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100+ Free MTTC Mathematics (Secondary) (022) Practice Questions

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As x approaches infinity, what is the end behavior of the rational function f(x) = (3x^2 + 1) / (x^2 - 4)?

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2026 Statistics

Key Facts: MTTC Mathematics (Secondary) (022) Exam

220

Passing Scaled Score

MTTC Mathematics (Secondary) (022) test page

$129

Test Fee (2026)

MTTC Mathematics (Secondary) (022) test page

80 MC

Test Format

MTTC Mathematics (Secondary) (022) test page

2 hr 30 min

Testing Time

MTTC Mathematics (Secondary) (022) test page

4 subareas

Content Domains

MTTC Mathematics (Secondary) (022) test objectives

28%

Heaviest Subarea Weight

MTTC Mathematics (Secondary) (022) test objectives

18

Test Objectives

MTTC Mathematics (Secondary) (022) test objectives

6 weeks

Score Reporting Time

MTTC test scoring information

MTTC Mathematics (Secondary) (022) is Michigan's secondary mathematics content certification test, delivered by Pearson as a computer-based exam with 80 multiple-choice questions and a passing scaled score of 220. The questions are distributed across four subareas: Mathematical Processes and Number Concepts (22%), Patterns, Algebraic Relationships, and Functions (28%), Measurement and Geometry (22%), and Data Analysis, Statistics, Probability, and Discrete Mathematics (28%). The current public fee is $129 and the appointment runs 2 hours 45 minutes, with 2 hours 30 minutes of testing time. This free 100-question bank mirrors the official objective weighting so candidates can practice across every subarea.

Sample MTTC Mathematics (Secondary) (022) Practice Questions

Try these sample questions to test your MTTC Mathematics (Secondary) (022) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A student claims that because 3 + 5 = 8 and 8 is even, the sum of two odd numbers is always even. Which form of reasoning best describes a valid proof of this claim for ALL odd integers?
A.Representing odd integers generally as 2m + 1 and 2n + 1 and showing their sum equals 2(m + n + 1)
B.Testing many additional pairs of odd numbers and finding they are all even
C.Drawing a picture of dots arranged in pairs
D.Noting that the claim worked for 3 and 5
Explanation: A general (deductive) proof must hold for every case, so representing arbitrary odd integers as 2m + 1 and 2n + 1 and simplifying their sum to 2(m + n + 1) shows the result is divisible by 2 for all integers m and n. This algebraic generalization is a valid mathematical proof.
2Which statement is the contrapositive of "If a quadrilateral is a square, then it is a rectangle"?
A.If a quadrilateral is not a rectangle, then it is not a square
B.If a quadrilateral is a rectangle, then it is a square
C.If a quadrilateral is not a square, then it is not a rectangle
D.If a quadrilateral is not a rectangle, then it is a square
Explanation: The contrapositive of "if p then q" is "if not q then not p," and it is logically equivalent to the original statement. Negating and swapping gives "if not a rectangle, then not a square."
3A teacher wants students to estimate the product 48 x 52 mentally before computing. Which strategy gives a quick exact answer using the difference of squares pattern?
A.Recognize 48 x 52 = (50 - 2)(50 + 2) = 50^2 - 2^2 = 2500 - 4 = 2496
B.Round both factors to 50 and report 2500 as the exact product
C.Add 48 and 52 to get 100, then multiply by 2
D.Compute 48 x 50 and ignore the remaining 2
Explanation: Because 48 and 52 are equally spaced around 50, the product fits the difference-of-squares identity (a - b)(a + b) = a^2 - b^2 with a = 50 and b = 2, giving 2500 - 4 = 2496 exactly. This illustrates connecting number sense to algebraic structure.
4Mathematics is used in biology to model population growth with the equation P(t) = P0 e^(kt). In this model, what does the constant k represent when k > 0?
A.The continuous relative growth rate of the population
B.The initial population size
C.The carrying capacity of the environment
D.The doubling time of the population in years
Explanation: In the continuous exponential model P(t) = P0 e^(kt), P0 is the initial amount and k is the continuous relative (per-capita) growth rate. A positive k produces exponential growth; the larger k is, the faster the population grows.
5Which of the following numbers is irrational?
A.The square root of 7
B.0.252525... (repeating)
C.22/7
D.The square root of 1.44
Explanation: The square root of 7 cannot be expressed as a ratio of two integers and its decimal expansion is non-terminating and non-repeating, so it is irrational. Rational numbers are exactly those expressible as a fraction of integers.
6The decimal number 45 is written in base 2 (binary). What is its representation?
A.101101
B.110011
C.100101
D.101011
Explanation: Decompose 45 into powers of 2: 45 = 32 + 8 + 4 + 1 = 2^5 + 2^3 + 2^2 + 2^0. Writing the place values for 2^5 down to 2^0 gives 1 0 1 1 0 1, so 45 in binary is 101101.
7A complex number is given as 3 + 4i. What is its modulus (absolute value)?
A.5
B.7
C.25
D.The square root of 7
Explanation: The modulus of a complex number a + bi is the square root of (a^2 + b^2). For 3 + 4i, this is the square root of (9 + 16) = the square root of 25 = 5. This represents the distance from the origin in the complex plane.
8What is the greatest common divisor (GCD) of 84 and 120?
A.12
B.6
C.24
D.4
Explanation: Factor both numbers: 84 = 2^2 x 3 x 7 and 120 = 2^3 x 3 x 5. The GCD takes the lowest power of each shared prime: 2^2 x 3 = 12. Thus 12 is the largest integer dividing both.
9Two gears start aligned. One completes a rotation every 8 seconds and the other every 12 seconds. After how many seconds will they next be aligned at the starting position simultaneously?
A.24
B.20
C.48
D.96
Explanation: They realign when the elapsed time is a common multiple of both periods, so we need the least common multiple of 8 and 12. Since 8 = 2^3 and 12 = 2^2 x 3, the LCM is 2^3 x 3 = 24 seconds.
10Which property of the real numbers is illustrated by the statement a x (b + c) = a x b + a x c?
A.The distributive property of multiplication over addition
B.The associative property of multiplication
C.The commutative property of addition
D.The identity property of multiplication
Explanation: The distributive property links multiplication and addition by stating that multiplying a sum equals the sum of the individual products. This is the foundation for expanding and factoring algebraic expressions.

