240's FTCE Mathematics 6-12 Study Guide Is 98% Test-Aligned
240's FTCE Mathematics 6-12 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.
98%
test-aligned
64
Fully covered
3
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.
2734
Practice Questions
506
Flashcards
248
Study Materials
61
Videos
Why Test Alignment Matters for Your FTCE Mathematics 6-12 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 FTCE Mathematics 6-12 (026) 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 FTCE 026 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
6 domains · 67 competencies reviewed · 98% 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.
KNOWLEDGE OF NUMBER SENSE, OPERATIONS, AND PROPORTIONALITY (DOMAIN 1)
Covered
319 Qs16 Materials32 Cards12 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Compare and convert between rational numbers represented in various ways (i.e., fractions, terminating and repeating decimals, percentages, number line). | M.Structure of Number Systems | Covered | 11 | 1 | 5 | 1 | Covered by 1 topic (11 questions, 1 materials, 5 cards, 1 videos). |
| 2. Solve problems by performing operations with rational numbers, using estimates and algorithms, and evaluate multi-step expressions using order of operations (e.g., expressions with rational exponents, multiple levels of grouping symbols, radicals, absolute value). | M.Operational Properties; M.Identities; M.Order of Operations; M.Order of Operations - Grouping; M.Operations with Radicals | Covered | 104 | 5 | 10 | 3 | Covered by 5 topics (104 questions, 5 materials, 10 cards, 3 videos). |
| 3. Estimate irrational numbers, including square roots, and compare them to rational numbers. | M.Square Roots and Radicals; M.Order Real Numbers by Magnitude | Covered | 37 | 2 | 6 | 1 | Covered by 2 topics (37 questions, 2 materials, 6 cards, 1 videos). |
| 4. Represent real number approximations with scientific notation. | M.Exponential and Scientific Notation | Covered | 12 | 1 | 2 | 1 | Covered by 1 topic (12 questions, 1 materials, 2 cards, 1 videos). |
| 5. Solve problems involving ratios and proportions (e.g., mixtures, comparisons, rates, measurement conversions, graphs, percent growth, taxes, depreciation). | M.Fraction, Decimal, Percentage Conversions; M.Representations of Fractions in Word Problems; M.Ratios; M.Unit Rates; M.Ratios, Proportions, Percents; M.Proportional Reasoning - Word Problems; M.Converting Units - Dimensional Analysis | Covered | 155 | 7 | 11 | 6 | Covered by 7 topics (155 questions, 7 materials, 11 cards, 6 videos). |
KNOWLEDGE OF PRECALCULUS AND CALCULUS (DOMAIN 5)
Partially covered
366 Qs45 Materials99 Cards3 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 5. Determine and apply arithmetic and geometric sequences, defined explicitly or recursively, in mathematical and real-world problems. | M.Patterns - Developing an Expression; M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Mathematical Induction for Creating Formulas | Covered | 73 | 4 | 7 | 3 | Covered by 4 topics (73 questions, 4 materials, 7 cards, 3 videos). |
| 1. Solve mathematical and real-world problems involving quantities that can be represented by vectors (e.g., displacement, velocity, acceleration, force, magnetic fields), using addition, subtraction, and scalar multiplication of vectors represented both algebraically and on the coordinate plane. | 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 | 31 | 6 | 13 | 0 | Covered by 6 topics (31 questions, 6 materials, 13 cards, 0 videos). |
| 3. Apply the Fundamental Theorem of Algebra and the Factor Theorem to analyze polynomials (e.g., using the graph of a polynomial to help determine its algebraic formula). | M.Polynomials; M.Advanced Factoring Polynomials; M.Remainder Theorem; M.Factor Theorem; M.Rational Root Theorem; M.Conjugate Root Theorem; M.Rational Functions | Covered | 46 | 7 | 18 | 0 | Covered by 7 topics (46 questions, 7 materials, 18 cards, 0 videos). |
| 2. Solve mathematical and real-world problems using exponential and logarithmic functions and equations (e.g., exponential functions with base e and natural logarithms) and apply the properties of logarithmic functions. | M.Logarithmic Functions; M.Logarithmic Functions - Graph; M.Logarithmic Functions - Change Base | Covered | 20 | 3 | 3 | 0 | Covered by 3 topics (20 questions, 3 materials, 3 cards, 0 videos). |
