For your math entrance exam, your college may ask you to take an online placement test in advanced math, also known as college math.
Are you required to do CPT testing in advanced math? If so, here is a free advanced math test for the CPT.
The advanced algebra and functions part of the math exam contains twenty questions.
This free sample is from our CPT test math downloads, which have 400 total questions.
Math for Entrance Exam – Online Placement Test
Instructions: To practice math for your entrance exam, try the questions below. The solutions are provided in the next section.
Example 1:
Consider a right-angled triangle, where side X and side Y form the right angle, and side Z is the hypotenuse. If X = 3 and Y = 4, what is the length of side Z?
A. 2
B. 3
C. 4
D. 5
Example 2:
53 = 125 is equal to which of the following?
A. 125 = log53
B. 125 = log35
C. 5 = log3125
D. 3 = log5125
Example 3:
x−5 = ?
A. 1 − x5
B. 1 / x5
C. −1 + x5
D. −1 − x5
Example 4:
For the following equation, i represents an imaginary number.
(6 − 3i) − (−2 − i) = ?
A. 4 − 4i
B. 8 − 4i
C. 8 − 2i
D. 8 + 2i
Math for Entrance Exam – Solutions
Solution 1:
The correct answer is D.
The length of the hypotenuse is always the square root of the sum of the squares of the other two sides of the triangle:
Step 1 – Calculate the sum of the squares of sides X and Y.
So for X = 3 and Y = 4:
32 + 42 =
9 + 16 =
25
Step 2 – Take the square root of the above number to get the hypotenuse length:
The square root of 25 is 5.
Solution 2:
The correct answer is D.
Logarithmic functions are just another way of expressing exponents.
Remember that:
yx is always the same as x = logy
Solution 3:
The correct answer is B.
Remember that a negative exponent is always equal to 1 divided by the variable:
Therefore:
x−5 = 1 / x5
Solution 4:
The correct answer is C.
To solve this type of problem, do the operations on the parentheses first:
REMEMBER: Two negatives together make a positive.
(6 − 3i) − (−2 − i) = 6 − 3i + 2 + i
Then group the real and imaginary numbers together:
6 − 3i + 2 + i =
6 + 2 − 3i + i =
8 − 2i