remainder when 47 is divided by 5?

1
2 (Correct answer)
0
3

Correct answer: 2

47 ÷ 5 = 9 remainder 2, since 5 × 9 = 45 and 47 - 45 = 2.

Question 29: Two numbers are in the ratio 4:7. Their sum is 99. What is the larger number?

36
56
49
63 (Correct answer)

Correct answer: 63

Let the numbers be 4x and 7x; then 4x + 7x = 99, so x = 9 and the larger number is 7 × 9 = 63.

Question 30: 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 31: What is the prime factorization of 60?

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

Correct answer: 2² × 3 × 5

60 = 4 × 15 = 2² × 3 × 5.

Question 32: A rectangle has a perimeter of 36 cm and a width of 6 cm. What is its length?

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

Correct answer: 12 cm

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

Question 33: Two angles are complementary. One measures 34°. What is the other?

46°
56° (Correct answer)
146°
66°

Correct answer: 56°

Complementary angles sum to 90°, so the other angle is 90° - 34° = 56°.

Question 34: A family has 3 children. What is the probability that all 3 are girls (assuming equal probability)?

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

Correct answer: 1/8

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

Question 35: Tom is 3 times as old as his sister. In 4 years, he will be twice her age. How old is Tom now?

6
12 (Correct answer)
9
15

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 36: 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 = 25d + 0.10m (Correct answer)
C = 25 + 0.10(d + m)
C = (25 + 0.10)dm
C = 25m + 0.10d

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 37: Which graphical representation is best used to show the distribution of a data set?

Line Graph
Pie Chart
Bar Chart
Histogram (Correct answer)

Correct answer: Histogram

A histogram is used to show the distribution of a data set by grouping data points into ranges.

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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