| 4. Select rational functions representing mathematical and real-world problems in written and graphical form, and interpret key features of the graphs. | M.Exponential Functions - Real World Problems | Covered | 17 | 1 | 5 | 0 | Covered by 1 topic (17 questions, 1 materials, 5 cards, 0 videos). |
| 6. Determine limits using theorems concerning sums, products, and quotients of functions. | M.Limits and Continuity; M.Limits and Continuity - Asymptote Equations; M.One-Sided Limits; M.Limits That Do Not Exist; M.Operation Rules for Limits | Covered | 43 | 5 | 11 | 0 | Covered by 5 topics (43 questions, 5 materials, 11 cards, 0 videos). |
| 7. Determine derivatives of algebraic, exponential, logarithmic, and trigonometric functions and combinations of functions formed using arithmetic operations and compositions. | M.Derivatives and Slopes; M.Higher Order Derivatives and Slopes; M.Derivatives and Trig Functions; M.Derivatives and Exponential Functions; M.Derivatives and Logarithmic Functions | Covered | 46 | 5 | 22 | 0 | Covered by 5 topics (46 questions, 5 materials, 22 cards, 0 videos). |
| 8. Apply differentiation to determine features of functions representing mathematical and real-world problems (e.g., intervals, concavity, local maxima and minima, tangent lines of graphs). | M.Continuity and Differentiability; M.Calculus - Rates; M.Calculus - Velocity and Acceleration | Covered | 22 | 3 | 7 | 0 | Covered by 3 topics (22 questions, 3 materials, 7 cards, 0 videos). |
| 9. Apply properties of integration and substitution to determine anti-derivatives of algebraic, exponential, logarithmic, and trigonometric functions and combinations formed by using arithmetic operations. | M.Integration; M.Integration by Parts; M.Integrating Exponentials; M.Integrating Trigonometric Functions; M.Integrals Yielding Logarithms | Covered | 31 | 5 | 8 | 0 | Covered by 5 topics (31 questions, 5 materials, 8 cards, 0 videos). |
| 10. Apply definite integrals to solve mathematical and real-world problems involving distance, area, and volume. | M.Approximating Area; M.Accumulations; M.Areas by Integration; M.Volumes by Integration; M.Distance by Integration | Covered | 31 | 5 | 7 | 0 | Covered by 5 topics (31 questions, 5 materials, 7 cards, 0 videos). |
| 11. Calculate binomial expansions to a positive integral power or determine a specified term in the expansion. | M.Binomial Expansion | Partially covered | 6 | 1 | 4 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
KNOWLEDGE OF ALGEBRA (DOMAIN 2)
Covered
580 Qs60 Materials87 Cards12 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Generate equivalent expressions (e.g., polynomials, radical expressions, rational expressions) to determine a quantity of interest within a context or solve for an unknown. | M.Properties of Exponents; M.Properties of Exponents - Applying Multiple Properties; M.Radicals and Exponents; M.Simplifying Radicals | Covered | 53 | 4 | 4 | 1 | Covered by 4 topics (53 questions, 4 materials, 4 cards, 1 videos). |
| 4. Solve equivalent algebraic expressions (e.g., polynomials, radical expressions, rational expressions) in mathematical and real-world problems using operations (e.g., associative, commutative and distributive laws, order of operations, laws of exponents) and properties of equality. | M.Properties of Equality; M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Evaluation; M.Quadratic Expression Evaluation | Covered | 74 | 6 | 15 | 3 | Covered by 6 topics (74 questions, 6 materials, 15 cards, 3 videos). |
| 7. Evaluate systems of linear equations or linear inequalities that describe quantities or relationships in mathematical and real-world contexts. | M.Solve for x - Nonlinear; M.Solve for x - Linear (Multiple Variables); M.Solving Systems of Linear Equations; M.Solving Systems of Linear Equations - Word Problems; M.Solve for x - Radical | Covered | 47 | 5 | 1 | 2 | Covered by 5 topics (47 questions, 5 materials, 1 cards, 2 videos). |
| 6. Solve absolute value and quadratic inequalities with one or two variables, within real-world or mathematical contexts representing solutions algebraically or graphically. | M.Interpreting Inequalities; M.Solving Linear Inequalities; M.Solve Linear Inequalities - Graphically; M.Solving Systems of Linear Inequalities; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Absolute Value Inequalities | Covered | 49 | 8 | 9 | 2 | Covered by 8 topics (49 questions, 8 materials, 9 cards, 2 videos). |
