A farm stand near Traverse City sells half of its cherry boxes plus 3 more in the morning. In the afternoon it sells half of what is left plus 2 more, and 7 boxes remain. How many boxes did it start with?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 002 (problem-solving strategies and connections)
A proof by contradiction that √2 is irrational begins with which assumption?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 001 (mathematical reasoning and communicating mathematical ideas)
A signal travels 3.0 × 10⁸ meters each second. How many seconds does it take to travel 1.5 × 10¹¹ meters?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 004 (number theory and operations on number systems)
A student conjectures that n² + n + 11 is prime for every whole number n. Which value of n is a counterexample?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 001 (mathematical reasoning and communicating mathematical ideas)
Show all 48 questions (44 more)
Mathematical processes and number concepts, continued
How many positive divisors does 1,008 have?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 004 (number theory and operations on number systems)
In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, …, the ratio of a term to the term before it approaches which number?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 002 (problem-solving strategies and connections)
Let U be the whole numbers 1 through 10, A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8, 10}. How many elements are in the complement of A ∪ B?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 003 (number systems and equivalent representations)
Premise 1: every rhombus is a parallelogram. Premise 2: figure F is not a parallelogram. Which conclusion follows by valid deduction?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 001 (mathematical reasoning and communicating mathematical ideas)
What is the product (3 − 2i)(1 + 4i)?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 004 (number theory and operations on number systems)
Which list puts −π, −22/7, −√10 and −3.2 in order from least to greatest?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 003 (number systems and equivalent representations)
Which set is NOT closed under the operation named?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea I, objective 003 (number systems and equivalent representations)
Patterns, algebraic relationships and functions 13
A colony of invasive mussels in a lake triples every 4 years. A survey counts 200 mussels today. If the pattern holds, how many will there be in 12 years?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 008 (polynomial, rational, radical, exponential, logarithmic and trigonometric functions)
A model rocket’s height in feet t seconds after launch is h(t) = −16t² + 72t + 5. What is its greatest height?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 007 (linear and quadratic functions)
A sequence is defined by a₁ = 5 and aₙ = 2aₙ₋₁ − 3 for n > 1. What is a₅?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 005 (mathematical patterns)
Given f(x) = 3x − 7 and g(x) = x² + 2, find the value of f(g(2)).Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 006 (patterns of change and functional relationships)
On which interval is f(x) = x³ − 6x² + 5 decreasing?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 009 (differential and integral calculus)
The point (4, −6) lies on the graph of y = f(x). Which point must lie on the graph of y = −2f(x − 3) + 1?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 006 (patterns of change and functional relationships)
What is the period of y = 3 sin(4x − π) + 2?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 008 (polynomial, rational, radical, exponential, logarithmic and trigonometric functions)
What is the solution of the system 3x − 2y = 19 and 5x + 4y = −5?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 007 (linear and quadratic functions)
What is the solution set of log₂(x − 3) + log₂(x + 3) = 4?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 008 (polynomial, rational, radical, exponential, logarithmic and trigonometric functions)
What is the sum of the first 40 terms of the arithmetic sequence 7, 11, 15, 19, …?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 005 (mathematical patterns)
What is the value of the definite integral of 3x² − 2x from x = 1 to x = 3?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 009 (differential and integral calculus)
Which function is the inverse of f(x) = (3x + 4)/5?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 006 (patterns of change and functional relationships)
Which values of x satisfy x² − 4x − 12 < 0?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea II, objective 007 (linear and quadratic functions)
Measurement and geometry 11
A pump delivers 12 gallons of water per minute. What is that rate in quarts per second? (1 gallon = 4 quarts)Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 010 (attributes of measurement and measuring units)
A silo is a cylinder of radius 3 m and height 10 m, topped by a hemisphere of the same radius. What is its total volume?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 011 (measurement of two- and three-dimensional shapes)
A student measures a rod as 24.4 cm. Its accepted length is 25.0 cm. What is the percent error of the measurement?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 010 (attributes of measurement and measuring units)
Each interior angle of a regular polygon measures 156°. How many sides does the polygon have?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 012 (points, lines, angles, planes, congruence and similarity)
The equation x² + y² + 10x − 2y − 23 = 0 describes a circle. Where is its center, and what is its radius?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 013 (transformations and coordinate and vector methods)
From a point on level ground 80 meters from the base of a lighthouse, the angle of elevation to its top is 35°. About how tall is the lighthouse?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 011 (measurement of two- and three-dimensional shapes)
Given vectors u = ⟨3, −4⟩ and v = ⟨1, 8⟩, what is the magnitude of u + 2v?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 013 (transformations and coordinate and vector methods)
In triangle ABC, the exterior angle at vertex C measures 128° and angle A measures 57°. What is the measure of angle B?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 012 (points, lines, angles, planes, congruence and similarity)
Point P(5, −2) is rotated 90° counterclockwise about the origin and the image is then reflected across the x-axis. What are the final coordinates?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 013 (transformations and coordinate and vector methods)
