• 50 questions

FTCE Math 5-9 Practice Test

Unofficial practice for FTCE Middle Grades Mathematics 5–9, from rational numbers and algebra to geometry, data and teaching practice.

Which list orders 5/8, 0.6, 2/3 and 62% from least to greatest?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Exam mode: 50 questions, 150 minutes.

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Unofficial practice questions, not affiliated with the Florida Department of Education or Pearson. Bank checked October 9, 2026.

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All 50 questions

Number sense, operations and proportionality 8

  • A batch of muffins takes 3/4 cup of flour. How many batches can be made from 5 1/4 cups? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 9
  • A car bought for $18,000 loses 15% of its value in the first year and 10% of what remains in the second. What is it worth after two years? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 6
  • Between which two numbers does √30 lie? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 3
  • One lighthouse flashes every 15 seconds and another every 20 seconds. They flash together at midnight. After how many seconds do they next flash together? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 5
  • What is (3.0 × 10⁵)(4.2 × 10⁻²) in scientific notation? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 4
Show all 50 questions (45 more)

Number sense, operations and proportionality, continued

  • What is the value of 18 − 2[7 − (1 − 4)²]? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 2
  • What is the value of 27^(2/3) × 4^(−1/2)? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 8
  • Which list orders 5/8, 0.6, 2/3 and 62% from least to greatest? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 1 (number sense, operations, and proportionality), skill 1

Algebra 15

  • $2,000 is invested at 5% interest compounded once a year. Which amount is in the account after 3 years? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 9
  • A ball is thrown so that its height in feet after t seconds is h = −16t² + 48t + 4. What is its greatest height? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 7
  • A table pairs x = 0, 1, 2, 3 with y = 5, 15, 45, 135. Which type of function fits the table? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 2
  • For f(x) = 2x² − 3x + 1, what is f(−2)? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 2
  • How is the graph of g(x) = (x + 2)² − 5 related to the graph of f(x) = x²? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 10
  • Three notebooks and two pens cost $9.50. One notebook and four pens cost $6.50. What does one notebook cost? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 6
  • What are the solutions of 2x² + 3x − 4 = 0? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 8
  • What are the solutions of x² − 4x − 45 = 0? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 8
  • What is the 30th term of the sequence 9, 14, 19, 24, …? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 1
  • What is the solution of |2x − 5| ≤ 7? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 4
  • Where is the vertex of the graph of y = |x − 3| + 2? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 4
  • Which equation is the line through (−2, 5) and (4, −1)? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 5
  • Which expression is equal to (2x³y)² · (3x⁻¹y²)? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 3
  • Which expression is equal to √72 + √18? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 3
  • Which line is perpendicular to y = (2/3)x − 4 and passes through (4, 1)? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 2 (algebra), skill 5

Geometry 10

  • A trapezoid has parallel sides of 7 cm and 13 cm and a height of 8 cm. What is its area? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 2
  • A triangle has sides of 9, 12 and 16. What kind of triangle is it? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 7
  • Each interior angle of a regular polygon measures 150°. How many sides does it have? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 8
  • How far apart are the points (−1, 3) and (11, −2) on the coordinate plane? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 5
  • The point (3, −5) is rotated 90° counterclockwise about the origin. Where is its image? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 9
  • Two angles of a triangle measure 35° and 55°, and no two sides are equal. How is the triangle classified? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 1
  • Two cylinders are similar, with heights in the ratio 2 to 3. The smaller holds 40 cm³. How much does the larger hold? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 6
  • What are the center and radius of the circle x² + y² + 8x − 2y − 8 = 0? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 11
  • What is the surface area of a closed box that measures 2 cm by 5 cm by 6 cm? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 3
  • Which set of lengths cannot be the sides of a triangle? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 3 (geometry), skill 7

Data analysis, statistics and probability 7

  • A bag holds 3 red and 5 green balls. One ball is drawn, put back, and a second is drawn. What is the probability that both are red? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 8
  • A line fitted to class data is y = 2.5x + 40, where x is hours studied and y is the test score. What does the y-intercept mean here? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 7
  • A school of 900 students wants to know which lunch its students prefer. Which sample supports the best inference about the whole school? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 5
  • A spinner has 4 equal sections, one of them blue. In 60 spins it lands on blue 18 times. How does that compare with the theoretical prediction? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 9
  • In a random sample of 60 of a school's 900 students, 21 ride a bicycle to school. What is the best estimate of how many students in the school do so? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 4
  • Six houses on one street sold for $210,000, $215,000, $220,000, $225,000, $230,000 and $700,000. Which measure best describes a typical price? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 2
  • What is the interquartile range of 4, 7, 7, 9, 10, 12, 21? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 4 (data analysis, statistics, and probability), skill 1

