240's OAE Mathematics Study Guide Is 99% Test-Aligned
240's OAE Mathematics study guide is built around the official exam framework so you can study what is actually tested. This page shows exactly how the guide maps to the real exam — SMR by SMR and competency by competency — so you can see where coverage is strongest, where some depth gaps remain, and how each part of the guide supports your prep.
99%
test-aligned
71
Fully covered
2
Partially covered
0
Coverage gap
Based on a competency-by-competency review of the official framework and the lessons, practice questions, flashcards, videos, and study materials included in this guide.
2802
Practice Questions
546
Flashcards
267
Study Materials
56
Videos
Why Test Alignment Matters for Your OAE Mathematics Study Guide
Certification test standards are broad, but the exam questions are very specific. Our team of curriculum experts uses the 240 Study Guide Creation Process to ensure the most aligned, specific content for your OAE Mathematics (027) test — so you are not wasting time on broad subject review that may not show up on exam day.
Why 240 Is the Best Choice for the OAE 027 Study Guide
- Built around the official exam framework
- Organized by the competencies actually used on the exam
- Shows exactly what is covered and where depth is partial
- Includes aligned questions, flashcards, study materials, and videos
- Helps candidates study what is actually tested instead of broad generic content
Transparent coverage is a strength. We show where the guide is strong, where depth is partial, and where a gap has been identified so you can make an informed study decision.
How to Read This Alignment Review
5 domains · 73 competencies reviewed · 99% test-aligned
Covered— competency is comprehensively supported by the guide
Partially covered— core content is covered, but some depth gaps remain
Coverage gap identified— a content gap has been identified
This study guide is based on the current official exam framework
We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.
MATHEMATICAL PROCESSES AND NUMBER SENSE (DOMAIN I)
Partially covered
SMR I.0001 Understand mathematical problem solving.
318 Qs21 Materials51 Cards8 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Identify an appropriate problem-solving strategy for a particular problem. | M.Selecting Appropriate Solution Strategies; M.Prioritizing Relevant and Missing Information; M.Using Structure to Analyze Complex Problems | Covered | 29 | 3 | 1 | 0 | Covered by 3 topics (29 questions, 3 materials, 1 cards, 0 videos). |
| B. Analyze the use of estimation in a variety of situations (e.g., rounding, area, plausibility). | M.Reasonableness of Results; M.Sense Making and Perseverance; M.Rounding; M.Mental Math and Estimation | Covered | 50 | 4 | 8 | 1 | Covered by 4 topics (50 questions, 4 materials, 8 cards, 1 videos). |
| C. Solve mathematical and real-world problems involving integers, fractions, decimals, and percents. | M.Operational Properties; M.Operational Algorithm Relationships; M.Order of Operations; M.Order of Operations - Grouping; M.Inverse Operations; M.Fraction, Decimal, Percentage Conversions; M.Fraction Composition and Decomposition; M.Representations of Fractions in Word Problems; M.Fraction Operations - Multiply and Divide; M.Fraction Operations - Mixed Numbers; M.Connecting Situations with Operations | Covered | 176 | 11 | 39 | 5 | Covered by 11 topics (176 questions, 11 materials, 39 cards, 5 videos). |
| D. Solve mathematical and real-world problems involving ratios, proportions, and average rates of change. | M.Ratios; M.Unit Rates; M.Proportional Reasoning - Word Problems | Covered | 63 | 3 | 3 | 2 | Covered by 3 topics (63 questions, 3 materials, 3 cards, 2 videos). |
SMR I.0002 Understand mathematical communication, connections, and reasoning.
106 Qs13 Materials25 Cards1 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Translate between representations (e.g., graphic, verbal, symbolic). | M.Alternate Representations of Problems; M.Variety of Representations; M.Variety of Representations for Older Children; M.Verbal to Symbolic Expression - Basic | Covered | 61 | 4 | 13 | 1 | Covered by 4 topics (61 questions, 4 materials, 13 cards, 1 videos). |
| B. Recognize connections between mathematical concepts. | M.Mathematical Connections; M.Rational Expressions | Covered | 19 | 2 | 2 | 0 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 0 videos). |
| C. Analyze inductive and deductive reasoning. | M.Inductive vs Deductive Reasoning | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| D. Apply principles of logic to solve problems. | M.Formal Reasoning Rules; M.Evaluating Truth of Statements; M.Logic Terminology and Symbols; M.Using Logic for Truth; M.Using Logic for Equivalence | Covered | 11 | 5 | 7 | 0 | Covered by 5 topics (11 questions, 5 materials, 7 cards, 0 videos). |
| E. Demonstrate knowledge of the historical development of major mathematical concepts, including contributions from diverse cultures. | M.Historical Events and Contributions | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR I.0003 Understand number theory.
