Math assessment

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(20 Questions)

(30 Questions)

This evaluation was prepared by Athabasca University for its students and potential students, and is intended as a guideline only. The information given about appropriate courses applies only to Athabasca University's course offerings. If you wish to enquire if you are ready to take a particular mathematics course, then we invite you to consult with the mathematics coordinator.

Question 1 (of 20)

Question 2 (of 20)

Question 3 (of 20)

Question 4 (of 20)

Question 5 (of 20)

Question 6 (of 20)

Question 7 (of 20)

Question 8 (of 20)

Question 9 (of 20)

Question 10 (of 20)

Question 11 (of 20)

The locations of the points P and Q are:

P = (−4,2), Q = (2,4)

P = (−4,2), Q = (4,2)

P = (2,4), Q = (2,−4)

P = (2,−4), Q = (4,2)

None of Above

Question 12 (of 20)

Question 13 (of 20)

Joe purchases melons at a cost of $1.25 per melon and oranges at a cost of $0.85 per orange. If Joe buys $9.25 worth of produce, including four melons, then how many oranges did Joe purchase?

Question 14 (of 20)

Sally has half a chocolate cake. She cuts it in half, and each half in half again. Sally then takes three of the cake pieces and leaves the rest for her brother. How much of the cake does Sally get to keep?

Question 15 (of 20)

Question 16 (of 20)

Given the following list of properties, a rectangle is a shape such that:

i. All sides are the same length.
ii. All angles are right angles.
iii. Opposite sides are parallel.
iv. Only two sides are parallel.

Question 17 (of 20)

Question 18 (of 20)

Question 19 (of 20)

Which of the following best describes the number 17.325?

Question 20 (of 20)

A car travels northward in at 100 kph for three-quarters of an hour, then travels east at 90 kph for half an hour. How far has the car travelled?

Question 1 (of 20)

Question 2 (of 20)

Question 3 (of 20)

When simplified, the expression 3x + 5y − 15 − 6(3x + 2y − 3) equals:

Question 4 (of 20)

Question 5 (of 20)

Question 6 (of 20)

Question 7 (of 20)

Question 8 (of 20)

Question 9 (of 20)

Question 10 (of 20)

Question 11 (of 20)

Question 12 (of 20)

A biologist measures the weights of ten frogs. Their weights, in grams, are given by the following: 12.4, 13.0, 13.1, 13.2, 13.5, 13.7, 14.0, 14.0, 14.1, 14.0. What is the median weight of the frogs?

Question 13 (of 20)

Question 14 (of 20)

Question 15 (of 20)

The points (1,3) and (−2,5) lie on a line. What is the equation of the line?

Question 16 (of 20)

Consider the following sequence: 2, 6, a, b, 18, 22.
In order for this to be an arithmetic sequence, the values of a and b are given by:

Question 17 (of 20)

Question 18 (of 20)

Question 19 (of 20)

Question 20 (of 20)

Question 1 (of 30)

Question 2 (of 30)

Question 3 (of 30)

Question 4 (of 30)

Question 5 (of 30)

Question 6 (of 30)

If ƒ(x) = x² - 4x + 7, then:

ƒ has a maximum value at x = −2

ƒ has a maximum value at x = 4

ƒ has a minimum value at x = 2

ƒ has a minimum value at x = 4

none of the above

Question 7 (of 30)

Question 8 (of 30)

Question 9 (of 30)

A 13-m ladder is placed against the side of the building. If the bottom of the ladder is 5 m from the base of the building, then how far up the wall does the ladder extend?

Question 10 (of 30)

Question 11 (of 30)

Question 12 (of 30)

Question 13 (of 30)

A simple figure is shown in Figure 4a. A second figure is given by Figure 4b. Which of the following best describes how 4b was obtained from 4a?

Rotation

Reflection

Translation

Rotation and reflection

Question 14 (of 30)

Question 15 (of 30)

Question 16 (of 30)

Question 17 (of 30)

Question 18 (of 30)

Question 19 (of 30)

Question 20 (of 30)

Examine the figure above. What is the domain and range of the function ƒ of x?

domain = all real numbers,
range = all real numbers

domain = {real numbers x : −10 < x < 10},
range = {real numbers y : −10 < y < 10}

domain = {real numbers x : −10 ≤ x ≤ 10},
range = {real numbers y : −10 ≤ y ≤ 10}

domain = all real numbers except x = 0,
range = all real numbers

none of the above

Question 21 (of 30)

Which of the equations given below best describes the circle in the graph above?

