Virginia Placement Test Practice Questions and Answers - Practice Problems

Sep 26, 2026

Virginia Placement Test practice materials for mathematics, organized by unit and designed for targeted skill review. The document lists practice problems across core topics such as operations with positive fractions, decimals and percents, algebra basics, linear equations and inequalities, systems in two variables, exponents and factoring, rational expressions, rational exponents and radicals, and functions with quadratic equations and parabolas. It also provides unit-by-unit answer sections and preparation links to support efficient study planning.

LanguageEnglish

CategoryExam

FormatPDF

Pages30

Reading Time1 h 16 min

AccessFree to download

Practice Problems for UNIT 1 – Operations with Positive Fractions

Practice Problems for UNIT 2 – Operations with Positive Decimals and Percents

Practice Problems for UNIT 3 – Algebra Basics

Practice Problems for UNIT 4 – First Degree Equations and Inequalities in One Variable

Practice Problems for UNIT 5 – Linear Equations, Inequalities, and Systems of Equations in Two Variables

Practice Problems for UNIT 6 – Exponents, Factoring, and Polynomial Equations

Practice Problems for UNIT 7 – Rational Expressions and Equations

Practice Problems for UNIT 8 – Rational Exponents and Radicals

Practice Problems for UNIT 9 – Functions, Quadratic Equations, and Parabolas

Answers to Practice Questions for each UNIT

Links to objectives and free resources for preparation for The Virginia Placement Test for mathematics

Virginia Placement Test Practice Questions and Answers Table of Contents Practice Problems for UNIT 1 – Operations with Positive Fractions............................................................. 1 Practice Problems for UNIT 2 – Operations with Positive Decimals and Percents....................................... 3 Practice Problems for UNIT 3 – Algebra Basics ............................................................................................. 6 Practice Problems for UNIT 4 – First Degree Equations and Inequalities in One Variable ........................... 7 Practice Problems for UNIT 5 – Linear Equations, Inequalities, and Systems of Equations in Two Variables ....................................................................................................................................................... 8 Practice Problems for UNIT 6 – Exponents, Factoring, and Polynomial Equations .................................... 11 Practice Problems for UNIT 7 – Rational Expressions and Equations ......................................................... 13 Practice Problems for UNIT 8 – Rational Exponents and Radicals.............................................................. 14 Practice Problems for UNIT 9 – Functions, Quadratic Equations, and Parabolas....................................... 16 Answers to Practice Questions for UNIT 1 – Operations with Positive Fractions....................................... 20 Answers to Practice Questions for UNIT 2 – Operations with Positive Decimals and Percents................. 21 Answers to Practice Questions for UNIT 3 – Algebra Basics....................................................................... 22 Answers to Practice Questions for UNIT 4 – First Degree Equations and Inequalities in One Variable.....22 Answers to Practice Questions for UNIT 5 – Linear Equations, Inequalities, and Systems of Equations in Two Variables.............................................................................................................................................. 23 Answers to Practice Questions for UNIT 6 – Exponents, Factoring, and Polynomial Equations ................ 25 Answers to Practice Questions for UNIT 7 – Rational Expressions and Equations..................................... 26 Answers to Practice Questions for UNIT 8 – Rational Exponents and Radicals.......................................... 26 Answers to Practice Questions for UNIT 9 – Functions, Quadratic Equations, and Parabolas................... 27 Link to objectives for each of the units....................................................................................................... 28 Link to free resources for preparation for The Virginia Placement Test for mathematics......................... 28 Practice Problems for UNIT 1 – Operations with Positive Fractions 1. If you have four quarters, three dimes, two nickels, and two pennies, what fraction of the whole coin collection is in dimes? 2. Write 5 ~~ ~~78~~ ~~ as an improper fraction. 3. Write 295 as a mixed number. 4. Express 3● 3● 3● 5● 5 using exponents. 5. Find the prime factorization of 180. Express your answer in exponential form. 6. Write ~~ ~~2490 in simplest form. 7. Write the ratio of 14 days to 3 weeks in simplest form. 8. Write the ratio of 4 teachers to 134 students in simplest form. 9. Write the rate of 400 miles in 8 hours in simplest form. 10. Find the LCM for8,12, and 36 . 11. Find the LCD for 1 , 1 , and 1 . 5 4 9 12. Enter the correct symbol (<, >, =) . ~~ ~~34~~ ~~ ? 1115 3 5 13. Add or subtract. ~~ ~~ + ~~ ~~ 16 16 25 17 14. Add or subtract. ~~ ~~ − ~~ ~~ 64 64 1 3 15. Add or subtract. 4 ~~ ~~ − 2 ~~ ~~ 4 4 3 4 16. Add or subtract. ~~ ~~ + ~~ ~~ 12 50 7 5 17. Add or subtract. ~~ ~~ − ~~ ~~ 18 24 18. Add or subtract. 41− 23 ~~ ~~37 12 14 19. Multiply. ~~ ~~ ● ~~ ~~56 42 5 3 20. Multiply. 1 ~~ ~~ ●~~ ~~16 4

FAQs

How are the practice problems organized in this document?

The practice problems are grouped by units (UNIT 1 through UNIT 9), covering progressively broader mathematics topics. Each unit has a corresponding answer section later in the document.

What topics are included across UNIT 1 to UNIT 9?

The units cover operations with positive fractions; positive decimals and percents; algebra basics; first degree equations and inequalities in one variable; linear equations/inequalities and systems in two variables; exponents, factoring, and polynomial equations; rational expressions and equations; rational exponents and radicals; and functions with quadratic equations and parabolas.

Is there additional study support besides the questions and answers?

Yes. The document includes links to objectives for each unit and links to free resources to help with preparation for the Virginia Placement Test for mathematics.

Sep 26, 2026

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