170 Qs12 Materials34 Cards4 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyze the group structure of the real numbers. | M.Structure of Number Systems; M.Characteristics of Rational Numbers; M.Order Real Numbers by Magnitude | Covered | 47 | 3 | 14 | 2 | Covered by 3 topics (47 questions, 3 materials, 14 cards, 2 videos). |
| B. Use complex numbers and their operations. | M.Complex Numbers and the Complex Plane; M.Complex Numbers and Their Conjugates; M.Complex Numbers - Inverses; M.Polynomial Identities - Complex Numbers; M.Complex Numbers - Modulus | Covered | 35 | 5 | 12 | 0 | Covered by 5 topics (35 questions, 5 materials, 12 cards, 0 videos). |
| C. Analyze the properties of numbers and operations. | M.Characteristics of Rational Numbers; M.Properties of Exponents | Covered | 33 | 2 | 9 | 0 | Covered by 2 topics (33 questions, 2 materials, 9 cards, 0 videos). |
| D. Apply the principles of basic number theory (e.g., prime factorization, greatest common factor, least common multiple). | M.Factors; M.Prime Factorization; M.Fraction Operations - Add and Subtract | Covered | 63 | 3 | 9 | 2 | Covered by 3 topics (63 questions, 3 materials, 9 cards, 2 videos). |
PATTERNS, ALGEBRA, AND FUNCTIONS (DOMAIN II)
Covered
SMR II.0004 Understand relations and functions.
216 Qs19 Materials40 Cards5 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrate knowledge of relations and functions and their applications. | M.Forms of Equations; M.Dependent and Independent Variables; M.Verbal to Symbolic Linear Equations; M.Relation and Function Representations | Covered | 76 | 4 | 18 | 2 | Covered by 4 topics (76 questions, 4 materials, 18 cards, 2 videos). |
| B. Perform operations with functions, including compositions and inverses. | M.Function Composition and Inversion; M.Determine the Validity of an Inverse; M.Linear Expression Addition and Subtraction; M.Properties of Equality; M.Rearranging Formulas - Isolate | Covered | 56 | 5 | 11 | 2 | Covered by 5 topics (56 questions, 5 materials, 11 cards, 2 videos). |
| C. Analyze characteristics of functions. | M.Determine the Validity of an Inverse; M.Surjective vs Injective; M.Direct and Indirect Variation; M.Even and Odd Functions | Covered | 23 | 4 | 9 | 0 | Covered by 4 topics (23 questions, 4 materials, 9 cards, 0 videos). |
| D. Interpret different representations of functions. | M.Relation and Function Representations; M.Understanding Linear Functions and Their Properties; M.Linear Equations - Rearrange to Slope-Intercept Form; M.Linear Equations - Standard Form; M.Linear Equations - Point-Slope Form; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Sketch a Polynomial - From Roots; M.Conjectures from Graphs | Covered | 103 | 8 | 11 | 1 | Covered by 9 topics (103 questions, 8 materials, 11 cards, 1 videos). |
SMR II.0005 Understand linear, quadratic, and higher-order polynomial functions.