(x + 2)² + (y − 3)² = 16

(x − 2)² + (y − 3)² = 4

(x − 2)² + (y + 3)² = 16

(x − 2)² + (y + 3)² = 4

(x + 2)² + (y + 3)² = 16

Question 22 (of 30)

Solve the following system of equations for x, y and z:

x + y + z = 4
x + y + 2z = 5
4x + 4y + 6z = 18
Then choose which of the following statements is true about this linear system.

Which of the equations given below best describes the circle in the graph above?

(x,y,z) = (1,2,1) is the unique solution to the system

This system has a unique solution

This system is inconsistent

This system is a dependent linear system

none of the above

Question 23 (of 30)

Question 24 (of 30)

A line passes through the y-axis at (0,2) and has slope −3. What is the equation of the line?

Question 25 (of 30)

The graph of a function ƒ(x) is given in Figure 1. Which of the curves in Figure 2 is a graph of the function g(x) = ƒ(x − 3)?

none of the above

Question 26 (of 30)

4 log 3 − 2 log 5 equals:

The graph of a function ƒ(x) is given in Figure 1. Which of the curves in Figure 2 is a graph of the function g(x) = ƒ(x − 3)?

log 56

log (81/25)

log 106

undefined

none of the above

Question 27 (of 30)

Suppose thatƒ(x)is defined as ƒ(x) = x². Which of the following is the equation for the above graph g(x)?

g(x) = (x − 1)² + 3

g(x)=(x + 1)² + 3

g(x) = (x − 1)² + 2

g(x) = (x + 1)² + 2

none of the above

Question 28 (of 30)

A trading company ships 3 crates of oranges the first year, 6 crates of oranges the second year, 12 crates of oranges the third year, and 24 crates of oranges the fourth year. If the company's shipping record continues to follow this pattern, then the total number of crates the company can expect to ship in the seventh year is:

Question 29 (of 30)

Question 30 (of 30)

Section A Complete

Below are the question(s) you answered incorrectly with the corresponding correct answers:

Question 1.
5 + 7 × 4 − 3 =

Correct Answer: 30
Your Answer:

Question 2.
3 − (4 − 2) × (25÷5) + 2 =

Correct Answer: -5
Your Answer:

Question 3.
2/3 + 2/6 =

Correct Answer: 1
Your Answer:

Question 4.
3/5 × 10/21 =

Correct Answer: 2/7
Your Answer:

Question 5.
1437.245 + 31.156 =

Correct Answer: 1468.401
Your Answer:

Question 6.
3/4 + 4/7 =

Correct Answer: 37/28
Your Answer:

Question 7.
If x = 4, then 4x + 7 =

Correct Answer: 23
Your Answer:

Question 8.
If x = 2 and y = 3, then −3x + 4y =

Correct Answer: 6
Your Answer:

Question 9.
2x + 5x − 3x =

Correct Answer: 4x
Your Answer:

Question 10.
(5x + 3)2 − 2(3x − 5) =

Correct Answer: 4x + 16
Your Answer:

Question 11.
Question Image

The locations of the points P and Q are:

Correct Answer: P = (−4,2), Q = (2,4)
Your Answer:

Question 12.
Question Image

Examine the right triangle above. The area of this triangle is equal to:

Correct Answer: 6
Your Answer:

Question 13.
Joe purchases melons at a cost of $1.25 per melon and oranges at a cost of $0.85 per orange. If Joe buys $9.25 worth of produce, including four melons, then how many oranges did Joe purchase?

Correct Answer: 5
Your Answer:

Question 14.
Sally has half a chocolate cake. She cuts it in half, and each half in half again. Sally then takes three of the cake pieces and leaves the rest for her brother. How much of the cake does Sally get to keep?

Correct Answer: 3/8 of an entire cake
Your Answer:

Question 15.
Question Image

Which of the angles in the triangle above are acute?

