TSI – College Level Math Practice Test 2025

TSI – College Level Math Practice Test
Tutorial Services – Mission del Paso Campus



1. Factor the Following Polynomials
a. 6 x 5  8x 4  2 x 3 b. x 2  25 c. x 3  27

d. ab + 3a + 2b + 6 e. 2 x 2  9 x  5 f. x 2  6x  9

2. Perform the indicated operation
a. (3x +7y) + (4x2 – 3x + 7) + (y – 1) d. (4x2 – 6xy + 9y2) – (8x2 – 6xy - y2)

3x 5 yb 9
b. (x -4)(2x + 9) e.
9 xy 7
3x 4  25 x 2  20
c. (-3xa + 4b)2 f.
x3

3. Simplify the following Expressions
a. 3(5 – 7)4 c. 45 – 62 ÷ 32 + 1

6 35 1 9
b. d. 
2 4 4

4. Solve Each Linear Equation
a. 2(x + 3) = x + 5 c. P = 2L + 2W solve for W
x 2 3 m  4 3m  1
b.   d.  1
2 3 4 3 5

5. Solve each word problem
a. Maria rode her bicycle at an average speed of 18 mph on level roads and then slowed
down to 10mph on the hilly roads of the trip. The entire trip covered 98 miles. How long
did the entire trip take if traveling the level roads took the same time as traveling the hilly
roads? {Remember, d = r·t }

b. The bottom of Jim’s backpack contains 20 coins in nickels and dimes. If the coins have a
total value of $1.85, find the number of each type of coin.

c. The sum of three consecutive integers is 13 more than twice the smallest integer. Find
the integers.

d. Laura invested $24,000 in two accounts: a mutual fund paying 8% annual interest and a
CD paying 9% annual interest. If her annual interest was $2,020 how much did she
invest in each account?
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, 6. Solve the Following Quadratic Equations
a. m 2  5m  6  0 b. (x + 5)(x – 1) = 2
1 2 5
c. x  x d. x 2  7 x  4  0
8 2


7. Solve the following Radical Equations
a. 2x  3  9 b. 3
x 1  5  3
c. 4 x  x2 d. 2x  5  2x  3


8. Rational Expressions: Perform the indicated operation
5 4 x 5
a.  b.  2
x  3x 2 x  6
2
2x  6 x  9

a 2  9 a 2  5a  6 3 a2
c.  d.  2
a  6 a2  a  6 4a  8 a  2a


9. Rational Expressions: Solve the following equations
x x 6
a.   12 b. 7+ 5
2 3 a
6 4 3 2x
c.  d. 2 
x 3 x 3 x x3


10. Solve the following absolute value equations
x 3x  1
a.  1  11 b.  2
2 2

c. 2x  5  7 d. 3x  2  5 x  8


11. Exponents & Radicals: Simplify
49
a. 32 b.
4x 2

c. 3
 8a 21b 6 d. x 2 x 3


12. Exponents & Radical: Perform the indicated operation
2
a. 3 45 x 3  x 5 x b.
6
8 3
c. 3 8 x 2 y 3  2 x 32 y 3 d.
2 3


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, 13. Imaginary Numbers (i): Perform the indicated operation
a.  24 b. (4 - 7i) + (2 + 3i) c. 6i(2 – 3i) d. ( 5  5i )( 5  5i )
7
e. f. i 8 g. (7i)(-9i) h. (6 - 2i)(3 + i)
4  3i

14. Simplify the following complex fractions.




a. b. c. d.

15. Functions: Perform the indicated operation Let f(x) = x – 1 and let g(x) = 2x – 3

a. (f + g)(x) b. (f · g)(x)
f 
c. (f – g)(x) d.  (x)
g

16. Functions: Find the following Let f(x) = x2 and let g(x) = x + 1
a. ( f  g )( x) b. ( g  f )(2)


17. Sequence & Series: Evaluate
6
i2 5
a.  b. 2 i

i 0 2 i 3


c. Find the sum of the first six terms of the arithmetic sequence 2, 5, 8, 11, 14, 17…
n
Sn  (a1  a n )
2

d. Find the sum of the first six terms of the geometric sequence 5, 10, 20, 40, 80, 160…
a1 (1  r n )
Sn 
1 r

18. Logarithmic & Exponential Functions: Perform the indicated operation
a. Find the inverse of the given function f(x) = 6x + 11
13
b. Find the inverse of the given function f(x) = x4
2
c. Solve: 4x = 64
1
d. Solve: 3x 
9
e. Solve: log 2 (3 x  1)  4
f. Write the equation using logarithmic notation: 49 = 72
g. Write the equation using exponential notation: log 1 16  4
2

h. Write as a single log: log 3 8  log 3 4
x3
i. Write as a sum, difference, or multiple: log 3
x2
j. Solve: ln (2x) = 2
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