NYSTCE Math CST Practice Test and Study Guide

What is the NYSTCE Math CST Exam?

All New York state teachers applying for an initial teaching certificate are required to take New York State Teacher Examinations (NYSTCEs). Generally, there are two mandatory NYSTCE's:

  • the Educating All Students (EAS) exam - focusing on pedagogy and diversity
  • the Content Specialty Test (CST) - centered on the teacher candidate's specific subject area

For middle-level and high school math teachers in New York, the NYSTCE Math CST Exam is the required subject area assessment for certification. With a passing score on this exam, individuals demonstrate their mastery of foundational mathematics and their capacity to be effective teachers in New York state schools.

Practice tests give you a better idea of the topics you have mastered and those you should keep studying.

NYSTCE Math CST Testing Time and Format

The total time allotted for the test is 3 hours and 45 minutes including a 15 minute tutorial and consent to a nondisclosure agreement ensuring the security and integrity of the exam's content. Once these tasks are finished, examinees have the remaining 3 and a half hours to finish the test.

NYSTCE Math CST Exam Components

The content of the NYSTCE Math CST Exam is divided among seven different competencies fundamental to mathematics education. Six are related to particular mathematical fields or discipline—from algebra, to calculus, to statistics—and one pertains to teaching practice and the communication of math concepts to students.

The first six mathematical knowledge components are made up of multiple-choice questions, the seventh consists of one constructed-response question. The following sections of this article will take a closer look at each component, but the table below offers an overview.

Component Estimated number
of questions
Estimated percentage
of test score
Question type
Number and Quantity 9 8% Multiple-choice
Algebra 23 20% Multiple-choice
Functions 19 17% Multiple-choice
Calculus 11 10% Multiple-choice
Geometry and Measurement 17 15% Multiple-choice
Statistics and Probability 11 10% Multiple-choice
Pedagogical Content
Knowledge
1 20% Constructed-response

Number and Quantity

This component will assess the examinee's understanding of everything from arithmetic operations to complex numbers and abstract algebraic concepts. Individuals will demonstrate their knowledge of:

  • the fundamental properties of rational numbers and apply these properties in problem-solving.
  • matrices and complex numbers and their applications to different mathematical fields
  • representing and interpreting numbers presented in the complex plane
  • performing operations on complex numbers

This section is composed of about nine multiple-choice questions making up around 8% of the exam.

Algebra

The algebra competency tests an individual's ability to simplify and interpret algebraic expressions, their awareness of conventional notation, and their ability to apply algebra to problem-solve. Test-takers can expect to:

  • work with polynomials and their graphs
  • apply concepts such as completing the square
  • derive algebraic equations from real-world scenarios
  • interpret polynomial equations and inequalities and their inputs and outputs

This competency consists of around 23 multiple-choice questions, or about 20% percent of the exam.

Functions

This component focuses on interpreting functions and using them to describe real-world situations and models. Individuals will be required to demonstrate:

  • different types of functions such as linear, quadratic, exponential, trigonometric and the types of outputs these produce.
  • understanding of a real-world scenario that involves some variable rate of change such as the growth of a bacterial colony
  • an understanding of trigonometric operations and the unit circle

This section consists of approximately 19 multiple-choice questions making up 17% of the exam score.

Calculus

This component will require an understanding of the foundational principles of calculus and its practical applications. Test-takers should be familiar with:

  • limits, derivatives, and integrals, the notation associated with them, and should also able to use them to interpret graphical data or real-world situations
  • solving problems that involve first order differential equations

There are about 11 multiple-choice questions associated with this component comprising roughly 10% of the exam.

Geometry and Measurement

The geometry and measurement component covers a broad range of concepts from theorems about the essential properties of shapes, to trigonometry and non-Euclidean geometry. Questions may require individuals to

  • use knowledge of the Pythagorean theorem or the relationships between between parallel and perpendicular lines to determine the angels of a diagram
  • know theorems about circles to identify the length of an arc or the measurement of a subtended angle
  • demonstrate proofs for various geometric theorems and principles

The approximately 17 multiple-choice questions of this component will make up roughly 15% of the exam.