Student reasoning and instructional practice 10

  • A plumber charges a $45 call fee plus $60 for each hour. A bill comes to $225. Which equation gives the number of hours, h? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 1
  • A student multiplies 4.8 × 0.52 and writes 24.96. Which estimate should the student be asked to make to judge the result? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 3
  • A student says the sum of two odd numbers is always even "because 3 + 5 = 8 and 7 + 9 = 16." Which response gives a valid general argument? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 3
  • A student solves 3(x − 4) = 18 by writing 3x − 4 = 18 and then x = 22/3. What went wrong, and what is the solution? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 8
  • A student writes 1/2 + 1/3 = 2/5. Which fact would best help the student see that the answer cannot be right? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 8
  • According to the IES practice guide on students struggling with mathematics, what should intervention regularly include as one way to build fluency? Institute of Education Sciences, practice guide Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006), Recommendation 6. Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5, skill 2
  • Grade 7 students find the constant of proportionality for the pairs (2, 5), (4, 10) and (6, 15). Under what name does the same number return in grade 8? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 4
  • On a 24-student exit ticket about the area of a 6 by 4 rectangle, 18 students answer 20. What should the teacher conclude and do next? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 7
  • To teach x² + 5x + 6 = (x + 2)(x + 3), a teacher plans three stages. Which order moves from concrete to representational to abstract? Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5 (student reasoning and instructional practice), skill 6
  • Which practice does the IES practice guide on algebra recommend for getting students to analyze algebraic reasoning and strategies? Institute of Education Sciences, practice guide Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (NCEE 2015-4010), Recommendation 1. Written to FTCE Middle Grades Mathematics 5–9 (025) Competencies and Skills, competency 5, skill 5

How this list was compiled: Our own questions, written to the competencies and skills of FTCE Middle Grades Mathematics 5–9 (025) in the test information guide on the Florida Teacher Certification Examinations website, https://www.fl.nesinc.com/studyguide/FL_SG_obj_025_redev.htm (copyright 2023 State of Florida, Department of State), read 2026-10-09: approximately 50 multiple-choice questions in 2 hours 30 minutes, five competencies weighted 15, 30, 20, 15 and 20 percent. This bank holds 50: 8, 15, 10, 7 and 10. Every number in a question is made up for the question, and each computed answer was worked out a second time from the numbers in the question (2026-10-09). Two questions on instruction rest on practice guides of the Institute of Education Sciences, named and linked under them (each opened 2026-10-09). Licence: Questions, choices and explanations are original work of this site.

How it works

This free FTCE Math 5-9 practice test follows Middle Grades Mathematics 5–9 (025): 50 questions of our own across its five competencies, each worked out. It is unofficial and not affiliated with, endorsed by or sponsored by the Florida Department of Education or Pearson.

Read the full guide

Five competencies and their weights

Algebra carries about 30% of the test. Geometry carries 20%, and so does student reasoning and instructional practice. Number sense, operations and proportionality carries 15%, as does data analysis, statistics and probability. The bank holds 15, 10, 10, 8 and 7 questions to match.

Exam mode

Exam mode keeps the real test's length and time limit. Work it with a scientific calculator beside you.

How the answers were checked

Every computed answer was worked out a second time from the numbers in its question. Two questions on instruction rest on practice guides of the Institute of Education Sciences, linked under them.

  • No reference sheet is provided on the real test, so the area, volume and distance formulas and the quadratic formula have to be known.
  • A fifth of the test is about teaching: finding a student's error, judging an argument, choosing a representation.

Questions and answers

Is this FTCE Math 5-9 practice test free?

Yes: all 50 questions, the timed exam and the paper test, with no account. None is taken or reworded from a real test or from the sample questions in the test information guide.

Is there an FTCE Math 5-9 practice test PDF?

Yes. After a round, Print opens a paper test that can hold all 50 questions, with an answer key if you want one. Choose Save as PDF in the print window to keep the file.

How many questions are on the FTCE 5-9 math test?

Approximately 50, all multiple choice, in 2 hours 30 minutes, according to the exam's page on the FTCE site. That is three minutes a question, which is why this FTCE 5-9 math practice test keeps the same clock.

What score passes FTCE Middle Grades Mathematics 5-9?

A scaled score of at least 200. A scaled score is not a percent, so no practice test for FTCE Math 5-9 can turn a count of right answers into it, and exam mode here gives no pass verdict.

Can you use a calculator on the FTCE Math 5-9?

An on-screen scientific calculator is provided and candidates may not bring their own. The exam page adds that hand-held calculators may be requested.

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