• 90 questions

CST Math Practice Test

Unofficial practice for New York's Mathematics CST (004), number through calculus, in the framework's own proportions.

A complex number has modulus 4 and argument 150°. What is its rectangular form?

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Exam mode: 90 questions, 150 minutes.

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Unofficial practice questions, not affiliated with the New York State Education Department or Pearson. Bank checked October 10, 2026.

The real test: what its own page says

Fee
$122
Format
Computer-based test: 90 selected-response items and 1 constructed-response item.
Time
3 hours 45 minutes in all: 15 minutes for the tutorial and nondisclosure agreement, then 3 hours 30 minutes of testing.
Test dates
All year by appointment, Mondays to Saturdays, some holidays excepted.
Test sites
Across New York State and around the country.
Test features
A page of definitions and formulas.

Checked October 10, 2026 against the Mathematics CST (004) page of the NYSTCE site. Rules change, so confirm with the agency itself before your test.

The test's own page

Next step More calculus practiceCST Multi-Subject math practice

All 90 questions

Number and quantity 9

  • A and B are 2 × 2 matrices. A has rows (3, −2) and (1, 5). B has rows (4, 0) and (−1, 6). What is the entry in row 1, column 2 of the product AB? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator k
  • A boat points due north and moves at 24 km/h through the water. A current flows due east at 7 km/h. What is the boat's speed over the ground? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator i
  • A complex number has modulus 4 and argument 150°. What is its rectangular form? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator g
  • A pump moves 45 gallons of water each minute. About how many cubic feet does it move in one hour? (1 cubic foot = 7.48 gallons) NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator d
Show all 90 questions (86 more)

Number and quantity, continued

  • Let u = ⟨3, −4⟩ and v = ⟨−1, 2⟩. What is the magnitude of 2u + 3v? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator j
  • What are the solutions of x² − 6x + 13 = 0? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator h
  • What is the product (4 − 3i)(2 + 5i)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator f
  • What is the value of 27^(2/3) × 16^(−3/4)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator c
  • Which set, with the operation named, is a group? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0001 Number and Quantity, performance indicator l

Algebra 23

  • A cubic polynomial with real coefficients has zeros 2 and 1 + 3i. What is its third zero? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator f
  • A map has a scale of 1 : 25,000. Two towns are 7.2 cm apart on the map. How far apart are they on the ground? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator b
  • A plumber charges an $85 call fee plus $64 for each hour of work. A bill comes to $309. How many hours were billed? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator a
  • A school play sells adult tickets at $8 and student tickets at $5. It sells 240 tickets for $1,515. How many adult tickets were sold? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator h
  • A town of 12,000 people grows by 3% each year. Which equation gives its population P after t years? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator h
  • At which points do y = x² − 4x + 1 and y = x − 3 intersect? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator k
  • For x ≠ 3 and x ≠ −4, which expression equals (x² − 9)/(x² + x − 12)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator g
  • The graphs of y = |x − 2| and y = 4 are drawn on the same axes. At which x-values do they intersect? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator l
  • One pipe fills a tank in 6 hours and a second pipe fills it in 9 hours. With both pipes open, how long does the tank take to fill? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator b
  • What are the solutions of 2x² − 5x − 12 = 0? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator j
  • What is the coefficient of x² in the expansion of (2x − 3)⁴? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator e
  • What is the product (2x² − 3x + 1)(x + 4)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator e
  • What is the remainder when p(x) = 2x³ − 5x² + x − 7 is divided by x − 2? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator f
  • What is the solution of the system 2x + 3y = 7 and x − 4y = −13? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator k
  • What is the solution of −3(x − 4) ≥ 2x − 8? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator j
  • What is the solution set of √(x + 7) = x − 5? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator i
  • What is the sum of the first 10 terms of the geometric series 3 + 6 + 12 + …? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator d
  • Which equation is the line through (−2, 7) and (4, −5)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator c
  • Which expression equals 1/(x − 1) − 1/(x + 1)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator g
  • Which expression is equivalent to (x + 3)² − (x − 3)²? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator a
  • Which interval is the solution of x² − x − 6 < 0? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator l
  • Which is the complete factorization of 2x³ − 18x? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator d
  • Which is x² − 10x + 7 written by completing the square? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0002 Algebra, performance indicator d