194 Qs24 Materials31 Cards8 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyze the relationship between a linear, quadratic, or higher-order polynomial function and its graph. | M.Parent Functions; M.Functional Transformations - Linear and Quadratic | Covered | 21 | 2 | 6 | 0 | Covered by 2 topics (21 questions, 2 materials, 6 cards, 0 videos). |
| B. Solve linear and quadratic equations and inequalities using a variety of methods. | M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope; M.Solve for x - Linear; M.Solve for x - Linear (Multiple Variables); M.Interpreting Inequalities; M.Solve Linear Inequalities - Graphically; M.Solving Linear Inequalities; M.Compound Inequalities on Number Line; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Quadratic Equations; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square; M.Quadratic Equation - Solve via Quadratic Formula; M.Advanced Quadratic Equation - Real World Problems | Covered | 132 | 17 | 16 | 7 | Covered by 17 topics (132 questions, 17 materials, 16 cards, 7 videos). |
| C. Solve systems of linear equations or inequalities using a variety of methods. | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Inequalities | Covered | 21 | 2 | 1 | 1 | Covered by 2 topics (21 questions, 2 materials, 1 cards, 1 videos). |
| D. Solve higher-order polynomial equations and inequalities in one and two variables. | M.Polynomials; M.Advanced Factoring Polynomials | Covered | 20 | 2 | 7 | 0 | Covered by 2 topics (20 questions, 2 materials, 7 cards, 0 videos). |
| E. Analyze the characteristics of linear, quadratic, and higher-order polynomial equations. | M.Quadratic Equations; M.Quadratic Equation - Solve via Quadratic Formula; M.Polynomials; M.Extraneous Solutions | Covered | 37 | 4 | 12 | 1 | Covered by 4 topics (37 questions, 4 materials, 12 cards, 1 videos). |
| F. Analyze real-world problems involving linear, quadratic, and higher-order polynomial functions. | M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope; M.Advanced Quadratic Equation - Real World Problems | Covered | 22 | 3 | 0 | 1 | Covered by 3 topics (22 questions, 3 materials, 0 cards, 1 videos). |
SMR II.0006 Understand exponential and logarithmic functions.
90 Qs10 Materials17 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Apply the laws of exponents and logarithms. | M.Properties of Logarithms; M.Exponential Functions; M.Logarithmic Functions; M.Logarithmic Functions - Change Base | Covered | 47 | 4 | 11 | 0 | Covered by 4 topics (47 questions, 4 materials, 11 cards, 0 videos). |
| B. Analyze the relationship between exponential and logarithmic functions. | M.Logarithmic Functions | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| C. Analyze exponential and logarithmic functions and their graphs. | M.Exponential Functions; M.Exponential Functions - Asymptotes; M.Exponential Functions - Reflections; M.Logarithmic Functions - Graph | Covered | 23 | 4 | 5 | 0 | Covered by 4 topics (23 questions, 4 materials, 5 cards, 0 videos). |
| D. Analyze real-world problems involving exponential and logarithmic functions. | M.Logarithmic Functions; M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest; M.Logarithmic Phenomena | Covered | 40 | 4 | 12 | 0 | Covered by 4 topics (40 questions, 4 materials, 12 cards, 0 videos). |
SMR II.0007 Understand rational, radical, absolute value, and piece-wise defined functions.
155 Qs21 Materials33 Cards3 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Manipulate rational, radical, and absolute value expressions, equations, and inequalities. | M.Rational Functions; M.Square Roots and Radicals; M.Radicals and Exponents; M.Simplifying Radicals; M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Operations with Radicals; M.Absolute Value Inequalities; M.Absolute Value Functions; M.Solve for x - Radical | Covered | 79 | 10 | 18 | 2 | Covered by 10 topics (79 questions, 10 materials, 18 cards, 2 videos). |
| B. Analyze the relationship between a rational, radical, absolute value, or piece-wise defined function and its graph. | M.Piecewise Functions; M.Rational Functions; M.Absolute Value Functions; M.Functional Transformations - Absolute Value; M.Functional Transformations - Radical | Covered | 40 | 5 | 8 | 0 | Covered by 5 topics (40 questions, 5 materials, 8 cards, 0 videos). |
| C. Analyze rational, radical, absolute value, and piece-wise defined functions in terms of domain, range, and asymptotes. | M.Piecewise Functions; M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions; M.Advanced Domain and Range of Functions - Piecewise; M.Advanced Domain and Range of Functions - Composition | Covered | 21 | 6 | 11 | 0 | Covered by 6 topics (21 questions, 6 materials, 11 cards, 0 videos). |
| D. Analyze real-world problems involving rational, radical, absolute value, and piece-wise defined functions. | M.Real-World Applications; M.Symbolic to Verbal; M.Solving Piecewise Functions | Covered | 26 | 3 | 5 | 1 | Covered by 3 topics (26 questions, 3 materials, 5 cards, 1 videos). |
MEASUREMENT AND GEOMETRY (DOMAIN III)
Covered
SMR III.0008 Understand measurement principles and procedures.