Correct Answer: A, B and C
Your Answer:

Question 16.
Given the following list of properties, a rectangle is a shape such that:

i. All sides are the same length.
ii. All angles are right angles.
iii. Opposite sides are parallel.
iv. Only two sides are parallel.

Correct Answer: ii, iii
Your Answer:

Question 17.
If 2x + 3 = −7, then x equals:

Correct Answer: −5
Your Answer:

Question 18.
If 4x + (x − 3) = 18, then x equals:

Correct Answer: 4.2
Your Answer:

Question 19.
Which of the following best describes the number 17.325?

Correct Answer: both a rational number and a real number.
Your Answer:

Question 20.
A car travels northward in at 100 kph for three-quarters of an hour, then travels ears at 90 kph for half and hour. How far has the car travelled?

Correct Answer: 120 km
Your Answer:

Section B Complete

Below are the question(s) you answered incorrectly with the corresponding correct answers:

Question 1.
Question Image

Examine the graph above. The equation of the line is given by:

Correct Answer: y = 2x + 1
Your Answer:

Question 2.
Question Image

Examine the graph above. The slope of the line is given by:

Correct Answer: -3
Your Answer:

Question 3.
When simplified, the expression 3x + 5y − 15 − 6(3x + 2y − 3) equals:

Correct Answer: −15x − 7y + 3
Your Answer:

Question 4.
If x = 3, then the expression x2 − 5x equals:

Correct Answer: -6
Your Answer:

Question 5.
When simplified, the expression 2x³y² × 3x²y³ equals:

Correct Answer: 6x⁵y⁵
Your Answer:

Question 6.
When simplified, the expression 4x(x + 3) − 2x(x − 3) equals:

Correct Answer: 2x² + 18x
Your Answer:

Question 7.
An approximate value for the expression 6.03 × 10⁷ + 5.03 × 10⁶ would be:

Correct Answer: 6.5 × 10⁷
Your Answer:

Question 8.
What is the mean of the following sample:
36, 32, 24, 26, 30, 38

Correct Answer: 31
Your Answer:

Question 9.
Question Image

Correct Answer: 20/17
Your Answer:

Question 10.
What is the probability of rolling a 4 or an even number on a 6-sided die?

Correct Answer: 1/2
Your Answer:

Question 11.
Solve the following equation for x: x² − 4 = 0

Correct Answer: x = +2, −2
Your Answer:

Question 12.
A biologist measures the weights of ten frogs. Their weights, in grams, are given by the following: 12.4, 13.0, 13.1, 13.2, 13.5, 13.7, 14.0, 14.0, 14.1, 14.0. What is the median weight of the frogs?

Correct Answer: 13.6
Your Answer:

Question 13.
If 2^x = 16, then x equals:

Correct Answer: 4
Your Answer:

Question 14.
Question Image

Examine figure above. The length of side c is given by:

Correct Answer:

Your Answer:

Question 15.
The points (1,3) and (−2,5) lie on a line. What is the equation of the line?

Correct Answer: 2x + 3y = 11
Your Answer:

Question 16.
Consider the following sequence: 2, 6, a, b, 18, 22.
In order for this to be an arithmetic sequence, the values of a and b are given by:

Correct Answer: (a, b) = (10, 14)
Your Answer:

Question 17.
If 5 - 3x > 15, then:

Correct Answer: x < −10/3
Your Answer:

Question 18.
If x = −4, then |x − 5| + |x + 5| equals:

Correct Answer: 10
Your Answer:

Question 19.
When expanded, the expression (x − 3)(x + 4) equals:

Correct Answer: x² + x −12
Your Answer:

Question 20.
If ƒ(x) = 3x² − 2x + 5 is divided by (x − 1), then the remainder is equal to:

Correct Answer: 6
Your Answer:

Section C Complete

Below are the question(s) you answered incorrectly with the corresponding correct answers:

Question 1.
Question Image

Correct Answer: −5/3
Your Answer:

Question 2.
If log₁₀ 13 = t, then 10^2t equals:

Correct Answer: 169
Your Answer:

Question 3.
If x² − 6x + 9 = 0, then x equals:

Correct Answer: 3
Your Answer:

Question 4.
If 2x² − 8x + 6 = 0, then x equals:

Correct Answer: 3, 1
Your Answer:

