A grain of pollen is 0.000082 meters wide. Write that width in scientific notation.Answer: 8.2 × 10⁻⁵ meters. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), f. scientific notation
A store takes 15% off a pair of boots priced at $64. What do the boots cost now?Answer: $54.40. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), b. fractions, decimals and percentages
Add 2/3 + 3/4.Answer: 17/12. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), b. fractions, decimals and percentages
Evaluate 8^(2/3).Answer: 4. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), e. rules of exponents, rational and negative exponents
Exactly one of these numbers cannot be written as a ratio of two integers. Which one?Answer: √18. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), a. real numbers
Show all 80 questions (75 more)
Real number systems, continued
What is the prime factorization of 180?Answer: 2² · 3² · 5. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), d. prime and composite numbers, prime factorization
Which fraction, in lowest terms, equals the decimal 0.625?Answer: 5/8. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), b. fractions, decimals and percentages
Which of these numbers belongs to the integers but not to the natural (counting) numbers?Answer: −15. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), a. real numbers
Which property of real numbers is shown by 3(x + 4) = 3x + 12?Answer: The distributive property. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: I. Real Number Systems (11% of the exam), c. operations with real numbers and their properties
Sets and logic 13
A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. What is A ∩ B?Answer: {3, 4}. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
The conditional statement p → q is false in exactly one case. Which one?Answer: p is true and q is false. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (conditional statements)
How many rows does a truth table need for a compound statement built from three simple statements p, q and r?Answer: 8. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (truth tables)
How many subsets does a set with 4 elements have, counting the empty set and the set itself?Answer: 16. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
Let p be a false statement and q a true one. Which of these compound statements is false?Answer: p ∧ q (p and q). Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (conjunction, disjunction, conditional, biconditional)
Of 100 students, 60 take math, 45 take art and 20 take both. How many take neither?Answer: 15. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
Set A has 12 elements, set B has 9 elements, and 4 elements are in both. How many elements are in A ∪ B?Answer: 17. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
When is the biconditional p ↔ q true?Answer: When p and q have the same truth value. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (biconditional statements)
Which list shows the set {x | x is a natural number less than 5}?Answer: {1, 2, 3, 4}. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), a. introduction to sets (set-builder notation)
Which set is a subset of {1, 2, 3, 4}?Answer: {2, 4}. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
Which statement is logically equivalent to ¬(p ∧ q), "not (p and q)"?Answer: ¬p ∨ ¬q (not p, or not q). Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (conjunction and disjunction, truth tables)
Which statement is the contrapositive of "If a shape is a square, then it has four sides"?Answer: If a shape does not have four sides, then it is not a square. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), c. logic (conditional statements)
With U = {a, b, c, d, e, f, g} as the universal set and V = {a, e}, which set is V′, the complement of V?Answer: {b, c, d, f, g}. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: II. Sets and Logic (16% of the exam), b. subsets, set operations, Venn diagrams
Metric system, conversions and geometry 10
A closed carton measures 5 inches by 4 inches by 3 inches. How many square inches of cardboard cover its six faces?Answer: 94. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), e. surface area and volume of 3D solid objects
A cyclist rides at 15 miles per hour. With 5,280 feet in a mile, how many feet does she cover each second?Answer: 22. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), b. conversions, including dimensional analysis
A hiking trail is 4.75 kilometers long. How long is it in meters?Answer: 4,750. Source: NIST, Metric (SI) Prefixes: kilo means 1000. DSST outline area III. Metric system, conversions and geometry (13% of the exam), a. metric and U.S. customary unit systems
A shelf is 30 inches wide, and one inch is 2.54 centimeters. How wide is the shelf in centimeters?Answer: 76.2. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), b. conversions between metric and U.S. customary units
A tablet holds 250 milligrams of medicine. How many grams is that?Answer: 0.25. Source: NIST, Metric (SI) Prefixes: milli means one-thousandth. DSST outline area III. Metric system, conversions and geometry (13% of the exam), a. metric and U.S. customary unit systems
Angles P and Q are supplementary, and angle P measures 112°. What is the measure of angle Q?Answer: 68°. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), c. properties of lines, angles and pairs of angles
Lines m and n are parallel, and a transversal crosses both. An angle at line m measures 118°. What is the measure of the corresponding angle at line n?Answer: 118°. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), c. properties of lines, angles and pairs of angles
One gallon is 4 quarts. How many quarts are in 2.5 gallons?Answer: 10. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), a. metric and U.S. customary unit systems
One mile is about 1.609 kilometers. About how many miles is a 5-kilometer race?Answer: 3.1. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), b. conversions between metric and U.S. customary units
What is the area of a circle with a radius of 3 centimeters?Answer: 9π square centimeters. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: III. Metric system, conversions and geometry (13% of the exam), d. perimeter and area of 2D geometric objects
