Grade 7 math in the shares of Pennsylvania's test design, from unit rates to probability, steps under every answer.
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Unofficial practice questions, not affiliated with the Pennsylvania Department of Education. Bank checked October 13, 2026.
The real test: PSSA mathematics, grade 7
Questions
43
Core items
43, worth 52 points: 40 multiple-choice or technology-enhanced items worth 1 point each and 3 open-ended items worth 4 points each.
Items that do not count
Each form adds 8 multiple-choice or technology-enhanced items and 1 open-ended item for field testing and psychometric use.
Sections
Two. Each has 24 multiple-choice or technology-enhanced items and 2 open-ended items, with an estimated testing time of 78 minutes.
Reporting categories
Ratios and Proportional Relationships and Expressions and Equations 24 to 28% of the core each; Geometry 18 to 22%; The Number System and Statistics and Probabi
Calculator
In grades 4 to 8 only a portion of the test is non-calculator. Devices with wireless links or a computer algebra system are not permitted.
Results
Four performance levels: advanced, proficient, basic and below basic.
At 6 a.m. the temperature was −4.5°F. It rose 11.2 degrees by noon and then fell 8 degrees by evening. What was the evening temperature?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.1
The lowest point of a canyon trail is 86 feet below the trailhead and the highest is 142 feet above it. What is the difference in height between the two points?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.1
On a horizontal number line, an arrow starts at −3 and moves 7 units to the left. Which equation does the arrow show?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.2
The price of a share fell by $13.50 in all over 6 days, by the same amount each day. What was the change in price each day?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.3
What is −3 1/3 × 1 1/5?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.3
What is −7/8 + 1/6?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.1
Which fraction has a decimal form that repeats and does not terminate?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-N.1.1.3
Show all 44 questions (37 more)
Ratios and Proportional Relationships 11
A graph shows dollars earned, y, against hours worked, x. It is a line through (0, 0) and (1, 14.5). What does the point (1, 14.5) mean?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.5
A restaurant bill is $48. The family adds an 18% gratuity. What is the total?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.6
A salesperson earns a 6% commission on sales. In one week she sells $3,450 of goods. What is her commission?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.6
A snail crawls 3/8 foot in 1/4 minute. What is its speed in feet per minute?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.1
A worker lays 3/4 square yard of tile in 1/6 hour. At that rate, how many square yards are laid in an hour?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.1
Apples cost $2.40 for 1.5 pounds, and the cost c is proportional to the weight n in pounds. Which equation shows the relationship?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.4
The cost of notebooks is proportional to the number bought: 4 cost $7.00 and 10 cost $17.50. What is the constant of proportionality, in dollars per notebook?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.3
The equation d = 62.5t gives the miles d a train travels in t hours. What is the constant of proportionality, and what does it mean?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.3
Four graphs are drawn on a coordinate plane. Which one shows a proportional relationship?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.2
Nia puts $1,200 in an account that pays 2.5% simple interest each year. How much is in the account after 3 years?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.6
Which table shows y proportional to x?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.A-R.1.1.2
Expressions and Equations 11
A driver is paid $40 a day plus $2.50 for each package delivered. Which inequality shows the number of packages p that brings the day’s pay to at least $115?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.2.2
A gym charges a $25 sign-up fee and $18.50 a month. Dana has paid $210 in all. For how many months has she paid?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.2.1
Club dues of $60 go up by 15%. Which calculation gives the new dues?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.1.1
Four friends each buy a movie ticket and a $3.50 snack. They pay $62 in all. What is the price of one ticket?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.2.1
Lena hikes 2 3/4 miles east, then 1.6 miles more east, then turns around and walks 0.85 mile back west. How far is she from where she started?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.1.1
Rosa multiplies 19.8 × 5.1 on paper and writes 1,009.8. Which estimate shows whether her answer is reasonable?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.3.1
The solution of −3x + 5 > 14 is graphed on a number line. What does the graph look like?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.2.2