Functions 19

  • A geometric sequence has a₂ = 12 and a₅ = 96. What is a₈? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator e
  • A sequence is defined by a₁ = 2 and aₙ = 3aₙ₋₁ − 1. What is a₄? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator a
  • A table gives y = 5, 15, 45, 135 for x = 0, 1, 2, 3. Which model fits the data exactly? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator g
  • An arithmetic sequence has a₅ = 17 and a₁₂ = 45. Which is its explicit formula? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator e
  • For f(x) = 2x² − 3x, which expression equals f(a + 1) − f(a)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator a
  • For f(x) = 3x − 2 and g(x) = x² + 1, which is (f ∘ g)(x)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator d
  • The graph of y = g(x) passes through (6, −1). Through which point must the graph of y = g(x − 5) + 7 pass? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator f
  • The height of a rider on a Ferris wheel, in meters, is h(t) = 18 + 15 sin(πt/20), with t in seconds. How long does one full turn take? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator j
  • Money is invested at 5% a year, compounded continuously. About how long does it take to double? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator h
  • sin θ = −8/17 and θ is in the third quadrant. What is tan θ? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator i
  • What are the solutions of 2 sin² x − sin x − 1 = 0 for 0 ≤ x < 2π? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator l
  • What is the average rate of change of f(x) = x³ − 2x on the interval from x = 1 to x = 3? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator b
  • What is the domain of f(x) = √(6 − 2x)/(x + 1)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator b
  • What is the inverse of f(x) = (3x − 2)/(x + 5)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator f
  • What is the solution of log₃ x + log₃ (x − 8) = 2? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator h
  • What is the vertex of the graph of f(x) = −2x² + 12x − 7? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator c
  • Where it is defined, which expression equals (1 − cos² x)/(sin x cos x)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator k
  • Which describes the graph of f(x) = (x² − 4)/(x² − x − 2) at x = 2? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator c
  • Which function is odd? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0003 Functions, performance indicator f

Calculus 11

  • A farmer has 120 m of fencing for three sides of a rectangular pen. The fourth side is a straight river bank. What is the greatest area the pen can have? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator g
  • A particle moves on a line with velocity v(t) = 6t − 3t² meters per second. What total distance does it travel from t = 0 to t = 3? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator h
  • A right-endpoint Riemann sum with 4 equal subintervals estimates the area under f(x) = x² from x = 0 to x = 2. What is the estimate? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator b
  • The Maclaurin series for cos x begins 1 − x²/2 + … What is the next nonzero term? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator f
  • On which interval is f(x) = x³ − 6x² + 9x + 2 decreasing? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator e
  • What is the derivative of f(x) = x⁴e^(3x)? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator d
  • What is the derivative with respect to x of the integral of √(1 + t³) from t = 1 to t = x²? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator c
  • What is the limit of ((2 + h)³ − 8)/h as h approaches 0? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator b
  • What is the limit of (x² − 9)/(x² − 5x + 6) as x approaches 3? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator a
  • What is the value of the integral of 2x(x² + 1)³ from x = 0 to x = 1? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator d
  • Which function solves dy/dx = 3y with y(0) = 4? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0004 Calculus, performance indicator i

Geometry and measurement 17

  • A 16-foot ladder rests against a wall at an angle of 72° to level ground. About how high up the wall does its top reach? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator f
  • A compass and straightedge are used to construct the perpendicular bisector of segment AB. Which property does every point on that line have? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator d
  • A metal block measures 5 cm by 4 cm by 2.5 cm and has a mass of 135 g. What is its density? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator l
  • A rectangular box measures 2 cm by 3 cm by 6 cm. How long is its space diagonal, from one corner to the opposite corner? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator a
  • A right triangle with legs 3 cm and 4 cm is rotated about the 4 cm leg. What is the volume of the solid it sweeps out? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator k
  • A sector is cut from a circle of radius 9 cm by a central angle of 80°. What is the area of the sector? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator g
  • A sphere and a cone each have a radius of 3 cm. What height must the cone have for the two volumes to be equal? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator j
  • A triangle has sides of 5 and 9 with an angle of 120° between them. How long is the third side? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator f
  • An inscribed angle of a circle intercepts an arc of 124°. What is the measure of the angle? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator g
  • The equation x² + y² − 10x + 6y + 18 = 0 is a circle. What are its center and radius? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator h
  • In spherical geometry a triangle is drawn on a sphere with arcs of great circles as its sides. What is true of the sum of its three angles? Wikipedia, "Spherical geometry". Framework section: Competency 0005, performance indicator m
  • The point (−4, 7) is reflected across the line y = −x. Where does it land? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator b
  • The sides of two similar triangles are in the ratio 3 : 4. The smaller triangle has an area of 27 cm². What is the area of the larger triangle? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator e
  • Two interior angles of a triangle measure (2x + 10)° and (3x − 5)°. The exterior angle at the third vertex measures 115°. What is x? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator c
  • Which equation is the parabola with focus (0, 3) and directrix y = −3? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator h
  • Which line passes through (4, 1) and is perpendicular to 2x − 3y = 6? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator i
  • Which three lengths can be the sides of a right triangle? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0005 Geometry and Measurement, performance indicator a