Question 5.
If 2x + y = 7 and 4x − 3y = 14, then:

Correct Answer: x = 7/2, y = 0
Your Answer:

Question 6.
If ƒ(x) = x² - 4x + 7, then:

Correct Answer: ƒ has a minimum value at x = 2
Your Answer:

Question 7.
If |2x − 3| ≤ 5, then:

Correct Answer: −1 ≤ x ≤ 4
Your Answer:

Question 8.
Question Image

Correct Answer: −3/2 < x < 2/3
Your Answer:

Question 9.
A 13-m ladder is placed against the side of the building. If the bottom of the ladder is 5 m from the base of the building, then how far up the wall does the ladder extend?

Correct Answer:

Your Answer:

Question 10.
Question Image

Correct Answer: 72 degrees
Your Answer:

Question 11.
The solutions for the equation x² - 6x + 7 = 0 are:

Correct Answer: none of the above

Your Answer:

Question 12.
Suppose ƒ(x) = x² − 4x + 4 and g(x) = 2x − 3.

Then g(ƒ(2)) − ƒ(g(2)) equals:

Correct Answer: -4
Your Answer:

Question 13.
Question Image

A simple figure is shown in Figure 4a. A second figure is given by Figure 4b. Which of the following best describes how 4b was obtained from 4a?

Correct Answer: Rotation
Your Answer:

Question 14.
If ƒ(x) = 3x + 2 and g(x) = 4x² − 3, then ƒ(−1) + g(−1) equals:

Correct Answer: 0
Your Answer:

Question 15.
Question Image

Which of the angles in the triangle above are acute?

Correct Answer: x ≥ 2
Your Answer:

Question 16.
Question Image

Correct Answer:

Your Answer:

Question 17.
Question Image

Correct Answer: none of the above
Your Answer:

Question 18.
Suppose xy = x + y + 5. If y is written as a function of x, then y equals:

Correct Answer:

Your Answer:

Question 19.
log₂ 3 + log₂ 6 equals:

Correct Answer: log₂ 18
Your Answer:

Question 20.
Question Image

Examine the figure above. What is the domain and range of the function ƒ of x?

Correct Answer: none of the above
Your Answer:

Question 21.
Question Image

Which of the equations given below best describes the circle in the graph above?

Correct Answer: (x − 2)² + (y + 3)² = 16
Your Answer:

Question 22.
Solve the following system of equations for x, y and z:

x + y + z = 4
x + y + 2z = 5
4x + 4y + 6z = 18

Correct Answer: This system is a dependent linear system
Your Answer:

Question 23.
Question Image

Examine the figure above. The value of the ratio b/a is given by:

Correct Answer: cot θ
Your Answer:

Question 24.
A line passes through the y-axis at (0,2) and has slope −3. What is the equation of the line?

Correct Answer: y = 2 − 3x
Your Answer:

Question 25.
Question Image

The graph of a function ƒ(x) is given in Figure 1. Which of the curves in Figure 2 is a graph of the function g(x) = ƒ(x − 3)?

Correct Answer: A
Your Answer:

Question 26.
The graph of a function ƒ(x) is given in Figure 1. Which of the curves in Figure 2 is a graph of the function g(x) = ƒ(x − 3)?

Correct Answer: log (81/25)
Your Answer:

Question 27.
Question Image

Suppose thatƒ(x)is defined as ƒ(x) = x². Which of the following is the equation for the above graph g(x)?

Correct Answer: g(x) = (x − 1)² + 2
Your Answer:

Question 28.
A trading company ships 3 crates of oranges the first year, 6 crates of oranges the second year, 12 crates of oranges the third year, and 24 crates of oranges the fourth year. If the company's shipping record continues to follow this pattern, then the total number of crates the company can expect to ship in the seventh year is:

Suppose thatƒ(x)is defined as ƒ(x) = x². Which of the following is the equation for the above graph g(x)?

Correct Answer: 192
Your Answer:

Question 29.
Question Image

Correct Answer:

Your Answer:

Question 30.
Question Image

Examine the figure above. Which of the following best approximates the graph of y = sin(2x) −1?

Correct Answer: A
Your Answer:

Updated March 24, 2025 by Digital & Web Operations, University Relations (web_services@athabascau.ca)