• 80 questions

CST Multi Subject Math Practice Test

Unofficial practice for Part Two: Mathematics of the NYSTCE Multi-Subject test for grades 1 to 6, each answer worked out.

Which expression is equivalent to 4(3x − 2) − 2(x − 5)?

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

Print covers the next 40 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 40 questions, 75 minutes.

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Unofficial practice questions, not affiliated with the New York State Education Department or Pearson. Bank checked October 7, 2026.

Next step All three parts of the Multi-Subject CSTMore math word problems: CBEST math

All 80 questions

Number and operations 6

  • A pattern starts at 5 and follows the rule "add 6": 5, 11, 17, … What is the 20th term? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.1 Operations and Algebraic Thinking
  • A school needs buses for 187 students. Each bus seats 44 students. What is the fewest buses that will seat everyone? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.1 Operations and Algebraic Thinking
  • What is 0.6 × 0.45? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.2 Number and Operations: Base Ten and Fractions
  • What is 3,849,612 rounded to the nearest ten thousand? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.2 Number and Operations: Base Ten and Fractions
  • What is −3/4 − (−5/6)? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.2 Number and Operations: Base Ten and Fractions
  • Which expression is equivalent to 4(3x − 2) − 2(x − 5)? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0001, 1.1 Operations and Algebraic Thinking
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Ratios, proportional relationships and number systems 30

  • 18 is what percent of 48? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A $60 pair of shoes is marked 25% off, and 8% sales tax is then charged on the sale price. What is the total? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A block has a mass of 540 grams and a volume of 200 cubic centimeters. What is its density in grams per cubic centimeter? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • A faucet drips 15 milliliters of water each minute. How many liters does it drip in 8 hours? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A line through the origin passes through (4, 10). Which equation describes it? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A printer prints 156 pages in 6.5 minutes. At that rate, how many pages does it print each minute? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A salesperson earns $300 a week plus a 4% commission on sales. What is the pay for a week with $18,500 in sales? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • A square garden has an area of 196 square feet. What is its perimeter? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Enrollment rises from 250 students to 290. What is the percent increase? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • Every side of a rectangle is made 2.5 times as long. By what number is its area multiplied? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • Five pounds of apples cost $8.75. At the same price per pound, what do 8 pounds cost? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • For x greater than 0, what is the cube root of x⁶ multiplied by the square root of x⁴? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Green paint is mixed from blue and yellow in the ratio 3 : 5. How many liters of blue are in 40 liters of green? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • If x³ = 125/8, what is x? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • On a line, a slope triangle drawn between (0, 1) and (2, 4) has a run of 2 and a rise of 3. A second slope triangle on the same line has a run of 10. What is its rise? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • On a map, 1 inch stands for 40 miles. Two towns are 3.25 inches apart on the map. How far apart are they? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • Simplify (2x³)⁴ ÷ (4x⁵). NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Three pounds of rice cost $7.20, five pounds cost $12.00 and eight pounds cost $19.20. What is the constant of proportionality in dollars per pound? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • What is (3 × 10⁴) × (2.5 × 10⁻⁷)? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • What is (7⁰ + 2³)²? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • What is 5.2 × 10⁵ + 3 × 10⁴? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • What is 5⁻² × 10³? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • What is 12.5% of 360? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships
  • What is 27 raised to the power −2/3? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • What is √50 to the nearest tenth? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Which expression equals √72 in simplest radical form? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Which fraction equals 0.8333…, in which the 3 repeats? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Which fraction has a decimal form that ends? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Which of these is a rational number? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.2 Rational and Real Number Systems
  • Which table shows a proportional relationship between x and y? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0002, 2.1 Ratios and Proportional Relationships

Algebra, measurement, geometry and data 34

  • A 13-foot ladder leans against a wall with its foot 5 feet from the wall. How high up the wall does it reach? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A box plot shows a minimum of 12, a lower quartile of 18, a median of 25, an upper quartile of 31 and a maximum of 40. About what share of the data lies between 18 and 31? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • A circle has a circumference of 10π centimeters. What is its area? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A culture of 500 bacteria doubles every 3 hours. How many bacteria are there after 12 hours? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A person 6 feet tall casts a 4-foot shadow. At the same moment a tree casts a 22-foot shadow. How tall is the tree? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A phone plan costs $22 a month plus $0.15 for each text message. A monthly bill is $31. How many messages were sent? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • A quadratic polynomial has zeros at −2 and 5. Which could it be? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • A rectangle 10 meters by 6 meters has a right triangle with legs of 6 meters and 8 meters attached along its 6-meter side. What is the total area? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A rectangle has vertices at (1, 1), (7, 1), (7, 5) and (1, 5). What is its perimeter? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A room is 12 feet by 15 feet. How many square yards of carpet cover the floor? (1 yard = 3 feet) NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • A school wants to estimate what share of its 600 students walk to school. Which sample best supports a conclusion about the whole school? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • A spinner with four equal sections numbered 1 to 4 is spun twice. What is the probability that the two numbers add to 5? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • A student averages 82 on four tests. What score on a fifth test raises the average to 84? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • A table of a linear function shows x = 0, 2, 4 and y = 7, 13, 19. Which equation fits it? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Adult tickets cost $9 and child tickets cost $5. A group buys 40 tickets for $288. How many adult tickets did it buy? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Completing the square rewrites x² + 6x − 7 = 0 as (x + 3)² = k. What is k? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • The function f(x) = x² + 3 is defined for all real numbers x. What is its range? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • How many lines of symmetry does a regular hexagon have? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • If 3x + 2y = 16 and x = y + 2, what is x? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Maya has $50. She buys an $18 bus pass and spends the rest on snacks at $2.50 each. What is the greatest number of snacks she can buy? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Of 80 students, 30 play a sport and an instrument, 20 play only a sport, 18 play only an instrument and 12 do neither. What fraction of the instrument players also play a sport? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • Plan A starts at $200 and adds $15 each week. Plan B starts at $10 and doubles each week. After 6 weeks, which plan holds more, and by how much? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Solve 12 ÷ (x − 2) = 3. NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • Triangle ABC is rotated 90° counterclockwise about the origin. Where does the vertex A(2, 5) land? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • What are the solutions of 2x² − 8x = 10? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • What is (3x² − 2x + 4) − (x² + 5x − 6)? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • What is the greatest value of f(x) = −(x − 2)² + 9? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • What is the mean absolute deviation of 2, 4, 6, 8, 10? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • What is the measure of each interior angle of a regular octagon? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • What is the median of 4, 9, 7, 12, 6, 10? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.3 Data, Statistics, and Probability
  • What is the product (x − 4)(x² + 2x − 3)? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra
  • What is the volume of a box that is 2.5 feet by 2 feet by 1.2 feet? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.2 Measurement and Geometry
  • Which is the factored form of 6x² + 7x − 3? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0003, 3.1 Algebra