| 9. Solve quadratic equations over the real and complex number systems. | M.Operations with Complex Numbers; M.Complex Numbers and Their Conjugates; 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; M.Quadratic Equations with Complex Roots | Covered | 64 | 7 | 8 | 1 | Covered by 7 topics (64 questions, 7 materials, 8 cards, 1 videos). |
| 2. Determine key features of 2-variable relationships presented in various forms (e.g., tables, graphs, equations, written descriptions, function notation), and evaluate whether a relationship is a function. | M.Relation and Function Representations; M.Understanding Linear Functions and Their Properties | Covered | 54 | 2 | 7 | 0 | Covered by 2 topics (54 questions, 2 materials, 7 cards, 0 videos). |
| 3. Identify function types (i.e., linear, quadratic, cubic, exponential growth and decay, absolute value, square root, cube root, reciprocals of linear functions, step, piecewise linear), and determine whether a function is even or odd. | M.Absolute Value Functions; M.Piecewise Functions; M.Parent Functions; M.Even and Odd Functions | Covered | 27 | 4 | 5 | 0 | Covered by 4 topics (27 questions, 4 materials, 5 cards, 0 videos). |
| 5. Interpret slopes and intercepts of a linear function and determine the equation of a line (i.e., passes through two given points, through one given point, perpendicular to a given line, parallel to a given line, has a given slope). | M.Parallel and Perpendicular Lines and Formulas; 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 | Covered | 54 | 5 | 9 | 1 | Covered by 5 topics (54 questions, 5 materials, 9 cards, 1 videos). |
| 8. Interpret the x-intercepts, y-intercept, vertex, line of symmetry, and concavity of a quadratic function representing real-world and mathematical situations. | M.Quadratic Equations; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equations - Forms; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 37 | 5 | 6 | 2 | Covered by 5 topics (37 questions, 5 materials, 6 cards, 2 videos). |
| 10. Select graphical representations of and determine exponential functions representing real-world problems of exponential growth and decay. | M.Exponential Functions; M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions - Real World Problems - Annuities | Covered | 44 | 4 | 8 | 0 | Covered by 4 topics (44 questions, 4 materials, 8 cards, 0 videos). |
| 12. Determine the inverse of a given function with description of its domain and range, the composition of 2 functions, and interpret inverses and compositions in mathematical and real-world contexts. | M.Function Composition and Inversion; M.Determine the Validity of an Inverse; M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions; M.Advanced Domain and Range of Functions - Composition; M.Domain and Range - Set Notation | Covered | 39 | 7 | 17 | 0 | Covered by 7 topics (39 questions, 7 materials, 17 cards, 0 videos). |
| 11. Determine the impacts of shifting and scaling transformations on various representations (e.g., tables, graphs, formulas) presented in mathematical and real-world contexts. | M.Functional Transformations - Linear and Quadratic; M.Functional Transformations - Absolute Value; M.Functional Transformations - Radical; M.Functional Transformations - Exponential | Covered | 53 | 4 | 6 | 0 | Covered by 4 topics (53 questions, 4 materials, 6 cards, 0 videos). |
KNOWLEDGE OF GEOMETRY AND TRIGONOMETRY (DOMAIN 3)
Partially covered
741 Qs64 Materials156 Cards16 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Classify triangles, quadrilaterals, and solids based on their defining attributes. | M.Attributes of Polygons - Irregular Shapes; M.Attributes of Polygons - Advanced | Covered | 12 | 2 | 23 | 0 | Covered by 2 topics (12 questions, 2 materials, 23 cards, 0 videos). |
| 11. Solve mathematical and real-world problems involving the lengths and intersection angles of secants, chords, and tangent segments, the measures of central and inscribed angles in circles and semicircles, and the areas of sectors of circles. | M.Measurements in Circles; M.Measurements in Circles Advanced | Covered | 40 | 2 | 12 | 1 | Covered by 2 topics (40 questions, 2 materials, 12 cards, 1 videos). |