Algebra, graphs and functions 9
A line passes through (−2, 7) and (3, −3). What is its slope?Answer: −2. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), c. linear functions and their graphs
A printer turns out 45 pages in 6 minutes. At that rate, how many pages does it print in 14 minutes?Answer: 105. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), b. proportions
A rectangle's width x, in feet, must satisfy x² − 3x − 54 = 0. Which two numbers solve the equation?Answer: 9 and −6. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), d. quadratic equations and functions
For which value of x is 7x + 5 = 3x − 11 true?Answer: x = −4. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), b. linear equations with one variable
The formula C = (5/9)(F − 32) changes degrees Fahrenheit to degrees Celsius. What is C when F = 95?Answer: 35. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), a. evaluation of formulas
The parabola f(x) = x² + 4x − 1 opens upward. At which point is its vertex, the lowest point?Answer: (−2, −5). Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), d. quadratic equations and functions
What is the value of 40 − 12 ÷ 4 × 3 + 2³?Answer: 39. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), a. order of operations
Where does the graph of y = −2x + 5 cross the x-axis?Answer: At x = 2.5. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), c. linear functions and their graphs
Which expression is equivalent to 5(x − 2) − 2(3x − 4)?Answer: −x − 2. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: IV. Algebra, graphs and functions (11% of the exam), a. simplifying expressions
Linear systems and inequalities 7
A theater sells adult tickets for $8 and child tickets for $5. It sells 30 tickets for $195. How many adult tickets did it sell?Answer: 15. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), a. linear systems of equations in two variables, applications
How is the inequality y > x + 2 drawn on a graph?Answer: A dashed line with the region above it shaded. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), b. graph linear inequalities in two variables
The lines y = −3x + 4 and y = −3x − 2 are drawn on one graph. How many points do they share?Answer: None. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), a. graph and solve linear systems of equations in two variables
Solve −3x + 2 > 11.Answer: x < −3. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), b. linear inequalities in one or two variables
Which ordered pair makes the inequality y ≥ 3x + 2 true?Answer: (−1, 0). Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), b. linear inequalities in one or two variables
Which pair of values satisfies both 2x + y = 13 and x − y = 2?Answer: x = 5, y = 3. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), a. linear systems of equations in two variables
Which point satisfies both x + y ≤ 6 and x ≥ 2?Answer: (3, 2). Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: V. Linear Systems and Inequalities (9% of the exam), c. systems of linear inequalities in two variables
Exponents, logarithms and financial literacy 17
$2,500 is placed in an account that pays 8% a year, compounded annually. How much is in the account after 2 years?Answer: $2,916. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), c. simple and compound interest
$5,000 is invested at 4% a year, compounded quarterly, for 3 years. Which expression gives the balance?Answer: 5,000(1 + 0.04/4)¹². Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), c. simple and compound interest
A $1,200 laptop is bought with $200 down and 12 monthly payments of $90. What is the finance charge?Answer: $80. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), d. installment buying
A $10,000 student loan charges 5% simple interest a year. No payment is made during 4 years of school. How much interest builds up in that time?Answer: $2,000. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), d. installment buying, including student loans
A $200,000 mortgage is repaid with 360 monthly payments of $1,200. How much interest is paid over the whole loan?Answer: $232,000. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), d. installment buying, including home buying
A buyer makes a 20% down payment on a $250,000 home. How much is the mortgage loan?Answer: $200,000. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), d. installment buying, including home buying
A laptop bought for $1,500 loses 20% of its value each year. What is it worth after 3 years?Answer: $768. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), b. logarithmic and exponential functions
A stock sells for $40 a share and pays a dividend of $2 a share each year. What is its dividend yield?Answer: 5%. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), e. investing in stocks and bonds
A town of 2,000 people grows so that its population triples every 10 years. What will the population be after 30 years?Answer: 54,000. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), b. logarithmic and exponential functions
Evaluate log₂ 64.Answer: 6. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), a. properties of logarithms
How many years does $800 take to earn $120 of simple interest at 5% a year?Answer: 3. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), c. simple and compound interest
If log₅ x = 3, what is x?Answer: 125. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), b. logarithmic and exponential functions
Solve 2^x = 32.Answer: x = 5. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), b. logarithmic and exponential functions
What does an investor do when buying a bond?Answer: Lends money to the issuer, which promises to pay interest. Source: Investor.gov (U.S. Securities and Exchange Commission), "Bonds" and "Stocks". DSST outline area VI. Exponents and Logarithms including Financial Literacy (21% of the exam), e. investing in stocks and bonds
What is the simple interest on $2,000 borrowed at 5% a year for 3 years?Answer: $300. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), c. simple and compound interest
Which expression equals 3 log x, for x greater than 0?Answer: log x³. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), a. properties of logarithms