Statistics and probability 11

  • A committee of 3 is chosen at random from 5 teachers and 4 parents. What is the probability that it has exactly 2 teachers? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator i
  • A data set is 4, 7, 7, 9, 10, 12, 21. By the 1.5 × IQR rule, which values are outliers? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator a
  • A fair coin is flipped 5 times. What is the probability of exactly 2 heads? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator e
  • A line of best fit is ŷ = 2.5x + 10. One data point is (8, 27). What is the residual for that point? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator c
  • A researcher randomly assigns 60 students to one of two tutoring methods and compares their later test scores. What kind of study is this? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator g
  • For a class, the correlation between hours of television a week and test score is r = −0.92. Which conclusion do the data support? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator d
  • In a game, a player rolls one fair die. A 6 wins $10, a 4 or 5 wins $4, and any other number loses $5. What is the expected value of one play? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator j
  • In a random sample of 400 voters, 60% favor a school budget. About what is the margin of error for a 95% confidence interval? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator f
  • In a survey, 48 grade 7 students ride the bus and 32 walk. In grade 8, 54 ride the bus and 66 walk. What percent of the grade 8 students ride the bus? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator b
  • Test scores are normally distributed with a mean of 500 and a standard deviation of 100. By the 68–95–99.7 rule, about what percent of scores lie between 400 and 700? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator c
  • Two events have P(A) = 0.6, P(B) = 0.3 and P(A and B) = 0.18. Which statement about them is true? NYSTCE Field 004: Mathematics Test Design and Framework, May 2018: Competency 0006 Statistics and Probability, performance indicator h

How this list was compiled: Our own questions, written to the six selected-response competencies of the NYSTCE Field 004: Mathematics Test Design and Framework, May 2018, authorized for distribution by the New York State Education Department (https://www.nystce.nesinc.com/content/docs/NY_fld04_objs.pdf, read 2026-10-10): Number and Quantity 9 selected-response items of 90, Algebra 23, Functions 19, Calculus 11, Geometry and Measurement 17, Statistics and Probability 11. The bank holds the same numbers. Every answer is mathematics worked from what the question prints, and each one was worked out again on 2026-10-10. One geometry question states a result of spherical geometry that was read in the Wikipedia article it names. Licence: Questions, choices and explanations are original work of this site.

How it works

This CST math practice test follows New York's framework for the Mathematics Content Specialty Test (004). 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 the real test asks

The framework of May 2018 spreads its selected-response questions over number and quantity (9), algebra (23), functions (19), calculus (11), geometry and measurement (17) and statistics and probability (11). This bank holds the same numbers. One written response on teaching a concept carries 20% of the score and is not marked here.

Timing

The framework plans up to 150 minutes for the selected-response questions and up to 60 for the written response. Exam mode asks all 90 in 150 minutes.

How answers are checked

Every numeric answer is worked out a second time from what the question prints, and each explanation shows the working.

  • Calculus is about a tenth of the test, though the framework notes that New York's learning standards for mathematics have no calculus component.

Questions and answers

What is on the math CST practice test?

Rational exponents, complex numbers, vectors and matrices; polynomials, rational expressions and systems; sequences, logarithms and trigonometry; limits, derivatives and integrals; conic sections, the law of cosines and circle theorems; the normal distribution, conditional probability and expected value.

Can you use a calculator on the Mathematics CST?

Yes, and you supply it. The test's own page says a graphing calculator of your own must be brought to the test center, and it links the list of approved models.

What score do you need to pass the math CST?

The test's own page gives a passing score of 520. That is a scaled score and not a count of right answers, so this page shows your number right and no pass verdict.

Are these questions from the real Mathematics CST?

No. Every question is our own, written to the six selected-response competencies of the framework. None is taken or reworded from the real test or from the sample questions in its study guide.

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