317 Qs17 Materials36 Cards9 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyze the use of various units and unit conversions within the customary and metric systems. | M.Measurement Principles; M.Metric System; M.Choosing Appropriate Units; M.Converting Units - Proportional Reasoning; M.Converting Units - Dimensional Analysis | Covered | 95 | 5 | 16 | 4 | Covered by 5 topics (95 questions, 5 materials, 16 cards, 4 videos). |
| B. Apply the concepts of similarity, scale factors, and proportional reasoning to solve measurement problems. | M.Inversely Proportional vs Directly Proportional; M.Ratios, Proportions, Percents; M.Constants of Proportionality; M.Advanced Measurement Principles | Covered | 52 | 4 | 12 | 1 | Covered by 4 topics (52 questions, 4 materials, 12 cards, 1 videos). |
| C. Analyze precision, error, and rounding in measurements and computed quantities. | M.Measurement Principles; M.Advanced Measurement Principles | Covered | 20 | 2 | 14 | 0 | Covered by 2 topics (20 questions, 2 materials, 14 cards, 0 videos). |
| D. Apply the concepts of perimeter, circumference, area, surface area, and volume to solve real-world problems. | M.Area and Perimeter of Polygons; M.Measurements in Circles; M.Surface Area in 3D; M.Volume in 3D; M.Convert Between Surface Area and Volume; M.Dimensional Changes Affecting Area and Volume; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 170 | 8 | 10 | 4 | Covered by 8 topics (170 questions, 8 materials, 10 cards, 4 videos). |
SMR III.0009 Understand Euclidean geometry in two and three dimensions.
207 Qs19 Materials80 Cards3 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrate knowledge of axiomatic systems and of the axioms of non-Euclidean geometries. | M.Proofs; M.Coordinate Geometry; M.Euclidean Versus Non-Euclidean Geometry; M.Taxicab Measurements | Covered | 27 | 4 | 11 | 0 | Covered by 4 topics (27 questions, 4 materials, 11 cards, 0 videos). |
| B. Use the properties of polygons and circles to solve problems. | M.Measurements in Circles; M.Measurements in Circles Advanced; M.Angles and Measurements in Polygons; M.Solving with Shapes - Quadrilaterals; M.Attributes of Polygons - Advanced | Covered | 83 | 5 | 41 | 1 | Covered by 5 topics (83 questions, 5 materials, 41 cards, 1 videos). |
| C. Apply the Pythagorean theorem and its converse. | M.Pythagorean Theorem | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| D. Analyze formal and informal geometric proofs, including the use of similarity and congruence. | M.Proofs; M.Coordinate Geometry; M.Indirect Proofs; M.Prove Theorems - Lines and Angles; M.Prove Theorems - Triangles; M.Prove Theorems - Parallelograms; M.Prove Properties - Quadrilateral Inscribed in a Circle; M.Prove Slope Criteria | Covered | 66 | 8 | 25 | 0 | Covered by 8 topics (66 questions, 8 materials, 25 cards, 0 videos). |
| E. Use nets and cross sections to analyze three-dimensional figures. | M.Attributes of Three Dimensional Figures; M.Nets; M.Rotating 3D Objects | Covered | 35 | 3 | 8 | 1 | Covered by 3 topics (35 questions, 3 materials, 8 cards, 1 videos). |
SMR III.0010 Understand coordinate and transformational geometry.
