A jacket priced at $80 is marked down 25%. Later the sale price is raised by 25%. What is the final price?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0001 (mathematical problem-solving, communication and reasoning)
A peach grower near Fort Valley packs 1,260 peaches into boxes that hold 24 each. How many full boxes are packed, and how many peaches are left over?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0001 (mathematical problem-solving, communication and reasoning)
A student claims: “The sum of two odd numbers is always odd.” Which equation is a counterexample?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0001 (mathematical problem-solving, communication and reasoning)
How many positive divisors does 72 have?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0002 (numbers and number theory)
One bus leaves a depot every 12 minutes and another every 18 minutes. Both leave at 8:00 a.m. When do they next leave at the same time?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0002 (numbers and number theory)
Show all 58 questions (53 more)
Mathematical processes and number sense, continued
What is the product (5 − 2i)(1 + 3i)?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0002 (numbers and number theory)
Which of these numbers is irrational?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0002 (numbers and number theory)
Which statement is logically equivalent to “If a quadrilateral is a square, then it is a rectangle”?GACE Mathematics (6–12) (711) framework, Testlet 209 Mathematical Processes and Number Sense (6–12), competency 0001 (mathematical problem-solving, communication and reasoning)
Algebra and functions 12
A geometric sequence starts 3, 6, 12, … What is the sum of its first 6 terms?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0002 (advanced functions)
A north Georgia town of 12,000 people grows 5% each year. What is its population after 2 years?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0002 (advanced functions)
A plumber charges a flat call fee plus an hourly rate. A 2-hour job costs $155 and a 5-hour job costs $320. What is the flat call fee?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
A sample of 80 mg has a half-life of 6 hours. How much remains after 18 hours?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0002 (advanced functions)
For which values of k does x² + kx + 16 = 0 have no real solutions?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
If f(x) = 3x − 5, what is f⁻¹(10)?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0002 (advanced functions)
What are the asymptotes of f(x) = (2x + 6) ÷ (x − 4)?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0002 (advanced functions)
What are the zeros of f(x) = x³ − 3x² − 4x?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
What is the remainder when p(x) = x³ − 4x² + 2x + 5 is divided by x − 3?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
What is the solution of the system 2x + 5y = 1 and x − y = 4?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
What is the vertex of the parabola f(x) = 2x² − 12x + 7?GACE Mathematics (6–12) (711) framework, Testlet 210 Algebra and Functions (6–12), competency 0001 (linear, quadratic and higher-order polynomial functions)
Measurement and geometry 10
A 26-foot ladder leans against a wall with its foot 10 feet from the wall. How high up the wall does it reach?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
A car travels 45 miles per hour. What is its speed in feet per second? (1 mile = 5,280 feet)GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0001 (measurement principles and procedures)
A central angle of a circle measures 84°. An inscribed angle intercepts the same arc. What is the measure of the inscribed angle?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
A circle has its center at (2, −1) and passes through the point (5, 3). What is its equation?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
A cone has a radius of 6 cm and a height of 10 cm. What is its volume?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
A rectangular field measures 120 yards by 50 yards. What is its area in square feet?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0001 (measurement principles and procedures)
A road map of Georgia uses a scale of 1 inch to 25 miles. Two towns are 6.4 inches apart on the map. How far apart are they?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0001 (measurement principles and procedures)
The point (3, −2) is reflected across the line y = x. What are the coordinates of its image?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
Two similar triangles have corresponding sides in the ratio 2 : 5. The smaller has an area of 12 cm². What is the area of the larger?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0001 (measurement principles and procedures)
What is the measure of each interior angle of a regular 12-sided polygon?GACE Mathematics (6–12) (711) framework, Testlet 211 Measurement and Geometry (6–12), competency 0002 (Euclidean geometry in two and three dimensions)
Trigonometry and calculus 8
A ball's height in feet after t seconds is h(t) = −16t² + 96t + 4. When does it reach its greatest height?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0002 (essential concepts in calculus)
From a point on level ground 50 m from the base of a tower, the angle of elevation to the top is 60°. About how tall is the tower?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0001 (trigonometric functions)
If f(x) = 2x³ − 3x² + 5, what is f′(2)?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0002 (essential concepts in calculus)
In a right triangle, sin θ = 5/13 for an acute angle θ. What is tan θ?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0001 (trigonometric functions)
What are the amplitude and period of y = 4 sin(2x) − 1?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0001 (trigonometric functions)
What is 210° in radians?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0001 (trigonometric functions)
What is the limit of (6x² + x) ÷ (2x² − 5) as x approaches infinity?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0002 (essential concepts in calculus)
What is the value of the definite integral of 4x³ from x = 1 to x = 2?GACE Mathematics (6–12) (711) framework, Testlet 212 Trigonometry and Calculus (6–12), competency 0002 (essential concepts in calculus)
Statistics and probability 8
A club has 6 juniors and 4 seniors. Two members are chosen at random, one after the other, without replacement. What is the probability that both are seniors?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0002 (principles and techniques of probability)
A high school wants to estimate the share of all its students who ride the bus. Which sample is most likely to be representative?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0001 (principles and techniques of statistics)
A school raffle sells 200 tickets at $2 each, and one ticket wins a $100 prize. What is the expected net gain for the buyer of one ticket?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0002 (principles and techniques of probability)
A spinner has 8 equal sections numbered 1 to 8. It is spun twice. What is the probability that both spins land on a number greater than 6?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0002 (principles and techniques of probability)