Statistics and Probability

This component demonstrates the prospective teacher's understanding of the nature of statistical data, its uses and limitations, as well as an individual's command of various statistical tools and probabilistic principles. Test-takers may expect to:

  • work with and interpret different types visual data representations (dot plots, histograms, or two-way frequency tables)
  • evaluate various data sets using statistical metrics such as standard deviation, mean and median values, or interquartile range
  • know the rules of probability and the use of permutation and combination formulas

This section consists of an estimated 11 multiple-choice questions or 10% of the test.

Pedagogical Content and Knowledge

This component will require the test-taker to prove their understanding of basic pedagogical principles and apply them to a mathematics classroom setting. Individuals are expected to demonstrate their ability to:

  • design curricula that best enables students to process and understand mathematical content.
  • connect new content to prior learning
  • assess student progress
  • identify and address specific difficulties that students may face with material

This section consists of a single constructed-response question, which is a long-form question that may present a classroom scenario and ask for a lesson plan that demonstrates practical teaching skills and a comprehension of pedagogical concepts. This component's single question accounts for around 20% of the exam score.

How to Prepare for the NYSTCE Math CST Exam

The first step in preparing for the NYSTCE math test is to become familiar with all of the content the exam covers. A NYSTCE mathematics CST study guide will provide this information. Review each of the seven exam competencies and be aware of all the particular skills associated with each of them. With an understanding of the content, individuals can look for any gaps in their knowledge.

Next, it is important to gather appropriate study resources. These may include textbooks and notes from college coursework, exam prep books from retail stores or libraries, and online practice tests and preparation courses devoted to NYSTCE CST math review.

Candidates should then formulate a study plan. Organize study time appropriately to avoid having to cram the week of the test date. Set a schedule that devotes suitable study time to each component in the NYSTCE CST Mathmathetics study guide and book the test day far enough in the future to allow for a thorough review of all material.

NYSTCE Math CST Practice Tests

The practice test is one of the most effective tools in a test-taker's arsenal. A good NYSTCE math practice test can provide a comprehensive review of all the essential subject matter while simulating the format of the test questions themselves. Practice tests work by:

  • Reducing anxiety — few things are as nerve-racking as facing an important exam. Being uncertain of what the test will be like only amplifies uneasiness. By simulating the testing experience, NYSTCE math 004 practice tests help curb those test-day fears and anxieties.
  • Highlighting gaps in knowledge — NYSTCE CST mathematics covers a broad range of concepts and skills. Practice tests can shed light on the dark spots of an individual's knowledge, allowing them to focus their studies in the right places.
  • Spacing out learning — taking different practice tests as part of one's individual study plan is a great way to pace NYSTCE CST math review, allowing time to study, assess progress, and improve on weaknesses.
  • Applying knowledge — knowing something and using that knowledge are two different things. Practice tests make users apply their mathematical skills to specific problems.
  • Demystifying the whole process — practice tests can help alleviate any lingering uncertainties a test-taker may have about the content and style of the NYSTCE math exam.

NYSTCE Math CST Exam Registration Policies

Registration for the NYSTCE Math CST Exam is processed through the NYSTCE website. After creating an account, individual's can start the registration process. This will involve paying the $122 test fee, selecting a test date and location via an online scheduling tool, and agreeing to registration and testing policies. Registration policies include the following:

  • Privacy policy
  • Payment policy
  • Changing registration &mdash: location and/or date of an exam appointment must be changed no later than 24 hours before the scheduled test time.
  • Withdrawal/refund policy — any cancellations must occur at least 24 hours before the scheduled test time. Withdrawal refunds must be requested by a form through the NYSTCE account.

