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100+ Free NYSTCE Math CST Practice Questions

Pass your NYSTCE Mathematics Content Specialty Test (CST) (004) exam on the first try — instant access, no signup required.

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Key Facts: NYSTCE Math CST Exam

90 + 1

Selected-Response + Constructed Response

NYSTCE Mathematics (004) test design

80% / 20%

Selected-Response vs Constructed-Response Score Weight

NYSTCE Field 004 test design

3h 30m

Total Testing Time

NYSTCE Mathematics (004) test design

520

Scaled Passing Score

NYSTCE Mathematics (004) test page

$122

Current Exam Fee

NYSTCE Mathematics (004) test page

20%

Algebra, the Largest Content Competency

NYSTCE Field 004 framework

17%

Functions Competency Weight

NYSTCE Field 004 framework

10%

Calculus Weight Despite Not Being in NY Standards

NYSTCE Field 004 framework

The official NYSTCE Mathematics (004) test design lists 90 selected-response items and 1 constructed-response item, 210 minutes (3 hours 30 minutes) of testing time inside a 3 hour 45 minute appointment, a 520 scaled passing score, and a $122 fee. Selected-response items count for 80% of the score and the constructed response for 20%. The framework's heaviest content competencies are Algebra (20%), Functions (17%), and Geometry and Measurement (15%); Calculus and Statistics and Probability are 10% each and Number and Quantity is 8%. Note that calculus is included even though it is not in the New York State Learning Standards for Mathematics.

Sample NYSTCE Math CST Practice Questions

Try these sample questions to test your NYSTCE Math CST exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following best describes the set of rational numbers?
A.Numbers that can be written as a ratio of two integers with a nonzero denominator
B.Numbers that have non-repeating, non-terminating decimal expansions
C.Only the positive whole numbers and zero
D.Numbers that cannot be expressed as fractions
Explanation: A rational number is any number expressible as a/b where a and b are integers and b is not zero. Their decimal expansions either terminate or repeat. Irrational numbers, by contrast, have non-terminating, non-repeating decimals.
2Simplify the expression 27^(2/3).
A.9
B.18
C.6
D.12
Explanation: A rational exponent a^(m/n) equals the nth root of a raised to the m power. The cube root of 27 is 3, and 3 squared is 9. Therefore 27^(2/3) = 9.
3What is the product of the complex numbers (3 + 2i) and (1 - 4i)?
A.11 - 10i
B.3 - 8i
C.-5 - 10i
D.11 + 14i
Explanation: Using FOIL: (3)(1) + (3)(-4i) + (2i)(1) + (2i)(-4i) = 3 - 12i + 2i - 8i^2. Since i^2 = -1, -8i^2 = 8. Combining real parts 3 + 8 = 11 and imaginary parts -12i + 2i = -10i gives 11 - 10i.
4A vector v has components (3, -4). What is its magnitude?
A.5
B.7
C.1
D.25
Explanation: The magnitude of a two-dimensional vector (a, b) is the square root of a^2 + b^2. Here that is the square root of 9 + 16 = 25, which is 5.
5If A is a 2x2 matrix with det(A) = 5, what is det(2A)?
A.20
B.10
C.5
D.40
Explanation: For an n x n matrix, det(kA) = k^n times det(A). With n = 2 and k = 2, det(2A) = 2^2 times 5 = 4 times 5 = 20.
6Which property guarantees that for all real numbers a and b, a + b = b + a?
A.Commutative property of addition
B.Associative property of addition
C.Distributive property
D.Identity property of addition
Explanation: The commutative property of addition states that the order of the addends does not change the sum. The associative property concerns grouping, and the distributive property links multiplication and addition.
7A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 5 cups of sugar?
A.7.5
B.6
C.10
D.3.33
Explanation: Set up the proportion 3/2 = x/5. Cross-multiplying gives 2x = 15, so x = 7.5 cups of flour. This uses proportional reasoning with consistent units.
8Express the repeating decimal 0.444... as a fraction in simplest form.
A.4/9
B.44/100
C.2/5
D.4/10
Explanation: Let x = 0.444.... Then 10x = 4.444..., and subtracting gives 9x = 4, so x = 4/9. This shows the decimal is rational.
9Using the Fundamental Theorem of Algebra, how many roots (counting multiplicity) does the polynomial x^4 - 1 have in the complex numbers?
A.4
B.2
C.1
D.3
Explanation: The Fundamental Theorem of Algebra guarantees that a degree-n polynomial has exactly n roots in the complex numbers, counting multiplicity. A fourth-degree polynomial therefore has 4 roots: 1, -1, i, and -i.
10A car travels 240 miles using 8 gallons of fuel. Expressed in appropriate units, what is its fuel efficiency?
A.30 miles per gallon
B.30 gallons per mile
C.1,920 miles per gallon
D.0.033 miles per gallon
Explanation: Fuel efficiency is distance divided by fuel consumed: 240 miles / 8 gallons = 30 miles per gallon. Attending to units confirms the correct interpretation.

