TSI Math Practice Test

Try our free TSI Math Practice Test. These TSI Math questions are designed to be similar to those found on the Texas Success Initiative Assessment. The four primary topics covered on this test are: (1) Elementary Algebra & Functions (2) Intermediate Algebra & Functions (3) Geometry & Measurement (4) Data Analysis, Statistics, & Probability. Start your TSI Math practice right now with our free practice questions.

Directions: For each question, choose the best answer from the four choices. You may use paper and a pencil for computations, but calculators are not permitted.

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Question 1
Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?

A
30 feet
B
40 feet
C
50 feet
D
60 feet
Question 1 Explanation: 
The correct answer is (A). The formula for the area of a rectangle is:
A = Width * Length
From the question we know that L = 2W and that A = 50. So we can plug these values into our equation and solve for W:
50 = W * L
50 = W * 2W
50 = 2W²
W² = 25
W = 5
We know that L = 2W, so L = 10
Perimeter = 2L + 2W
Perimeter = 2 * 10 + 2 * 5
Perimeter = 30
Question 2
What are the solutions to the equation x2 + 8x + 15 = 0?

A
(2, 3)
B
(3, 5)
C
(−2, −3)
D
(−3, −5)
Question 2 Explanation: 
The correct answer is (D). In order to factor the quadratic equation, we need to find the two factors of 15 (the constant term) that sum to 8 (the coefficient of x).
15 = 3 * 5
8 = 3 + 5
So, 3 and 5 are the two factors that meet our requirement. The fully factored form of the quadratic is:
(x + 3)(x + 5) = 0
Recall that if ab = 0, then either a = 0, or b = 0. If (x + 3)(x + 5) = 0
Then either (x + 3) = 0, or (x + 5) = 0
That is, either: x = −3, or x = −5
The roots of the quadratic are: −3, and −5
Question 3
Solve for x:

3(x + 1) = 5(x − 2) + 7

A
-2
B
2
C
½
D
3
Question 3 Explanation: 
The correct answer is (D). We can simplify the equation as follows:
3(x + 1) = 5(x − 2) + 7
3x + 3 = 5x − 10 + 7
3x + 3 = 5x − 3
We can add 3 to both sides to get the following:
3x + 6 = 5x
We can subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:
6 = 2x
3 = x
Question 4
Line I passes through the point (−1, 2). Which of the following CANNOT be the equation of line l?

A
y = 1 − x
B
y = x + 1
C
x = −1
D
y = x + 3
Question 4 Explanation: 
The correct answer is (B). The slope-intercept form of a line is:
y = mx + b
Since the line passes through (−1, 2), there are three possibilities: the line will have a slope (the “m” in front of the “x” variable), it will be vertical (x = −1), or it will be horizontal (y = 2). Plug x = −1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y = 2 is (B).
Question 5
What is the probability of selecting a male from a group of 4 males and 8 females?

A
gm4a
B
gm4b
C
gm4c
D
gm4d
Question 5 Explanation: 
The correct answer is (A). To find the probability of selecting a male, you need to divide the total number of males by the total number of people:
MPF
Question 6
If 2x + 5 = 8x, then 12x = ?

A
5
B
10
C
15
D
20
Question 6 Explanation: 
The correct answer is (B). Here is the easiest way to solve this:
2x + 5 = 8x
8x − 2x = 5
6x = 5
6x * 2 = 5 * 2
12x = 10
Question 7
An airline asked its agents to assign convenience ratings on a scale of 1-7 to 114 flights leaving one of its hub cities. The histogram below shows the distribution of the ratings. What is the median rating assigned by the agents?

Air2

A
3
B
4
C
5
D
6
Question 7 Explanation: 
The correct answer is (C). The median is the value at the midpoint of a frequency distribution of observed values. Since we have an even number of ratings, the median will be the average of the two middle numbers. In this case, the median rating will be the average of the 57th and 58th rating.

If we add the frequencies up, starting from the lowest rating, we find that both the 57th and the 58th rating will correspond to a rating of 5.

8 + 11 + 19 + 17 = 55. The next 23 ratings will be fives. That is to say, rating number 56 = 5, rating number 57 = 5, and rating number 58 = 5.

Therefore, the median rating is 5.
Question 8
What is the value of x in the following equation:

Equation1

A
1
B
4
C
8
D
16
Question 8 Explanation: 
The correct answer is (C). We can solve for x by first squaring both sides and solving as follows:
Exp1
Question 9
The market price of a house is directly proportional to the total area of the house in square feet. If the price of a 1,500 square foot home is $300,000 what is the price of a 2,000 square foot home?