About the MTTC Mathematics (Secondary) (022) Exam

The MTTC Mathematics (Secondary) (022) test is the subject-matter assessment for the Michigan secondary mathematics teaching endorsement. The computer-based test includes 80 multiple-choice questions organized into four subareas spanning mathematical processes and number concepts, patterns, algebraic relationships and functions, measurement and geometry, and data analysis, statistics, probability, and discrete mathematics. The same content framework is used for grade-banded Field 131 (Mathematics 7-12).

Questions

80 scored questions

Time Limit

2 hours 30 minutes of testing (2 hours 45 minutes total appointment)

Passing Score

220 scaled score

Exam Fee

$129 (Michigan Department of Education / Pearson)

MTTC Mathematics (Secondary) (022) Exam Content Outline

22% of this test

Mathematical Processes and Number Concepts (Subarea I)

Principles of mathematical reasoning, proof, and communicating mathematical ideas, problem-solving strategies and connections among mathematical ideas and other fields, number systems and equivalent representations including integers, rationals, reals, and complex numbers, and number theory and operations such as primes, divisibility, GCD, LCM, and modular arithmetic.

28% of this test

Patterns, Algebraic Relationships, and Functions (Subarea II)

Describing, analyzing, and generalizing patterns, using symbolic expressions to model change and functional relationships, properties and applications of linear and quadratic functions, polynomial, rational, radical, exponential, logarithmic, and trigonometric functions, and principles and applications of differential and integral calculus.

22% of this test

Measurement and Geometry (Subarea III)

Attributes of measurement and measuring units with precision and significant figures, spatial characteristics of two- and three-dimensional shapes including perimeter, area, surface area, and volume, geometric principles of points, lines, angles, planes, congruence, and similarity, and properties of transformations with coordinate and vector methods.

28% of this test

Data Analysis, Statistics, Probability, and Discrete Mathematics (Subarea IV)

Methods of collecting, organizing, and displaying data, describing, analyzing, and interpreting data with measures of center and spread, making predictions and inferences and study design, probability theory and probability distributions including the normal distribution, and principles of discrete mathematics such as counting, permutations, combinations, sequences, series, induction, and graph theory.

How to Pass the MTTC Mathematics (Secondary) (022) Exam

What You Need to Know

  • Passing score: 220 scaled score
  • Exam length: 80 questions
  • Time limit: 2 hours 30 minutes of testing (2 hours 45 minutes total appointment)
  • Exam fee: $129

Keys to Passing

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

MTTC Mathematics (Secondary) (022) Study Tips from Top Performers

1Allocate study time by subarea weight: Functions/Calculus and Data/Statistics are heaviest at 28% each, while Number Concepts and Geometry are 22% each
2Practice multi-step problems in algebra, functions, and calculus because Subarea II rewards both procedural fluency and conceptual understanding
3Drill probability, statistics, counting, sequences, and graph theory, since Subarea IV is the equal-heaviest content area
4Review core formulas (slope, distance, quadratic formula, area and volume, Law of Cosines, combinations and permutations) and know when to apply each
5Use estimation, unit analysis, and reasonableness checks to verify answers quickly under a roughly two-minutes-per-question pace
6Study examples that connect mathematics to real-world contexts and to teaching, since reasoning and modeling objectives appear throughout the test

Frequently Asked Questions

What is on the MTTC Mathematics (Secondary) (022) test?

The test covers four subareas: Mathematical Processes and Number Concepts (22%), Patterns, Algebraic Relationships, and Functions (28%), Measurement and Geometry (22%), and Data Analysis, Statistics, Probability, and Discrete Mathematics (28%). All four subareas are assessed entirely with multiple-choice questions across 18 detailed objectives.

How many questions are on the MTTC Mathematics (Secondary) (022) test and what is the format?

The computer-based test has 80 multiple-choice questions and no constructed-response or essay items. All questions count toward your scaled score, and you select one best answer for each item.

What is the passing score for MTTC Mathematics (Secondary) (022)?

You need a scaled score of 220 to pass the MTTC Mathematics (Secondary) (022) test, the standard passing score used across MTTC tests. Scores are typically reported within about six weeks of your test date.

How much does the MTTC Mathematics (Secondary) (022) test cost in 2026?

The current registration fee for the MTTC Mathematics (Secondary) (022) test is $129. Always confirm the exact amount in your Pearson registration portal before checkout, since additional service fees may apply depending on payment method.

How long is the MTTC Mathematics (Secondary) (022) test appointment?

The total appointment is 2 hours and 45 minutes, which includes about 15 minutes for a tutorial and the nondisclosure agreement, leaving 2 hours and 30 minutes for the 80 multiple-choice questions. Budget your time to average under two minutes per question.

What is the difference between MTTC test 022 and field 131?

Field 022 is the Mathematics (Secondary) test and field 131 is the grade-banded Mathematics 7-12 version. They share the same content framework and four subareas, so studying the 022 objectives prepares you for both fields.