| 2. Solve mathematical and real-world problems involving properties of angles, using the Triangle Sum Theorem, parallel lines cut by a transversal, relationships between angles of triangles, and the formula for the sum of interior angles of polygons. | M.Angles and Measurements in Polygons; M.Points, Lines, Planes, Angles | Covered | 31 | 2 | 33 | 1 | Covered by 2 topics (31 questions, 2 materials, 33 cards, 1 videos). |
| 4. Apply Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg criteria to prove pairs of triangles, overlapping triangles, and figures composed of triangles are congruent or similar, including the concept of congruence and similarity of triangles to solve mathematical and real-world problems. | M.Advanced Similar Shapes | Covered | 11 | 1 | 10 | 0 | Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos). |
| 3. Prove and apply relationships about lines, angles, triangles, and quadrilaterals in mathematical and real-world contexts. | M.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 Theorems - Similar Shapes | Covered | 50 | 6 | 26 | 0 | Covered by 6 topics (50 questions, 6 materials, 26 cards, 0 videos). |
| 10. Determine and justify geometric constructions (e.g., copy or bisect a segment or an angle). | M.Geometric Constructions; M.Advanced Geometric Constructions - Angles; M.Advanced Geometric Constructions - Lines; M.Advanced Geometric Constructions - Triangles; M.Advanced Geometric Constructions - Shapes; M.Advanced Geometric Constructions - Tangent Line | Covered | 50 | 6 | 2 | 0 | Covered by 6 topics (50 questions, 6 materials, 2 cards, 0 videos). |
| 5. Apply translations, rotations, reflections and scaling transformations and sequences, based on the relationship between a 2D geometric figure and its pre-image, to demonstrate congruence and similarity. | M.Rigid Transformations; M.Non-Rigid Transformations; M.Multiple Transformations | Covered | 40 | 3 | 10 | 0 | Covered by 3 topics (40 questions, 3 materials, 10 cards, 0 videos). |
| 6. Apply coordinate geometry to classify and justify properties of lines, triangles, quadrilaterals, and circles, and solve mathematical and real-world problems (e.g., using the distance formula to determine distances between points and between parallel lines). | M.Coordinate Geometry; M.The Coordinate Plane; M.Slope, Midpoint, and Distance; M.Circles and Ellipses | Covered | 55 | 4 | 11 | 2 | Covered by 4 topics (55 questions, 4 materials, 11 cards, 2 videos). |
| 7. Identify the shapes of 2D cross sections of 3D figures and of 3D figures generated by rotations of 2D figures. | M.Attributes of Three Dimensional Figures; M.Nets; M.Pyramids and Prisms; M.Types of Prisms; M.Rotating 3D Objects | Covered | 46 | 5 | 13 | 3 | Covered by 5 topics (46 questions, 5 materials, 13 cards, 3 videos). |
| 8. Solve mathematical and real-world problems involving proportional relationships between similar 2D and 3D figures, including problems involving scale factors of measurements of similar figures (e.g., perimeter, volume). | M.Proportional Reasoning - 2D Shapes; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons; M.Area and Perimeter of Polygons - Irregular Shapes; M.Solving with Shapes - Rectangles and Squares; M.Solving with Shapes - Quadrilaterals; M.Proportional Reasoning - Scale Drawings; M.Solving with Points, Lines, Planes, Angles | Covered | 140 | 8 | 11 | 4 | Covered by 8 topics (140 questions, 8 materials, 11 cards, 4 videos). |
| 9. Solve mathematical and real-world problems involving formulas for the perimeter, circumference and area of 2D figures and the surface area and volume of 3D figures. | M.Surface Area in 3D; M.Volume in 3D; M.Convert Between Surface Area and Volume; M.Dimensional Changes Affecting Area and Volume | Covered | 83 | 4 | 5 | 2 | Covered by 4 topics (83 questions, 4 materials, 5 cards, 2 videos). |
| 12. Select equations and graphs representing a conic section (e.g., circle, parabola) on a coordinate plane, and apply conic sections to model real-world situations. | M.Conic Sections; M.Conic Sections - Complete the Square; M.Conic Sections - Derive Parabola; M.Conic Sections - Derive Ellipses and Hyperbolas | Covered | 24 | 4 | 5 | 0 | Covered by 4 topics (24 questions, 4 materials, 5 cards, 0 videos). |
