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About the Test
Name of Test: Mathematics (023)
2 Hours and 45 min (includes 15min tutorial)
80 multiple-choice questions
Average time per question: 1 minute 48 seconds
Passing score: 220 out of 300 points
You are not penalized for wrong answers--so if you are stuck, go ahead and guess
Fee: $73
Takes ~18 days to get score (to see score schedule, clear here then click “view score report dates")
Online Scientific Calculator and Formulas page is provided
Content Breakdown (Framework)
Copy and paste this framework into your study guide document. Highlight areas of least confidence red, medium confidence orange, and most confidence green.
Numbers and Quantity - 14%
Understand real numbers and mathematical problem solving
Analyze the structure of the real numbers.
Analyze the properties of numbers and operations.
Apply the principles of basic number theory (e.g., prime factorization, greatest common factor, least common multiple) to solve real-life and mathematical problems.
Solve real-life and mathematical problems involving integers, fractions, decimals, and percents.
Solve real-life and mathematical problems involving ratios, proportions, and average rates of change.
Solve real-life and mathematical problems involving irrational numbers and exponents.
Understand complex numbers, vectors, and matrices
Apply complex numbers and their operations to solve problems.
Translate between representations of vector quantities (e.g., graphic, verbal, symbolic).
Perform vector operations and solve problems that can be modeled using vectors.
Demonstrate knowledge of matrix operations.
Apply properties of matrices to model and solve problems
Patterns, Algebra, and Functions - 30%
Understand relations and functions
Demonstrate knowledge of relations and functions and their applications.
Translate between different representations of functions.
Perform operations with functions, including compositions and inverses.
Analyze characteristics of functions.
Interpret different representations (e.g., equations, graphs, tables) of functions.
Analyze sequences and series, including limits and recursive definitions, and use them to solve problems.
Understand linear, quadratic, and higher-order polynomial functions
Analyze the relationship between a linear, quadratic, or higher-order polynomial function and its graph.
Solve linear and quadratic equations and inequalities using a variety of methods.
Solve systems of linear equations or inequalities using a variety of methods.
Solve higher-order polynomial equations and inequalities in one and two variables.
Analyze the characteristics of linear, quadratic, and higher-order polynomial equations.
Model and solve real-life problems involving linear, quadratic, and higher-order polynomial functions
Understand exponential and logarithmic functions
Apply the laws of exponents and logarithms.
Analyze the relationship between exponential and logarithmic functions.
Analyze exponential and logarithmic functions and their graphs.
Model and solve real-life and mathematical problems involving exponential and logarithmic functions.
Understand rational, radical, absolute value, and piecewise defined functions
Manipulate rational, radical, and absolute value expressions, equations, and inequalities.
Analyze the relationship between a rational, radical, absolute value, or piecewise defined function and its graph.
Analyze rational, radical, absolute value, and piecewise defined functions in terms of domain, range, and asymptotes.
Model and solve real-life and mathematical problems involving rational, radical, absolute value, and piecewise defined functions.
Measurement and Geometry - 21%
Understand measurement principles and procedures
Reason quantitatively and use units and unit conversions to solve problems.
Apply the concepts of similarity, scale factors, and proportional reasoning to model and solve measurement problems.
Analyze precision, error, and rounding in measurements and computed quantities.
Apply the concepts of perimeter, circumference, area, surface area, and volume to solve real-life and mathematical problems.
Understand Euclidean geometry in two and three dimensions
Demonstrate knowledge of inductive and deductive reasoning and of axiomatic systems.
Use the properties of triangles (e.g., centroid, orthocenter) and of right triangles (e.g., basic trigonometric ratios) to model and solve problems.
Use the properties of polygons and circles to model and solve problems.
Apply the Pythagorean theorem and its converse to model and solve real-life and mathematical problems.
Analyze formal and informal proofs, using geometric concepts (e.g., similarity, properties of angles, parallel lines).
