Number sense, operations, statistics and probability 20
A baker has 2 3/4 cups of pecans, and one batch of pralines uses 5/8 cup. How many batches can the baker make with the pecans on hand?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A box plot of quiz scores has a minimum of 52, a first quartile of 64, a median of 71, a third quartile of 80 and a maximum of 95. About what percent of the scores are 64 or higher?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
A committee of 3 students is chosen from a club of 8, and the order of choosing does not matter. How many different committees are possible?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
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Number sense, operations, statistics and probability, continued
A data set has a first quartile of 20 and a third quartile of 32. Using the 1.5 × IQR rule on the test's formula sheet, which of these values is an outlier?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
A drawer holds 6 black socks and 4 gray socks. Two socks are taken out without looking, one after the other, and the first is not put back. What is the probability that both are gray?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
A jacket marked $80 is sold at 25% off, and 7% sales tax is then charged on the sale price. What is the total paid?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A number cube is rolled 150 times and lands on 5 exactly 33 times. What is the experimental probability of rolling a 5?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
A printer prints 135 pages in 4.5 minutes. At the same rate, how long does it take to print 420 pages?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A sheet of foil is 9 × 10⁻² millimeters thick. How many sheets make a stack 3.6 × 10⁷ millimeters high? Give the answer in scientific notation.GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A student multiplies four pairs of numbers and sorts the products into rational and irrational. Which product belongs with the rational numbers?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A student rewrites (2³ × 2⁻⁵) ÷ 2⁻⁴ as a single power of 2. Which power is correct?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A student works out −3² + 4 × (−2)³ ÷ 8 and gets 5, but the value is −13. Which mistake explains the answer of 5?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
A teacher has 84 pencils and 126 erasers and wants to make identical kits that use all of both. What is the greatest number of kits she can make?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
Between which two consecutive whole numbers does √130 lie, and to which is it closer?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
Enrollment at a middle school rose from 480 students to 552 students. What was the percent change?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
One January day in Blue Ridge the low temperature was −7.5°C and the high was 4.25°C. How many degrees did the temperature rise from the low to the high?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
Seven students report their minutes of reading last night: 12, 15, 15, 18, 20, 22 and 73. By how much is the mean greater than the median?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
Two fair number cubes, each numbered 1 through 6, are rolled. What is the probability that the two numbers shown differ by exactly 1?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
Two shuttle buses leave a Macon depot together at 6:00 a.m. One returns to the depot every 18 minutes and the other every 24 minutes. When are both next at the depot at the same time?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0001 (numbers and operations)
What is the mean absolute deviation of the data set 4, 6, 7, 9, 14?GACE Middle Grades Math (4–8) (704) framework, Testlet 101 Number Sense, Number Operations, Statistics, and Probability (4–8), competency 0002 (statistics and probability)
Algebra and functions 15
A fence line must be perpendicular to the line y = (2/3)x − 1 and must pass through the point (4, 1). Which equation describes the fence line?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0003 (linear relations and applications)
A function machine g subtracts 4 from its input, and a machine f turns an input x into 2x² − 3x. The number 6 goes through g, and that result then goes through f. What comes out?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0001 (patterns, relations and functions)
A line has the equation 5x + 2y = 30. At which point does it cross the x-axis?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0003 (linear relations and applications)
A plumber charges a flat fee plus the same rate for each hour. A 2-hour job costs $155 and a 5-hour job costs $290. What is the flat fee?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0003 (linear relations and applications)
A rectangular flower bed is 6 feet longer than it is wide and covers 55 square feet. How wide is the bed?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0002 (algebraic techniques and applications)
A relation is a function when each input has exactly one output. Which relation below fails that test?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0001 (patterns, relations and functions)
A school play sold 140 tickets for $940 in all. Adult tickets cost $9 and student tickets cost $5. How many adult tickets were sold?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0002 (algebraic techniques and applications)
A tile pattern has 5 tiles in its first row, and each row after that has 3 times as many tiles as the row before it. How many tiles are in the first 5 rows together?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0001 (patterns, relations and functions)
An arithmetic sequence begins 7, 11.5, 16, 20.5. What is its 40th term?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0001 (patterns, relations and functions)
On a coordinate map a straight trail runs from the point (−3, 10) to the point (5, −2). What is the slope of the trail?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0003 (linear relations and applications)
What are the domain and range of f(x) = √(x − 3) + 2 over the real numbers?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0001 (patterns, relations and functions)
Which expression is equal to (4x³y⁻²)² ÷ (8x⁻¹y) for nonzero x and y?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0002 (algebraic techniques and applications)
Which product of two binomials is equal to 6x² − 7x − 20?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0002 (algebraic techniques and applications)
Which system of equations has no solution?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0003 (linear relations and applications)