NYSTCE Math CST Exam Test Day Policies

During registration, individuals will also agree to testing policies that set the ground rules for conduct during the exam. Here are a few things to be aware of:

  • Bring identification — in order to verify identity, all test-takers must bring a government issued ID with a photo and a signature on it. Test administrators may also collect a digital signature, photograph, and/or palm scan on test day.
  • Personal items are prohibited — items such as purses, wallets, phones, and other electronic devices will not be allowed in the test room. Test-takers will be asked to return these items to their vehicles or will be provided with a secure area to store them.
  • Taking breaks — if an individual needs a break during the exam, they must raise their hand and alert a test administrator. Examinees must leave the testing room during a break and will be asked for identification upon returning.
  • Retakes are allowed — if an individual needs to, the exam may be retaken until a passing score is earned. There must be 60 days between attempts, and the test-taker must go through the registration process again.

NYSTCE Math CST Exam Score Reporting Policies

Test scores are reported to individual test-takers and to the New York State Department of Education. Additionally, during registration test-takers can stipulate other institutions (e.g., colleges or universities) that they would like to receive the scores. All tests, even incomplete ones, are scored, and once an individual is admitted to a testing center, their test scores can not be canceled. Scores may be voided, however, if a test-taker is found to have violated certain testing policies, so it is important to read and understand all policies before taking the exam.

Frequently Asked Questions

  • How many questions on the CST math exam?

    There are 91 total questions on the NYTCE Math CST test. 90 of the questions are selected-response (or multiple-choice), and one is a longer constructed-response question.

  • How long is the math CST exam?

    The total time allotted for the NYSTCE Math CST exam is 3 hours and 45 minutes. This includes 15 minutes (before the start of the test) to take a tutorial and consent to a nondisclosure agreement, and 3 hours 30 minutes to complete the exam itself.

  • Can you use a calculator for the math CST?

    Test-takers are allowed to bring their own graphing calculators to the exam. A full list of approved graphing calculators can be found on the NYSTCE website.

Exam

Take a NYSTCE Mathematics Practice Test Online

Exam Instructions:

Complete the practice test below to test your knowledge of NYSTCE Mathematics.
Choose your answers below. Complete the 15 questions then click "See Results."

You have answered 0 out of 15 correctly.

The correct answers are highlighted with green below. Create an account to study for NYSTCE Mathematics.

Sign Up
  1. What is the average value of the following set of numbers? {-10, -4, -2, 5, 5, 7, 8, 9}

    • Correct Answer
  2. Use the diagram below to answer the question that follows. Circle O has a radius of 4. The line AD is tangent to the circle at point A, and AD = 6. If line AB is the diameter of Circle O, and the chord BC is part of the secant BD, what is the length of the chord BC?
    <b>Use the diagram below to answer the question that follows.</b>  Circle <i>O</i> has a radius of 4. The line <i>AD</i> is tangent to the circle at point <i>A</i>, and <i>AD</i> = 6. If line <i>AB</i> is the diameter of Circle <i>O</i>, and the chord <i>BC</i> is part of the secant <i>BD</i>, what is the length of the chord <i>BC</i>?
    • Correct Answer
  3. Use the diagram below to answer the question that follows. The line AE and line BD are parallel. If CE = 3AC, what is the ratio of the area of the triangle CDE to the area of the triangle ABC?
    <b>Use the diagram below to answer the question that follows.</b> The line <i>AE</i> and line <i>BD</i> are parallel. If <i>CE</i> = 3<i>AC</i>, what is the ratio of the area of the triangle <i>CDE</i> to the area of the triangle <i>ABC</i>?
    • Correct Answer
  4. When an empty electric capacitor is connected to a battery with voltage VB, the voltage across the capacitor V is related to time t in seconds by _____, where A is a constant. If it takes t = 5 s to charge the empty capacitor to one-fourth of the battery voltage, how many seconds does it take to charge the empty capacitor to the half of the battery voltage?
    When an empty electric capacitor is connected to a battery with voltage <i>V</i><span style="vertical-align: sub">B</span>, the voltage across the capacitor V is related to time <i>t</i> in seconds by &#95;&#95;&#95;&#95;&#95;, where A is a constant. If it takes <i>t</i> = 5 s to charge the empty capacitor to one-fourth of the battery voltage, how many seconds does it take to charge the empty capacitor to the half of the battery voltage?
    • Correct Answer
  5. Daniel has five lotto tickets that he can win a toy with probability 1/6, a candy with 1/3 or nothing with 1/2. With his 5 tickets, what is the probability that he wins two toys and two candies?