Which single logarithm is equal to log 4 + log 9?Answer: log 36. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VI. Exponents and Logarithms including Financial Literacy (21% of the exam), a. properties of logarithms
Counting, probability and statistics 15
A bag holds 5 red and 3 blue marbles. One marble is drawn and kept out, and it is red. What is the probability that the next marble drawn is red?Answer: 4/7. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), d. odds and conditional probability
A club of 8 members elects a president, a vice president and a secretary. No one may hold two offices. How many results are possible?Answer: 336. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), b. permutations and combinations
A fair six-sided die is rolled twice. What is the probability that both rolls are a 6?Answer: 1/36. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), c. simple and compound events
A spinner has 8 equal sections numbered 1 to 8. What is the probability that it stops on a number less than 4?Answer: 3/8. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), c. simple and compound events
A traveler packs 4 shirts, 3 pairs of pants and 2 pairs of shoes. How many outfits of one shirt, one pair of pants and one pair of shoes are possible?Answer: 24. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), a. fundamentals of probability, including the counting principle
The eight values 2, 4, 4, 4, 5, 5, 7 and 9 are a whole population. What is the population standard deviation?Answer: 2. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), f. range, variance and standard deviation
The high temperatures on five days were 61, 64, 70, 72 and 78 degrees. What was the mean high temperature?Answer: 69 degrees. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), e. mean, median and mode
How many different committees of 3 people can be chosen from 10 people?Answer: 120. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), b. permutations and combinations
In how many different orders can 5 books be lined up on a shelf?Answer: 120. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), b. permutations and combinations
On a box plot, what does the box itself show?Answer: The middle 50% of the data, from the lower quartile to the upper quartile. Source: NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.3.7, Box Plot. DSST outline area VII. Counting, Probability Theory and Statistics (19% of the exam), g. graphical representation
One card is drawn from ten cards numbered 1 to 10. What is the probability that its number is odd or greater than 7?Answer: 7/10. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), c. simple and compound events
The probability of an event is 1/5. What are the odds in favor of the event?Answer: 1 to 4. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), d. odds and conditional probability
Six houses on one street sold for 180, 195, 210, 230, 250 and 400 thousand dollars. What was the median price, in thousands of dollars?Answer: 220. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), e. mean, median and mode
What is the mode of 2, 3, 3, 5, 7, 7, 7 and 9?Answer: 7. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), e. mean, median and mode
What is the range of 12, 5, 19, 8 and 14?Answer: 14. Source: Prometric, DSST Math for Liberal Arts fact sheet, content outline: VII. Counting, Probability Theory and Statistics (19% of the exam), f. range, variance and standard deviation
How this list was compiled: Our own questions, written to the content outline of the DSST Math for Liberal Arts fact sheet (Prometric, revised 1/2026, https://getcollegecredit.com/wp-content/uploads/2025/11/Math-for-Liberal-Arts-1.pdf, read 2026-10-08): real number systems 11%, sets and logic 16%, metric system, conversions and geometry 13%, algebra, graphs and functions 11%, linear systems and inequalities 9%, exponents and logarithms including financial literacy 21%, counting, probability theory and statistics 19%. The bank holds 9, 13, 10, 9, 7, 17 and 15 questions, the same shares of 80. Every answer is arithmetic, algebra or logic on what the question itself prints, recomputed on 2026-10-08; the four questions that rest on a definition name the public page it was read in (NIST, Investor.gov). Licence: Questions, choices and explanations are original work of this site.
How it works
This free DSST Math for Liberal Arts practice test has 80 questions of our own, as many as the real exam, each with its working. It is unofficial and not affiliated with Prometric, which owns the DSST program.
Read the full guide
Seven areas and their weights
The fact sheet (revised 1/2026, read October 8, 2026) weights them: exponents, logarithms and financial literacy 21%; counting, probability and statistics 19%; sets and logic 16%; metric system, conversions and geometry 13%; real number systems 11%; algebra, graphs and functions 11%; linear systems and inequalities 9%. The bank holds 17, 15, 13, 10, 9, 9 and 7 questions.
80 questions, 2 hours
The real exam allows 2 hours for its 80 questions, and exam mode here does the same.
How the math is written
Powers are written 2⁵ or 8^(2/3). ∩ and ∪ are intersection and union. ∧, ∨, → and ↔ are and, or, if-then and if-and-only-if, and ¬ is not.
Money questions are the largest area: simple against compound interest, down payments, finance charges, dividend yield.
A truth table for n simple statements has 2ⁿ rows, the same count as the subsets of a set with n elements.
Questions and answers
Is there a DSST Math for Liberal Arts study guide?
Prometric's free fact sheet gives the outline and three reference textbooks. On this page the topic filter turns that outline into seven short practice sets, and every answer shows its steps.
Can you use a calculator on the DSST Math for Liberal Arts exam?
Yes. The fact sheet says a non-programmable calculator may be used on this exam.
Is DSST Math for Liberal Arts the same as college algebra?
No. DSST has a separate Fundamentals of College Algebra exam. Math for Liberal Arts is broader: by its outline only 11% is algebra, graphs and functions, and sets, logic, geometry, finance and probability make up most of the rest.
How is the DSST Math for Liberal Arts exam scored?
Of its 80 questions, 75 are scored. The American Council on Education recommends 3 semester hours of lower-level credit for a score of 400, and each college sets its own policy.