Which values of x make the inequality −3(x − 4) > 18 true?GACE Middle Grades Math (4–8) (704) framework, Testlet 102 Algebra and Functions (4–8), competency 0002 (algebraic techniques and applications)
Measurement and geometry 15
A 6-foot post casts a 4.5-foot shadow at the same time that a pine tree casts a 33-foot shadow. How tall is the tree?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0002 (Euclidean geometry in two and three dimensions)
A ball has a diameter of 18 centimeters. What is its volume, in terms of π?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0001 (measurement principles, procedures and applications)
A circle has a radius of 12 centimeters. What is the length of the arc cut off by a central angle of 150°?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0001 (measurement principles, procedures and applications)
A marker at (5, −2) on a design grid is turned 90° counterclockwise about the origin. Where does the marker land?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0003 (coordinate and transformational geometry)
A rectangular garden bed measures 2.8 meters by 4.5 meters. How long is its diagonal?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0002 (Euclidean geometry in two and three dimensions)
A sprinkler delivers 2.5 liters of water each second. How many cubic meters of water is that in one hour? (1 cubic meter = 1,000 liters)GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0001 (measurement principles, procedures and applications)
A student has straws cut to several lengths, in centimeters. Which three straws can be joined end to end to form a triangle?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0002 (Euclidean geometry in two and three dimensions)
A trapezoid has parallel sides of 14 meters and 22 meters and a height of 9 meters. What is its area?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0001 (measurement principles, procedures and applications)
A triangle with a vertex at (−6, 9) is dilated about the origin with a scale factor of 2/3. Where is the image of that vertex?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0003 (coordinate and transformational geometry)
An exterior angle of a triangle measures 115°. The two interior angles that are not next to it measure (3x + 5)° and (2x + 10)°. What is the measure of the third interior angle?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0002 (Euclidean geometry in two and three dimensions)
The interior angles of a polygon add up to 1,620°. How many sides does the polygon have?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0002 (Euclidean geometry in two and three dimensions)
On a town map with coordinates in blocks, the library is at (−1, 2) and the school is at (7, −4). What is the straight-line distance between them?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0003 (coordinate and transformational geometry)
Point P(4, −3) is reflected across the y-axis, and its image is then translated 2 units up. Where is the final image?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0003 (coordinate and transformational geometry)
Two similar solids have corresponding edges in the ratio 2 : 5. The smaller solid has a volume of 16 cubic centimeters. What is the volume of the larger?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0001 (measurement principles, procedures and applications)
What is the midpoint of the segment with endpoints (−3, 8) and (9, −2)?GACE Middle Grades Math (4–8) (704) framework, Testlet 103 Measurement and Geometry (4–8), competency 0003 (coordinate and transformational geometry)
How this list was compiled: Our own questions, written to the framework of the GACE Middle Grades Math (4–8) assessment (704) on the GACE website of the Evaluation Systems group of Pearson, https://www.gace.es.pearson.com/studyguide/framework/704 and https://www.gace.es.pearson.com/test/704, read 2026-10-09: three testlets of about 40, 30 and 30 selected-response questions (Number Sense, Number Operations, Statistics, and Probability; Algebra and Functions; Measurement and Geometry), 100 in all, with competency shares of 62.5/37.5% in the first testlet and a third each in the other two. This bank holds 20, 15 and 15, split 12/8, 5/5/5 and 5/5/5. Formulas named in the explanations are on the test's public reference sheet, Middle Grades Math (4–8) Formulas and Notations, https://www.gace.es.pearson.com/static/docs/GT704_Formulas.pdf. Every answer is arithmetic or reasoning from the numbers in the question, and each was worked out a second time. Licence: Questions, choices and explanations are original work of this site.
How it works
This free GACE Middle Grades Math practice test follows Middle Grades Math (4–8), assessment 704: 50 questions of our own, each worked out. It is unofficial and not affiliated with the Georgia Professional Standards Commission or Pearson.
Read the full guide
The three testlets
Number sense, operations, statistics and probability fill testlet 101, about 40 of the 100 questions. Algebra and functions (102) and measurement and geometry (103) take about 30 each. This bank halves those counts, competency by competency: 20, 15 and 15.
Clock and exam mode
Testlet 101 runs 90 minutes and the other two 60 each, a little over two minutes a question. Exam mode gives these 50 questions 105 minutes.
The formula sheet
The test shows a Formulas and Notations sheet on screen, so percent change, the 1.5 × IQR outlier rule and the volume of a sphere are there to use, not to memorise. Where an answer rests on the sheet, the explanation says so.
Numbers and operations is the largest competency: 62.5% of the first testlet, about a quarter of the whole test.
Questions and answers
Is this the middle school math GACE practice test?
Yes. Georgia calls the certificate field Middle Grades, and the test is Middle Grades Math (4–8), code 704. Every question here is our own, written to its framework; none is taken or reworded from the real test or its sample questions.
Is there a GACE middle school math study guide?
The GACE website publishes one for test 704, built round the same framework of three testlets and eight competencies that the questions here follow.
How many questions are on the GACE Middle Grades Mathematics test?
One hundred, all selected-response, across three testlets. Testing time adds up to 3 hours 30 minutes, and the GACE site adds 15 minutes per testing session for a tutorial and a nondisclosure agreement.
What is a passing score on the GACE Middle Grades Math test?
To pass, a candidate takes all three testlets, meets the minimum (the floor) on each, and reaches an assessment-level score of 220. That score is not a percent, so exam mode here reports the number right and stops there.
Can you use a calculator on the GACE Middle Grades Math test?
The GACE site lists an on-screen scientific calculator and a Formulas and Notations sheet as reference materials for test 704, provided on screen for all three testlets.