    • Correct Answer
  6. Use the diagram below to answer the question that follows. A 6-foot-tall person is walking away from the base of a streetlight with the height 20 feet. As the person walks away at the constant speed of 5 feet per second, the light casts a shadow in front of the person as shown in the diagram. Find the length of the shadow 3 seconds after the person starts waking from the streetlight.
    <b>Use the diagram below to answer the question that follows.</b> A 6-foot-tall person is walking away from the base of a streetlight with the height 20 feet. As the person walks away at the constant speed of 5 feet per second, the light casts a shadow in front of the person as shown in the diagram. Find the length of the shadow 3 seconds after the person starts waking from the streetlight.
    • Correct Answer
  7. Use the diagram below to answer the question that follows. Circle O has a radius of 6, and the measure of angle OAD is 24°. If line AC and line OB bisect each other, what is the measure of the arc AB?
    <b>Use the diagram below to answer the question that follows.</b>  Circle <i>O</i> has a radius of 6, and the measure of angle <i>OAD</i> is 24&#176;. If line <i>AC</i>  and line <i>OB</i> bisect each other, what is the measure of the arc <i>AB</i>?
    • Correct Answer
  8. Which function can the fundamental theorem of calculus be applied in the domain (-2, 20)?
    • Correct Answer
  9. Use the diagram below to answer the question that follows. In the diagram below, AB = 8, AC = 3, CD = 49 and the measure of angle BAC and angle CBD is 60° and 90°, respectively. What is the length of BD?
    <b>Use the diagram below to answer the question that follows.</b> In the diagram below, <i>AB</i> = 8, <i>AC</i> = 3, <i>CD</i> = 49 and the measure of angle <i>BAC</i> and angle <i>CBD</i> is 60&#176; and 90&#176;, respectively. What is the length of <i>BD</i>?
    • Correct Answer
  10. Which one is one-to-one function for any value of x, over which the function is defined?
    • Correct Answer
  11. Use the diagram below to answer the question that follows. A cube of ice with the edge length L is submerged into water to melt. If the length of each edge of the ice cube is decreasing at a constant rate of C, what is the rate of change of the volume of the ice cube when the volume of the ice cube is one-eighth of the original size?
    <b>Use the diagram below to answer the question that follows.</b> A cube of ice with the edge length <i>L</i> is submerged into water to melt. If the length of each edge of the ice cube is decreasing at a constant rate of <i>C</i>, what is the rate of change of the volume of the ice cube when the volume of the ice cube is one-eighth of the original size?
    • Correct Answer
  12. Given an ellipse,_____ , which statement is true?
    Given an ellipse,&#95;&#95;&#95;&#95;&#95; , which statement is true?
    • Correct Answer
  13. Use the diagram below to answer the question that follows. Kelly and Monica are jogging on a track. Kelly is jogging at 2 m/s, and Monica is jogging twice as fast as Kelly. If Monica is 600 m behind Kelly, how long does it take Monica to catch up with Kelly?
    <b>Use the diagram below to answer the question that follows.</b> Kelly and Monica are jogging on a track. Kelly is jogging at 2 m/s, and Monica is jogging twice as fast as Kelly. If Monica is 600 m behind Kelly, how long does it take Monica to catch up with Kelly?
    • Correct Answer
  14. Solve the following system of linear equations.
    Solve the following system of linear equations.
    • Correct Answer
  15. Use the diagram below to answer the question that follows. A tile with length x and width y is used to fill the floor with dimension L and W. Find the expression for the number of tiles used for filling the floor.
    <b>Use the diagram below to answer the question that follows.</b>  A tile with length <i>x</i> and width <i>y</i> is used to fill the floor with dimension <i>L</i> and <i>W</i>. Find the expression for the number of tiles used for filling the floor.
    • Correct Answer