TSI - College Level Math Practice Test Tutorial Services - Mission del Paso Campus - Factor, Operations, and Problem Solving

Sep 27, 2026

Uploaded by Bintang

TSI College Level Math Practice Test Tutorial Services (Mission del Paso Campus) provides a multi-section assessment and practice guide covering core algebra through advanced topics. It includes factoring polynomials, simplifying expressions, performing operations on rational expressions, and solving linear, quadratic, radical, rational, absolute value, and logarithmic/exponential problems. The test further evaluates inequality solving, graphing linear equations and relations with domain/range, identifying vertices and intercepts, standard forms for conics, and matrix systems including determinants and inverses, plus word problems and unit applications.

LanguageEnglish

CategoryExam

FormatPDF

Pages17

Reading Time43 min

AccessFree to download

Factor the Following Polynomials

Perform the Indicated Operation

Simplify Expressions

Solve Linear Equations

Solve Word Problems

Solve Quadratic Equations

Solve Radical Equations

Rational Expressions: Perform Operations

Rational Expressions: Solve Equations

Absolute Value Equations

Exponents & Radicals

Imaginary Numbers

Complex Fractions

Functions (Operations and Evaluation)

Sequence & Series

Logarithmic & Exponential Functions

Solve Inequalities

Graphing Linear Equations

Graphing Relations, Domain & Range

Vertex and x-intercepts

Conic Sections

Systems of Equations and Matrices

| TSI – College Level Math Practice Test Tutorial Services – Mission del Paso Campus
1. Factor the Following Polynomials
a. 6x5 􀀐 8x4 􀀎 2x3 b. x 2 􀀐 25 c. x 3 􀀎 27
d. ab + 3a + 2b + 6 e. 2x2 􀀎 9x 􀀐 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) | | | | | --- | --- | --- | --- | | b.
c. | (x-4)(2x + 9)
(-3xa + 4b)2 | e.
f. | 3x5 yb 9 9xy 7
3x4 􀀐 25x2 􀀐 20
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
b. ~~ ~~x2 􀀎 ~~ ~~23 􀀠 34~~ ~~ d. ~~ ~~m~~ ~~~~ ~~4 􀀐 ~~ ~~3m5􀀐1 􀀠 1
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?
Saved C: Accuplacer College Level Math Assessment Page 1 of 17

| | | | 6. Solve the Following Quadratic Equations a. m 2 􀀎 5m 􀀐 6 􀀠 0 b. (x + 5)(x – 1) = 2 c. ~~ ~~18 x 2 􀀎 x 􀀠 52~~ ~~ d. x 2 􀀎 7x 􀀎 4 􀀠 0 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 a. ~~ ~~x~~ ~~2~~ ~~~~ ~~3x 􀁹 ~~ ~~2x4􀀐~~ ~~6~~ ~~ b. ~~ ~~2xx􀀎~~ ~~6 􀀎 ~~ ~~x~~ ~~2~~ ~~~~ ~~9 c. ~~ ~~aa2~~ ~~􀀐􀀐69 􀁸 ~~ ~~aa22~~ ~~􀀐􀀐5aa􀀐􀀐66~~ ~~ d. ~~ ~~4a3􀀐~~ ~~8 􀀐 ~~ ~~aa2~~ ~~~~ ~~22a 9. Rational Expressions: Solve the following equations a. ~~ ~~x2 􀀐 ~~ ~~x3 􀀠 12 b. 7 + 6a 􀀠 5 c. ~~ ~~x~~ ~~6􀀎~~ ~~3 􀀠 x~~ ~~~~ ~~3~~ ~~ d. 2 􀀎 ~~ ~~3x 􀀠 x2x􀀎3 10. Solve the following absolute value equations a. ~~ ~~x 􀀐1 􀀠 11 b. 3x 􀀎 1 􀀠 􀀐2 2 2 c. 2x 􀀎 5 􀀠 7 d. 3x 􀀎 2 􀀠 5x 􀀐 8 11. Exponents & Radicals: Simplify a. 32 b. 494x2~~ ~~ c. 3 􀀐 8a21b 6 d. x 􀀐2x 􀀐3 12. Exponents & Radical: Perform the indicated operation a. 3 45x3 􀀎 x 5x b. ~~ ~~~~ ~~26 c. 3 􀀐 2x 32y 3 d. ~~ ~~~~ ~~82~~ ~~~~ ~~~~ ~~33 Saved C: Accuplacer College Level Math Assessment Page 2 of 17 13. Imaginary Numbers (i): Perform the indicated operation a. 􀀐 24 b. (4-7i) + (2 + 3i) c. 6i(2 – 3i) d. ( 5 􀀐 5i)( 5 􀀎 5i) e. ~~ ~~4~~ ~~7􀀎~~ ~~3i~~ ~~ f. i 8 g. (7i)(-9i) h. (6-2i)(3 + i) 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) c. (f – g)(x) d. 􀂨􀂧􀂩 ~~ ~~fg~~ ~~􀂷􀂹􀂸(x) 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 a. 􀂦i0 i~~ ~~~~ ~~2~~ ~~ b. 􀂦i3 2 i c. Find the sum of the first six terms of the arithmetic sequence 2, 5, 8, 11, 14, 17… Sn 􀀠 n2 (a1 􀀎 an ) d. Find the sum of the first six terms of the geometric sequence 5, 10, 20, 40, 80, 160… S 􀀠 a1 (1 􀀐 r n ) n 1 􀀐 r 18. Logarithmic & Exponential Functions: Perform the indicated operation a. Find the inverse of the given function f(x) = 6x + 11 b. Find the inverse of the given function f(x) = 132 x 􀀐 4 c. Solve: 4x = 64 d. Solve: 3x 􀀠 19 e. Solve: log 2 (3x 􀀐1) 􀀠 4 f. Write the equation using logarithmic notation: 49 = 72 g. Write the equation using exponential notation: log 1 16 􀀠 􀀐4 2 h. Writ

FAQs

What math topics are covered in this practice test?

The practice test covers factoring, simplifying expressions, solving linear/quadratic/radical/absolute value equations, rational expressions, inequalities, graphing linear equations and relations, vertices and conic sections, and systems of equations with matrices.

Are word problems included, and do they use given formulas?

Yes. Word problems appear, including an average-speed distance-time scenario that references d = r·t, plus coin and investment problems requiring equation setup and solving.

Does the test include functions, sequences, and logarithms?

Yes. It includes function operations and finding values, evaluating arithmetic and geometric sequences, and practicing inverse functions plus logarithmic and exponential equations and rewrites.

Sep 27, 2026

Uploaded by Bintang