Use two-dimensional diagrams and representations (e.g., nets, cross sections, vertex-edge graphs) to analyze three-dimensional figures
Understand coordinate and transformational geometry
Analyze two- and three-dimensional figures using coordinate systems.
Apply concepts of distance, midpoint, and slope to classify figures and model and solve problems in the coordinate plane.
Analyze conic sections, their equations, and the relationship between the equation of a conic section and its graph.
Determine the effects of transformations on the graph of a function or relation.
Analyze transformations and symmetries of figures and of the graphs of functions in the coordinate plane.
Trigonometry and Calculus - 21%
Understand trigonometric functions
Apply trigonometric functions to solve problems involving distance and angles.
Apply trigonometric functions to solve problems involving the unit circle.
Manipulate trigonometric expressions and solve equations using techniques such as trigonometric identities.
Analyze the relationship between a trigonometric function and its graph.
Use trigonometric functions to model periodic relationships
Understand differential calculus
Evaluate limits.
Demonstrate knowledge of continuity.
Analyze the derivative as the slope of a tangent line and as the limit of the difference quotient.
Calculate the derivatives of functions (e.g., polynomial, exponential, logarithmic).
Apply differentiation to analyze the graphs of functions.
Apply differentiation to solve real-life and mathematical problems involving rates of change and optimization.
Understand integral calculus
Apply the fundamental theorem of calculus to model and solve
problems.
Analyze the integral as the area under a curve and as the limit of the Riemann sum.
Calculate the integrals of functions (e.g., polynomial, exponential, logarithmic).
Apply integration to analyze the graphs of functions.
Apply integration to solve real-life and mathematical problems, including problems involving solids of revolution.
Statistics and Probability - 14%
Understand principles and techniques of statistics.
Use appropriate formats for organizing and displaying data.
Analyze data in a variety of representations.
Analyze the use of measures of central tendency and variability.
Analyze the effects of bias and sampling techniques
Understand principles and techniques of probability.
Apply the rules of probability to compute probabilities of simple and compound events and conditional probabilities.
Use counting principles (e.g., permutations, combinations) and set theory to calculate probabilities and solve problems.
Use a variety of graphical representations to calculate probabilities.
Select simulations that model real-life events.
Analyze uniform, binomial, and normal probability distributions.
Study Resources
Green=Free resource
Pink=Paid resource
***=Top rated study resource
Official MOCA test questions from the MOCA test developer:
Free Sample Questions: http://www.mo.nesinc.com/Content/StudyGuide/MO_SG_SRI_023.htm
***$29.95 The official full MOCA practice test***
If you can only purchase one study resource, this is the one to pick. Though you can only take it twice, you can review the questions and answers anytime within 120 days of purchasing
Digital Materials the test development companies that make the MOCA and other content area tests:
$24.99 NES Study Guide (select “Secondary Mathematics”)
The study guide portion does not have much study content (mostly it’s a list of possible topics), but there are lots of practice questions and the best part is that you can look up practice questions by topic
$29.95 A practice test from NES which has a similar framework to the MOCA test: full NES practice test
Resources from online study sites:
Free Practice Test (diagnostic, too): 240 tutoring
You can see your overall score without an account, but to see the diagnostic report you need to create a free account.
$39.99 They offer a monthly membership for study materials (materials, flashcards, quizzes, practice test)
Free: Look up specific topics at https://www.khanacademy.org/
Study.com membership $60 a month: Study.com math materials
Print resources:
***Mometrix study book, created by a study guide company and aligns with the MOCA framework. Includes content by category and a practice test. The content can tend to be more surface level but it is a great resource, overall. An essential study resource.***
Free to borrow, SLU SOE has a couple copies, contact karissa.sywulka@slu.edu to see if one is available
$39.99-$72.99 Purchase your own
Free books at Pius library
There are teacher edition math textbooks that you can use to study specific topics. Ask Martha Allen for assistance.
Missouri Student Test Questions:
These are practice tests for student-level math exams for Missouri. These practice questions should be on similar topics to the MoCA
Formulas you will have available on the test:
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