167 Qs13 Materials44 Cards4 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyze two- and three-dimensional figures using coordinate systems. | M.The Coordinate Plane; M.Polar Coordinates; M.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, Angles | Covered | 68 | 4 | 23 | 3 | Covered by 4 topics (68 questions, 4 materials, 23 cards, 3 videos). |
| B. Apply concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane. | M.Slope, Midpoint, and Distance; M.Spatial Reasoning; M.Circles and Ellipses | Covered | 38 | 3 | 7 | 1 | Covered by 3 topics (38 questions, 3 materials, 7 cards, 1 videos). |
| C. Analyze conic sections. | M.Conic Sections; M.Conic Sections - Derive Parabola; M.Conic Sections - Derive Ellipses and Hyperbolas | Covered | 21 | 3 | 4 | 0 | Covered by 3 topics (21 questions, 3 materials, 4 cards, 0 videos). |
| D. Determine the effects of geometric transformations on the graph of a function or relation. | M.Non-Rigid Transformations; M.Rigid Transformations | Covered | 22 | 2 | 8 | 0 | Covered by 2 topics (22 questions, 2 materials, 8 cards, 0 videos). |
| E. Analyze transformations and symmetries of figures in the coordinate plane. | M.Non-Rigid Transformations; M.Multiple Transformations; M.Rigid Transformations | Covered | 40 | 3 | 10 | 0 | Covered by 3 topics (40 questions, 3 materials, 10 cards, 0 videos). |
TRIGONOMETRY AND CALCULUS (DOMAIN IV)
Covered
SMR IV.0011 Understand trigonometric functions.
100 Qs11 Materials5 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Apply trigonometric functions to solve problems involving distance and angles. | M.Laws of Sines and Cosines; M.Trigonometric Ratios; M.Inverse Trigonometric Ratios | Covered | 31 | 3 | 2 | 1 | Covered by 3 topics (31 questions, 3 materials, 2 cards, 1 videos). |
| B. Apply trigonometric functions to solve problems involving the unit circle. | M.The Unit Circle | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| C. Manipulate trigonometric expressions and equations using techniques such as trigonometric identities. | M.Advanced Trigonometric Identities - Special Triangles; M.Advanced Trigonometric Identities - Pythagorean Identities; M.Advanced Trigonometric Identities - More | Covered | 21 | 3 | 0 | 0 | Covered by 3 topics (21 questions, 3 materials, 0 cards, 0 videos). |
| D. Analyze the relationship between a trigonometric function and its graph. | M.Trigonometric Ratio Graphs; M.Trigonometric Ratio Graphs - Real Word Problems; M.Technology and Trigonometric Function Problems | Covered | 28 | 3 | 3 | 0 | Covered by 3 topics (28 questions, 3 materials, 3 cards, 0 videos). |
| E. Use trigonometric functions to model periodic relationships. | M.Analyze and Solve Trigonometric Functions | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
SMR IV.0012 Understand differential calculus.
127 Qs13 Materials35 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Evaluate limits. | M.Teaching the Concept of Limits in Sequences and Series; M.Limits and Continuity; M.Limits and Continuity - Asymptote Equations; M.One-Sided Limits; M.Limits That Do Not Exist | Covered | 46 | 5 | 6 | 0 | Covered by 5 topics (46 questions, 5 materials, 6 cards, 0 videos). |
| B. Demonstrate knowledge of continuity. | M.Limits and Continuity; M.Limits and Continuity - Asymptote Equations; M.Continuity and Differentiability | Covered | 37 | 3 | 9 | 0 | Covered by 3 topics (37 questions, 3 materials, 9 cards, 0 videos). |
| C. Analyze the derivative as the slope of a tangent line and as the limit of the difference quotient. | M.Calculus Connections to Formulas; M.Rates of Change - Average vs Instantaneous; M.Derivatives and Slopes | Covered | 33 | 3 | 10 | 0 | Covered by 3 topics (33 questions, 3 materials, 10 cards, 0 videos). |
| D. Calculate the derivatives of functions (e.g., polynomial, exponential, logarithmic). | M.Derivatives and Slopes; M.Derivatives and Trig Functions | Covered | 21 | 2 | 7 | 0 | Covered by 2 topics (21 questions, 2 materials, 7 cards, 0 videos). |
| E. Apply differentiation to analyze the graphs of functions. | M.Derivatives and Slopes; M.Higher Order Derivatives and Slopes | Covered | 35 | 2 | 20 | 0 | Covered by 2 topics (35 questions, 2 materials, 20 cards, 0 videos). |
| F. Apply differentiation to solve real-world problems involving rates of change and optimization. | M.Rates of Change - Average vs Instantaneous; M.Calculus - Rates; M.Calculus - Velocity and Acceleration | Covered | 24 | 3 | 7 | 0 | Covered by 3 topics (24 questions, 3 materials, 7 cards, 0 videos). |
SMR IV.0013 Understand integral calculus.