About the NYSTCE Math CST Exam

The NYSTCE Mathematics Content Specialty Test (CST) (004) is the New York subject-content exam required for mathematics teacher certification, generally at the grades 7-12 level. The exam measures deep content knowledge across number and quantity, algebra, functions, calculus, geometry and measurement, and statistics and probability, plus a scenario-based constructed response measuring pedagogical content knowledge — how a teacher designs instruction to help students reach a specific learning goal.

Questions

91 scored questions

Time Limit

3h 45m appointment (3h 30m testing)

Passing Score

520 (scaled)

Exam Fee

$122 (New York State Education Department / Pearson Evaluation Systems)

NYSTCE Math CST Exam Content Outline

20% of total score

Algebra

Generating equivalent expressions, rates and proportional relationships, factoring and completing the square, polynomial and rational expressions, solving linear, quadratic, and exponential equations, systems, and graphing.

17% of total score

Functions

Function notation and key features, multiple representations, transformations and inverses, arithmetic and geometric sequences, logarithmic and exponential functions, and trigonometric functions on the unit circle.

15% of total score

Geometry and Measurement

Pythagorean theorem, rigid motions and similarity, theorems about lines, triangles, and circles, conic sections, coordinate proofs, area and volume with Cavalieri's principle, and non-Euclidean geometry.

10% + 10% + 8% of total score

Calculus, Statistics and Probability, and Number and Quantity

Limits, derivatives, integrals, and differential equations; data summaries, distributions, inference, and probability rules; and real and complex numbers, rational exponents, vectors, and matrices.

20% of total score

Pedagogical Content Knowledge (Constructed Response)

One scenario-based written assignment that asks the candidate to describe an instructional strategy or intervention to help students achieve a learning goal or overcome a difficulty, with a clear rationale.

How to Pass the NYSTCE Math CST Exam

What You Need to Know

  • Passing score: 520 (scaled)
  • Exam length: 91 questions
  • Time limit: 3h 45m appointment (3h 30m testing)
  • Exam fee: $122

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

NYSTCE Math CST Study Tips from Top Performers

1Prioritize Algebra and Functions first — together they account for 37% of the test and underpin many other items
2Memorize the unit circle, trigonometric identities, and special right-triangle ratios for the functions and geometry domains
3Review core calculus skills (limits, power/chain/product rules, definite integrals, optimization) even if calculus is not in the NY standards
4Practice the 68-95-99.7 empirical rule, probability rules, permutations, combinations, and expected value for the statistics domain
5Rehearse the constructed response by naming a specific instructional strategy, using multiple representations, and giving a clear rationale
6Work timed mixed sets and review every miss by competency to balance your six content areas before test day

Frequently Asked Questions

How many questions are on the NYSTCE Mathematics CST (004)?

The current test design lists 90 selected-response items and 1 constructed-response item. The selected-response section counts for 80% of your score and the constructed response counts for 20%.

What passing score do I need for the NYSTCE Math CST (004)?

You need a scaled score of 520 to pass. Aim for consistent performance across all six content competencies and a strong, well-justified constructed response rather than estimating a raw-score cutoff.

How much does the NYSTCE Math CST (004) cost?

The current NYSTCE fee for the Mathematics CST (004) is $122. Always confirm the fee in your NYSTCE account at registration in case the testing program updates pricing.

How long is the NYSTCE Math CST (004) exam?

Total testing time is 210 minutes (3 hours 30 minutes) inside a 3 hour 45 minute appointment. The constructed response is designed for up to 60 minutes and the selected-response items for up to 150 minutes.

Which NYSTCE Math CST domains carry the most weight?

Algebra is the largest content competency at 20%, followed by Functions at 17% and Geometry and Measurement at 15%. Calculus and Statistics and Probability are 10% each, and Number and Quantity is 8%.

Does the NYSTCE Math CST really include calculus?

Yes. Even though calculus is not in the New York State Learning Standards for Mathematics, it is about 10% of the Field 004 framework, covering limits, derivatives, integrals, and differential equations.