Tickets cost $7.50 each and a group has $50. Solving 7.50t = 50 gives t ≈ 6.67. How many tickets can the group buy?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.2.3.1
Which expression is equivalent to (3.5a − 2) − (1.2a − 6)?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.1.1.1
Which expression is equivalent to −2/3(9x − 12)?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.1.1.1
Which is a factored form of 12y − 30?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.B-E.1.1.1
Geometry 8
A circular rug has a circumference of 10π feet. What is its area?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.2.2.1
A right prism has a right triangle as its base, with legs of 6 cm and 8 cm and a longest side of 10 cm. The prism is 10 cm tall. What is its volume?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.2.2.2
A right rectangular pyramid is sliced straight down through its top point, perpendicular to its base. What shape is the cross section?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.1.1.4
A triangle has angles of 35°, 35° and 110°. Which describes it?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.1.1.2
On a floor plan, 1/4 inch stands for 2 feet. A room is 2 inches by 1 1/2 inches on the plan. What is the real area of the room?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.1.1.1
Only one of these sets of three lengths can form a triangle. Which one?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.1.1.3
Two angles are supplementary. One measures (4x + 10)° and the other measures 50°. What is x?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.2.1.1
Two parallel lines are cut by a transversal. One of the angles formed measures 68°. What are the measures of its alternate interior angle and of the angle beside it on the same line?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.C-G.2.1.2
Statistics and Probability 7
A coin is flipped and a number cube with faces 1 to 6 is rolled. What is the probability of heads together with a number less than 3?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.3.2.3
A school of 600 students wants to know which lunch students like best. Which plan gives a random sample?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.1.1.1
A spinner has 8 equal sections numbered 1 to 8. What is the probability that it does not land on a multiple of 3?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.3.2.2
A thumbtack is tossed 250 times and lands point up 160 times. Based on these tosses, what is the probability that it lands point up?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.3.2.1
Class A’s quiz scores have a mean of 82 and Class B’s have a mean of 76. Each class has a mean absolute deviation of 3. How does the difference between the means compare with the variability?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.2.1.1
In a random sample of 80 students at a school, 28 walk to school. The school has 640 students. What is the best estimate of how many walk?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.1.1.2
Which probability describes an event that is neither likely nor unlikely?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 7 (April 2014), eligible content M07.D-S.3.1.1
Forty-four grade 7 math questions for Pennsylvania's PSSA, split across five reporting categories as the state's test design splits the real test. Unofficial: none comes from a test or a sampler. Not affiliated with the Pennsylvania Department of Education.
Read the full guide
The five reporting categories in 7th grade
Ratios and Proportional Relationships and Expressions and Equations are the two largest, about a quarter each: unit rates with fractions, percent problems, linear expressions, equations and inequalities. Geometry covers scale drawings, triangles, angles, circles and prisms. The Number System is operations with negative numbers and fractions. Statistics and Probability covers random samples and chance.
What an answer shows
The working comes first. Then comes a code such as M07.A-R.1.1.6, the line of Pennsylvania's eligible content that the question practices. Where a wrong choice is a common slip, the answer says which slip.
The anchors say formulas are provided for circles and for area, volume and surface area, so practice picking the right one.
Questions and answers
How many questions are on the 7th grade math PSSA?
43 count: 40 one-point items that are multiple choice or technology-enhanced, plus 3 open-ended items worth four points each, for 52 points. Nine more items on each form are tried out and not scored.
Are there PSSA practice tests for 7th grade in other subjects?
Seventh graders take two PSSA tests, English language arts and mathematics. Science is tested in grades 5 and 8 only. This page is math; the department posts its own samplers on its PSSA page.
How long is the 7th grade math PSSA?
It comes in two sections. The test design estimates 78 minutes for each, sets no time limit, and puts 24 multiple-choice or technology-enhanced items and 2 open-ended items in a section.
Can you use a calculator on the 7th grade math PSSA?
For most of the test, yes. The design keeps a non-calculator portion in grades 4 to 8. Under the state's calculator policy, phones, devices with wireless links and calculators with a computer algebra system stay out.