Exam scores have a mean of 70 and a standard deviation of 8. What is the z-score of a score of 86?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0001 (principles and techniques of statistics)
Five test scores have a mean of 82. Four of the scores are 75, 80, 88 and 90. What is the fifth score?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0001 (principles and techniques of statistics)
For summer months in one Georgia town, a line of best fit predicts the monthly electric bill y in dollars from the average daily high x in °F: y = 2.5x − 110. What does the slope mean?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0001 (principles and techniques of statistics)
In how many ways can a committee of 3 be chosen from 8 people?GACE Mathematics (6–12) (711) framework, Testlet 213 Statistics and Probability (6–12), competency 0002 (principles and techniques of probability)
Financial literacy 12
$5,000 is deposited at 4% interest compounded once a year. What is the balance after 2 years?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0003 (investing and the management of credit and debt)
A $2,400 loan charges 6% simple annual interest. How much interest is owed over 3 years?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0003 (investing and the management of credit and debt)
A 12-ounce bag of Georgia pecans costs $9.60 and a 20-ounce bag costs $15.00. Which is the better buy per ounce?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0001 (financial responsibility, decision-making and planning)
A credit card charges interest each month at one-twelfth of its 18% annual percentage rate. What is one month's interest on a $1,200 balance?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0003 (investing and the management of credit and debt)
A health plan has a $2,000 deductible and then 20% coinsurance. The year's first covered bill is $7,000. How much of that bill does the member pay?HealthCare.gov glossary, Deductible and Coinsurance (the terms; the arithmetic is recomputed); GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0002 (tools for informing consumers and managing risk)
A lender checks a number that predicts how likely a borrower is to pay a loan back on time. What is this number called?Consumer Financial Protection Bureau, What is a credit score? and What is a credit report? (https://www.consumerfinance.gov/ask-cfpb/what-is-a-credit-report-en-309/); GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0002
A pay stub shows gross pay of $2,500.00 and deductions of $275.00 for federal income tax, $191.25 for Social Security and Medicare, and $120.00 for health insurance. What is the net pay?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0001 (financial responsibility, decision-making and planning)
A student wants $4,500 for a down payment in 18 months and has $900 saved already. How much must be saved each month?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0001 (financial responsibility, decision-making and planning)
An investor spreads money among many different investments so that a loss in one may be made up by the others. What is this strategy called?Investor.gov (U.S. Securities and Exchange Commission), glossary: Diversification; GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0003 (investing and the management of credit and debt)
In a health insurance plan, what is the premium?HealthCare.gov glossary, Premium (and Deductible, for the copayment and coinsurance definitions); GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0002 (tools for informing consumers and managing risk)
Monthly take-home pay is $3,200. Rent takes 30% and 15% goes to savings. How much is left for everything else?GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0001 (financial responsibility, decision-making and planning)
Which of these is covered by FDIC deposit insurance at an FDIC-insured bank?FDIC, Understanding Deposit Insurance (what is covered and not covered); GACE Mathematics (6–12) (711) framework, Testlet 501 Financial Literacy, competency 0002 (tools for informing consumers and managing risk)
How this list was compiled: Our own questions, written to the framework of the GACE Mathematics (6–12) assessment (711) on the GACE website of the Evaluation Systems group of Pearson, https://www.gace.es.pearson.com/studyguide/framework/711 and https://www.gace.es.pearson.com/test/711, read 2026-10-07: six testlets of about 20, 30, 25, 20, 20 and 30 selected-response questions (Mathematical Processes and Number Sense; Algebra and Functions; Measurement and Geometry; Trigonometry and Calculus; Statistics and Probability; Financial Literacy), 145 in all. This bank holds 8, 12, 10, 8, 8 and 12, which is 40% of each testlet. Every numeric answer was worked out a second time from the numbers in the question. The four Financial Literacy questions that rest on a definition name the public page it was read on (FDIC, CFPB, Investor.gov, HealthCare.gov), read 2026-10-07. Licence: Questions, choices and explanations are original work of this site.
How it works
This free GACE math practice test follows Mathematics (6–12), assessment 711, the content test for secondary teachers: 58 questions of our own, each worked out. It is unofficial and not affiliated with, endorsed by or sponsored by the Georgia Professional Standards Commission or Pearson.
Read the full guide
What the test covers
The framework lists six testlets: mathematical processes and number sense (about 20 questions), algebra and functions (30), measurement and geometry (25), trigonometry and calculus (20), statistics and probability (20) and financial literacy (30). This bank holds 8, 12, 10, 8, 8 and 12, the same shares.
Timing
Each testlet has its own clock: 60 minutes for algebra and for geometry, 45 for each of the other four. Exam mode gives 120 minutes for the 58 questions, the same pace.
Financial literacy is about a fifth of the real test, and it is the one testlet without on-screen reference materials.
Those reference materials are a definitions and formulas sheet and a guide to the on-screen scientific calculator.
Questions and answers
How many questions are on the GACE math test?
Mathematics (6–12) has 145 selected-response questions in six testlets. The GACE site says test forms can include non-scored questions that are being tried out.
What is a passing score on the GACE math test?
The GACE site says a testlet-based assessment is passed by taking all the testlets, meeting the floor on each, and reaching an assessment-level score of 220 or higher. Exam mode here gives the number right and no pass verdict.
Is there a GACE math practice test PDF?
Yes. After a round, Print opens a paper test that can hold all 58 questions, with an answer key if you want one. Choose Save as PDF in the print window to keep the file.
Is this the GACE math 201 practice test?
No. This page follows Mathematics (6–12), assessment 711. On October 7, 2026 the GACE site listed no Program Admission assessment, said it is no longer required for entry into an educator preparation program, and used code 201 for a testlet of its Agriculture assessment.
Is this free GACE math practice test the real exam?
No. These are our own questions on the competencies the framework publishes. Nothing is taken or reworded from a real test or from the study guide's sample questions, and a score here says nothing about a score there.