A
$350,000
B
$400,000
C
$450,000
D
$500,000
Question 9 Explanation: 
The correct answer is (B). We can solve this by setting up a proportion using the ratio of area to price:
Q21
Cross multiply and solve for x:
1,500x = $600,000,000
x = $400,000
Question 10
Find the x-intercept of a line that has the following equation:

2y = 3x − 6

 
A
−2
B
−1
C
1
D
2
Question 10 Explanation: 
The correct answer is (D). At the x-intercept, y = 0. We can solve for the x-intercept by setting y = 0 in the equation of the line.
2y = 3x − 6
2(0) = 3x − 6
0 = 3x − 6
3x = 6
x = 2
Question 11
There are 80 students in a school. Each student is taking either algebra or pre-calculus. There are 60 students in the algebra class. If 15 students are taking both algebra and pre-calculus, what is the probability that a randomly selected student is taking pre-calculus but not algebra?

A
gm5a
B
gm5b
C
gm5c
D
gm5d
Question 11 Explanation: 
The correct answer is (A). We can set up a Venn diagram to help us determine the number of students taking pre-calculus but not algebra.
gm5ex
The number of students taking algebra but not pre-calculus = 45
We can figure out the number of students taking pre-calculus but not algebra (x) as follows:
45 + 15 + x = 80
x = 20
Therefore, the probability that a student is taking pre-calculus but not algebra is:
gm5ex2
Question 12
What is the value of x in the following equation:

Equation2

A
3
B
4
C
5
D
6
Question 12 Explanation: 
The correct answer is (A). We can solve for x by subtracting 2 from both sides of the equation, then multiplying both sides by 3, and finally dividing both sides by 2 to get the value of x:
Explanation22
Question 13
Diego’s current age is five times Martina’s age ten years ago. If Martina is currently m years old, what is Diego’s current age in terms of m?

A
5m
B
5m − 10
C
5m − 50
D
5m + (m − 10)
Question 13 Explanation: 
The correct answer is (C). Martina’s age ten years ago is:
m − 10
So Diego’s age is:
5(m − 10)
= 5m − 50
Question 14
alg1

A
alg1a
B
alg1b
C
alg1c
D
alg1d
Question 14 Explanation: 
The correct answer is (C). We can use the following rule of radicals to answer this question:
alg1ex22
Question 15
Joe’s department store sells pens for 60 cents each and pencils for 40 cents each. Diane purchased a total of 17 items (pens and pencils) for $8.20. How many pens did Diane purchase?

A
5
B
7
C
10
D
12
Question 15 Explanation: 
The correct answer is (B). The first step is to define the variables:

Let the number of pens Diane purchased = x
Let the number of pencils Diane purchased = y

We can find the number of pens Diane purchased by writing two equations and solving for x as follows.
PensEx
Question 16
A scoutmaster is preparing his troop for their annual fishing expedition. He surveys each of his scouts to find out how many fishing poles they own. What is the mode of the number of poles owned?

MK5

A
0
B
1
C
2
D
3
Question 16 Explanation: 
The correct answer is (A). The mode of the data is the number that appears the most often. In this case the largest number of scouts (7) own 0 fishing poles.
Question 17
Simplify: (x6)(x5)

A
2x11
B
2x30
C
x11
D
x30
Question 17 Explanation: 
The correct answer is (C). When multiplying exponents with the same base, you should add the exponents:
(x6)(x5) = x5 + 6
= x11
Question 18
The points represented by the (x, y) coordinate pairs in the table below all lie on line k.

Q18

What is the slope of line k?

A
−2
B
−3
C
2
D
5
Question 18 Explanation: 
The correct answer is (A). We are told that all the points lie on line k. Therefore, we can calculate the slope as the change in y divided by the change in x using any two of the points. Using points (1, 3) and (5, −5) the slope is calculated as follows:
Q18ex
Question 19
x4 − 16 = ?

A
(x + 2)(x − 2)(x2 + 4)
B
(x + 2)2(x − 2)2
C
(x + 2)3 (x − 2)1
D
(x − 2)4
Question 19 Explanation: 
The correct answer is (A). First we can rewrite the original expression:
Q19x
Question 20
What is the maximum value of this function:

ƒ(x) = −16x2 + 32x + 20

A
32
B
34
C
36
D
40
Question 20 Explanation: 
The correct answer is (C). The graph of the given function is a parabola that opens downward, as indicated by the −16. There are several techniques for finding the maximum value of a quadratic function of the form ƒ(x) = ax2 + bx + c. The easiest way to solve this problem is to use the formula for finding the coordinates of the vertex of a parabola as follows (recall that the vertex of a downward facing parabola will be its maximum value):

The vertex of a parabola is located at the point:
Q20x1
In this problem: a = −16, b = 32, c = 20

The y-coordinate of the vertex of the parabola will have a value of:
Q20x2
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