60 Qs10 Materials16 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyze the integral as the area under a curve and as the limit of the Riemann sum. | M.Riemann Sums; M.Integration; M.Foundational Theorems of Calculus | Covered | 22 | 3 | 8 | 0 | Covered by 3 topics (22 questions, 3 materials, 8 cards, 0 videos). |
| B. Calculate the integrals of functions (e.g., polynomial, exponential, logarithmic). | M.Integration; M.Integrals Yielding Logarithms | Covered | 15 | 2 | 4 | 0 | Covered by 2 topics (15 questions, 2 materials, 4 cards, 0 videos). |
| C. Apply integration to analyze the graphs of functions. | M.Areas by Integration; M.Distance by Integration | Covered | 15 | 2 | 3 | 0 | Covered by 2 topics (15 questions, 2 materials, 3 cards, 0 videos). |
| D. Apply integration to solve real-world problems. | M.Areas by Integration; M.Distance by Integration; M.Accumulations; M.Volumes by Integration; M.Calculus - Work; M.Calculus - Center of Mass | Covered | 31 | 6 | 8 | 0 | Covered by 6 topics (31 questions, 6 materials, 8 cards, 0 videos). |
STATISTICS, PROBABILITY, AND DISCRETE MATHEMATICS (DOMAIN V)
Partially covered
SMR V.0014 Understand principles and techniques of statistics.
296 Qs21 Materials77 Cards6 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Use appropriate formats for organizing and displaying data. | M.Graphs and Plots; M.Boxplots; M.Spreadsheet Fields; M.Appropriate vs Inappropriate Representations of Data; M.Interpolation of Data; M.Choosing a Graph or Plot | Covered | 69 | 6 | 19 | 2 | Covered by 6 topics (69 questions, 6 materials, 19 cards, 2 videos). |
| B. Analyze data in a variety of representations. | M.Data Analysis and Interpretation; M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis | Covered | 57 | 3 | 15 | 2 | Covered by 3 topics (57 questions, 3 materials, 15 cards, 2 videos). |
| C. Analyze the use of measures of central tendency and variability. | M.Measures of Center and Range; M.Statistics of One-Variable Data; M.Advanced Measures of Center and Range; M.Describing Data Patterns and Outliers; M.Effect of Change in Data on Measures of Center and Range; M.Correlation vs Causation; M.Level of Confidence; M.Chi-Square Test; M.Hypothesis Testing | Covered | 137 | 9 | 32 | 2 | Covered by 9 topics (137 questions, 9 materials, 32 cards, 2 videos). |
| D. Analyze the effects of bias and sampling techniques. | M.Appropriate vs Inappropriate Representations of Data; M.Surveys; M.Observations, Conclusions, and Relationships; M.Sampling Methods | Covered | 42 | 4 | 15 | 0 | Covered by 4 topics (42 questions, 4 materials, 15 cards, 0 videos). |
SMR V.0015 Understand principles and techniques of probability.
186 Qs21 Materials44 Cards5 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Determine probabilities of simple and compound events and conditional probabilities. | M.Probability; M.Expressing Probabilities; M.Simple and Compound Events | Covered | 61 | 3 | 10 | 2 | Covered by 3 topics (61 questions, 3 materials, 10 cards, 2 videos). |
| B. Use counting principles to calculate probabilities. | M.Sample Spaces to Determine Probabilities; M.Fundamental Counting Principle | Covered | 14 | 2 | 2 | 2 | Covered by 2 topics (14 questions, 2 materials, 2 cards, 2 videos). |
| C. Use a variety of graphical representations to calculate probabilities. | M.Probability Models; M.Diagrams; M.Diagrams - Venn Symbols; M.Tables to Determine Independence; M.Geometric Probability | Covered | 38 | 5 | 8 | 1 | Covered by 5 topics (38 questions, 5 materials, 8 cards, 1 videos). |
| D. Select simulations that model real-world events. | M.Probability Simulations | Partially covered | 7 | 1 | 3 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| E. Analyze uniform, binomial, and normal probability distributions. | M.Calculating Linear Regression; M.Linear Regression with Non-Linear Data; M.Central Limit Theorem and Large Numbers; M.Probability Distributions; M.Comparing to Probability Distribution; M.Probability Distributions - Expected Value; M.Probability Distributions - From Simulation; M.Normal Distribution; M.Using Distributions; M.Uniform Distributions | Covered | 66 | 10 | 28 | 0 | Covered by 10 topics (66 questions, 10 materials, 28 cards, 0 videos). |
SMR V.0016 Understand principles of discrete mathematics.