Two cones are similar. Their heights are 6 cm and 15 cm, and the smaller cone has a volume of 40 cm³. What is the volume of the larger cone?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 011 (measurement of two- and three-dimensional shapes)
Which set of matching parts does NOT guarantee that two triangles are congruent?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea III, objective 012 (points, lines, angles, planes, congruence and similarity)
Data analysis, statistics, probability and discrete mathematics 13
A box plot has minimum 12, first quartile 20, median 26, third quartile 34 and maximum 59. By the 1.5 × IQR rule, which statement is true?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 014 (collecting, organizing and displaying data)
A committee of 4 is chosen from 9 people, but two particular people refuse to serve together. How many committees are possible?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 018 (discrete mathematics)
A connected graph has 7 vertices and 12 edges. How many edges does any spanning tree of the graph have?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 018 (discrete mathematics)
A dart lands at a random point on a square board with sides of 20 cm. What is the probability that it lands within 5 cm of the center of the board?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 017 (probability and probability distributions)
A drawer holds 5 black, 4 gray and 3 white socks. Two socks are taken at random without replacement. What is the probability that they are different colors?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 017 (probability and probability distributions)
A linear regression of y on x has correlation coefficient r = −0.92. Which interpretation is correct?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 016 (predictions and inferences based on data)
A poll of 600 people reports 52% with a margin of error of 4 percentage points. If the sample size were four times as large, with the same proportion and confidence level, about what would the margin of error be?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 016 (predictions and inferences based on data)
A school wants to estimate how its 1,200 students travel to school. Which sampling plan is least likely to give a biased result?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 014 (collecting, organizing and displaying data)
A set of test scores has mean 70 and standard deviation 8. Every score is multiplied by 1.5 and then 5 points are added. What are the new mean and standard deviation?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 015 (describing, analyzing and interpreting data)
A table gives the points (0, 3), (1, 6), (2, 12) and (3, 24). Which function fits all four points?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 015 (describing, analyzing and interpreting data)
Heights in a population are normally distributed with mean 64 inches and standard deviation 3 inches. By the 68–95–99.7 rule, about what percent of heights are between 61 and 70 inches?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 017 (probability and probability distributions)
Maximize P = 5x + 4y subject to x + y ≤ 10, x ≤ 6, x ≥ 0 and y ≥ 0. What is the maximum value of P?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 018 (discrete mathematics)
What is the population standard deviation of the data set 4, 7, 7, 9, 13, to the nearest hundredth?Our own question, answer worked out twice. Outline: MTTC Mathematics (Secondary) (022) test objectives, Subarea IV, objective 015 (describing, analyzing and interpreting data)
How this list was compiled: Our own questions, written to the test objectives of MTTC Mathematics (Secondary), field 022, as the Michigan Test for Teacher Certification site prints them (https://www.mttc.nesinc.com/Content/STUDYGUIDE/MI_SG_OBJ_022.htm; test page https://www.mttc.nesinc.com/TestView.aspx?f=HTML_FRAG/MI022_TestPage.html), read 2026-10-09: 80 multiple-choice questions in 2 hours 30 minutes, passing score 220; Subarea I Mathematical Processes and Number Concepts (objectives 001 to 004, 22%), II Patterns, Algebraic Relationships, and Functions (005 to 009, 28%), III Measurement and Geometry (010 to 013, 22%), IV Data Analysis, Statistics, Probability, and Discrete Mathematics (014 to 018, 28%). This bank holds 11, 13, 11 and 13, with two or three questions for each of the 18 objectives. Every numeric answer was worked out a second time from the numbers in the question; the reasoning items rest on the definitions their explanations state. The sample questions of the study guide were not opened. Licence: Questions, choices and explanations are original work of this site.
How it works
These MTTC secondary math practice tests follow Mathematics (Secondary), field 022: 48 questions of our own, each worked out. They are unofficial and not affiliated with the Michigan Department of Education or Pearson.
Read the full guide
MTTC secondary math study guide: the four subareas
The test objectives, read October 9, 2026, weigh 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%. This bank holds 11, 13, 11 and 13 questions, with every one of the 18 objectives covered.
Timing
The real test asks 80 multiple-choice questions in 2 hours 30 minutes. Exam mode gives 90 minutes for the 48 here, the same pace.
Calculator and formulas
The test page says to bring a graphing calculator from its approved list, and that formulas are provided on screen. Work this bank with the calculator you will bring.
Calculus is one objective of 18, and discrete mathematics, with graphs and linear programming, is another. Neither is the bulk of the test.
Questions and answers
Is this MTTC math practice test for the 022 test or for Mathematics (7–12)?
For Mathematics (Secondary), field 022, the EX endorsement. Mathematics (7–12), field 131, is a separate test, and the test page says 022 cannot be used for its EQ endorsement. Check which code your program asks for.
Is there an MTTC math paper practice test?
Yes. After a round, Print lists the questions you just played and can add the rest of the 48, with an answer key if you tick it. The real test is taken on a computer.
What is the passing score on the MTTC secondary math test?
The test page gives a passing score of 220. It is not a percent of questions, and tests may include questions being tried out that do not count, so this page reports a number right and no verdict.
Is MTTC Mathematics (Secondary) 022 being retired?
The test page, read October 9, 2026, says the last administration date for field 022 will be in 2029. Until then it is given by appointment year-round at test centers in Michigan and nationwide.