Instruction in mathematics 10

  • A class counts pets: 8 dogs, 5 cats and 3 fish. In a picture graph each picture stands for 2 pets. How many pictures show the cats? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.3 Instruction in Measurement and Data
  • A student computes 503 − 267 and writes 364. What did the student most likely do? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.1 Instruction in Number and Operations and Algebraic Thinking
  • A student is asked for the perimeter of a rectangle 4 units by 6 units and answers 24. Which question from the teacher goes to the cause? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.3 Instruction in Measurement and Data
  • A student says 0.45 is greater than 0.5 "because 45 is greater than 5". Which next step addresses the error most directly? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.1 Instruction in Number and Operations and Algebraic Thinking
  • A student says 1/8 is greater than 1/6 "because 8 is greater than 6". Which representation addresses the error most directly? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.2 Instruction in Fractions and Ratios and Proportional Relationships
  • In the standard algorithm for 36 × 24, the second row of the work comes from the digit 2. What product does that row stand for? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.1 Instruction in Number and Operations and Algebraic Thinking
  • On an exit ticket, 6 of 24 students place 3/4 on a number line from 0 to 1 by counting tick marks, not the spaces between them. What is the most fitting next step? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.2 Instruction in Fractions and Ratios and Proportional Relationships
  • Paint mix A uses 2 parts red to 3 parts white. A student says 4 red to 5 white is the same shade "because 2 was added to each". Which mix is the same shade as A? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.2 Instruction in Fractions and Ratios and Proportional Relationships
  • Which sequence moves from concrete to abstract when teaching 3 × 14? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.1 Instruction in Number and Operations and Algebraic Thinking
  • Which story problem fits 3/4 ÷ 1/8? NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017: Part Two, Competency 0004, 4.2 Instruction in Fractions and Ratios and Proportional Relationships

How this list was compiled: Our own questions, written to Part Two: Mathematics (field 222) of the NYSTCE Multi-Subject: Teachers of Childhood (221/222/245) Assessment Design and Framework, October 2017 (https://www.nystce.nesinc.com/content/docs/NY_fld221_222_245_objs.pdf, read 2026-10-07): Number and Operations 3 selected-response items of 40, Ratios and Proportional Relationships and Number Systems 15, Algebra, Measurement, Geometry, and Data 17, Instruction in Mathematics 5. The bank holds twice those numbers: 6, 30, 34 and 10. Every answer is mathematics worked from what the question prints, and each one was worked out again on 2026-10-07. Licence: Questions, choices and explanations are original work of this site.

How it works

This CST Multi-Subject math practice test follows Part Two: Mathematics of New York's framework for Teachers of Childhood (Grade 1–Grade 6). It is unofficial and not affiliated with, endorsed by or sponsored by the New York State Education Department or Pearson.

Read the full guide

What Part Two covers

The framework spreads its 40 selected-response questions over number and operations (3), ratios, proportional relationships and number systems (15), algebra, measurement, geometry and data (17) and instruction in mathematics (5). This bank holds twice each number.

Timing

The framework plans up to 75 minutes for the 40 questions and up to 60 for one written response, 135 minutes in all. Exam mode asks 40 questions in 75 minutes. The written response, an analysis of student work, is not marked here.

How answers are checked

Each explanation shows the working, and every computed answer is worked out again from the numbers in the question.

  • Most Instruction questions start from a student's wrong answer. Work the problem the student's way first, then the right way.

Questions and answers

Is the math on the Multi-Subject CST only elementary school math?

No. Part Two is for teachers of grades 1 to 6, but its framework lists content well beyond those grades: rational exponents, scientific notation, quadratics, systems of equations, functions, similarity and probability models.

Can you use a calculator on the Multi-Subject math test?

Yes. The test's own page says a standard four-function calculator is provided on screen during Part Two: Mathematics. It also links a page of definitions and formulas for the part.

How is Part Two of the Multi-Subject CST scored?

The selected-response questions count for 80% of the Part Two score and the written response for 20%, the framework says. The test's own page gives 520 as the passing score for the part, a scaled score and not a count of right answers.

Are these real NYSTCE math questions?

No. Every question is our own, written to the Part Two competencies of New York's framework. None is taken or reworded from the real test or from the sample questions in its preparation materials.

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