111 Qs23 Materials50 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Apply concepts of permutations and combinations to solve problems. | M.Combinations and Permutations | Covered | 20 | 1 | 2 | 0 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos). |
| B. Analyze sequences and series including limits and recursive definitions. | M.Fibonacci Sequences; M.Recursion and Iteration; M.Concepts of Series and Sequence; M.Diverge or Converge; M.Find Sum of Series; M.Find Partial Sum of Series | Covered | 18 | 6 | 15 | 0 | Covered by 6 topics (18 questions, 6 materials, 15 cards, 0 videos). |
| C. Perform operations on matrices and vectors. | M.Matrices and Addition Subtraction; M.Matrices and Scalar Multiplication; M.Matrices and Multiplication; M.Matrices - Determinant and Inverse; M.Matrices to Solve Systems of Equations; M.Properties of Matrices; M.Advanced Matrices; M.Solving with Matrix Transformations; M.Vectors and Scalars; M.Solving with Vector Representations; M.Vector Multiplication - Cross Product; M.Vector Multiplication - Dot Product; M.Vector Multiplication by a Scalar; M.Vector Addition and Subtraction | Covered | 67 | 14 | 22 | 0 | Covered by 14 topics (67 questions, 14 materials, 22 cards, 0 videos). |
| D. Apply set theory to solve problems. | M.Domain and Range - Set Notation; M.Group, Ring, and Field Theory | Covered | 6 | 2 | 12 | 0 | Covered by 2 topics (6 questions, 2 materials, 12 cards, 0 videos). |
How 240 Creates The OAE Mathematics (027) Study Guide
Learn more →Every 240 study guide starts with the official exam framework. From there, we organize lessons, practice, and study tools around the categories the exam uses to measure candidate knowledge.
1
Review the official exam framework
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
2
Map the tested categories
We map every major area the exam is designed to cover so the guide reflects the real structure of the test.
3
Build lessons around tested content
We create study materials to support the official blueprint, not broad filler content.
4
Cross-check practice against exam expectations
We review practice content against the framework and real exam patterns so preparation stays targeted.
5
Review and update as standards change
When official frameworks change, we review guides and update alignment as needed.
Reviewed by subject-matter experts and maintained to reflect current standards.
Built By Teachers for Teachers
You're not on this journey alone. Our 240 teachers have firsthand experience with these exams. Real teachers with real experience are behind the scenes to help guide you into the classroom where YOU belong.
Why 240 Is Better Than Other Generic Study Guides
Not all study guides are built the same way. Here is what separates a test-aligned guide from a generic one — and why it matters when you are preparing for the OAE Mathematics.
Generic
Generic Prep
✕Covers broad subject areas without structure
✕No clear connection to the official exam framework
✕Practice questions may not reflect the real test format
✕May not update when official standards change
~Can be helpful for quick, broad review
Test-aligned
240 Test-Aligned OAE 027 Prep
✓Every lesson maps to an official domain or competency
✓Built directly from the official exam framework
✓Practice questions aligned to what the exam actually measures
✓A clear study path by tested category
✓Study smarter and enter test day more prepared
FAQs About the OAE Mathematics Study Guide
The questions teacher candidates ask us most often about the OAE Mathematics study guide.
1
Is 240 a good study guide for OAE Mathematics?
240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.
2
How closely does 240 align to the OAE 027 exam?
This guide is 99% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.
3
Does 240 cover every competency?
This page shows coverage transparently across covered, partially covered, and identified gaps so candidates can see exactly how the guide maps to the exam.
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What does “partially covered” mean?
Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.
Study What's Actually on the OAE 027 Exam
Start with a study guide built around the real exam. 240's guide maps lessons and study tools to official competencies so you can prepare more efficiently and more confidently.