| 13. Apply basic right triangle trigonometry and the Pythagorean Theorem to determine unknown sides of right triangles. | M.Angles in Triangles; M.Pythagorean Theorem; M.Apply Triangle Properties; M.Apply Triangle Inequalities; M.Measurements Inside Triangles | Covered | 61 | 5 | 22 | 2 | Covered by 5 topics (61 questions, 5 materials, 22 cards, 2 videos). |
| 14. Solve mathematical and real-world problems using trigonometric ratios and the laws of sines and of cosines. | M.Laws of Sines and Cosines; M.Trigonometric Ratios; M.Inverse Trigonometric Ratios; M.Analyze and Solve Trigonometric Functions | Covered | 42 | 4 | 2 | 1 | Covered by 4 topics (42 questions, 4 materials, 2 cards, 1 videos). |
| 15. Determine the values for and identify the graphs of the six trigonometric functions, including their key features. | M.Trigonometric Ratio Graphs | Covered | 19 | 1 | 3 | 0 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 0 videos). |
| 16. Select graphical representations of and solve periodic mathematical and real-world problems that are modeled with trigonometric functions. | M.Trigonometric Ratio Graphs - Real Word Problems | Partially covered | 7 | 1 | 0 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| 17. Convert between rectangular and polar coordinates, and select graphical representations of polar equations in the polar plane. | M.Polar Coordinates; M.Polar Coordinates - DM Theorem | Covered | 15 | 2 | 2 | 0 | Covered by 2 topics (15 questions, 2 materials, 2 cards, 0 videos). |
| 18. Select graphical representations of curves in a plane represented parametrically, and apply parametric equations to model problems involving motion in the plane. | M.Parametric Curves | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| 19. Interpret the language of logic, including the converse, inverse, and contrapositive of an “if … then” statement, and evaluate the validity of informal and formal geometric arguments. | M.Logic Terminology and Symbols; M.Using Logic for Truth; M.Using Logic for Equivalence | Covered | 5 | 3 | 5 | 0 | Covered by 3 topics (5 questions, 3 materials, 5 cards, 0 videos). |
KNOWLEDGE OF DATA ANALYSIS, STATISTICS, AND PROBABILITY (DOMAIN 4)
Partially covered
492 Qs39 Materials107 Cards11 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identify and determine appropriate measures of central tendency and measures of variation of a numerical data set. | M.Measures of Center and Range; M.Choosing Measures of Center; M.Advanced Measures of Center and Range | Covered | 83 | 3 | 12 | 2 | Covered by 3 topics (83 questions, 3 materials, 12 cards, 2 videos). |
| 2. Apply the mean and standard deviation of a numerical data set to fit it to a normal distribution and estimate population percentages. | M.Normal Distribution; M.Using Distributions | Covered | 29 | 2 | 6 | 0 | Covered by 2 topics (29 questions, 2 materials, 6 cards, 0 videos). |
| 3. Interpret information and patterns from a numerical data display and the shape of its distribution (i.e., symmetry, gaps, clusters, outliers, mode, range). | M.Describing Data Patterns and Outliers; M.Effect of Change in Data on Measures of Center and Range | Covered | 21 | 2 | 13 | 0 | Covered by 2 topics (21 questions, 2 materials, 13 cards, 0 videos). |
| 7. Determine the properties of correlations in bivariate data displayed in scatter plots and 2-way frequency tables, representing real-world situations. | M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis | Covered | 29 | 2 | 13 | 1 | Covered by 2 topics (29 questions, 2 materials, 13 cards, 1 videos). |
| 8. Select linear functions that fit to real-world bivariate numerical data that suggest a possible linear association, and interpret the x- and y-intercepts. | M.Calculating Linear Regression | Partially covered | 6 | 1 | 2 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| 4. Identify displays for univariate numerical and categorical data (e.g., histograms, box plots, bar charts, frequency tables). | M.Graphs and Plots; M.Boxplots; M.Choosing a Graph or Plot; M.Data Analysis and Interpretation; M.Appropriate vs Inappropriate Representations of Data; M.Interpolation of Data | Covered | 96 | 6 | 18 | 3 | Covered by 6 topics (96 questions, 6 materials, 18 cards, 3 videos). |
| 5. Determine population total, mean, and percentage using data from a survey, considering margin of error. | M.Central Limit Theorem and Large Numbers; M.Linear Data Transformations; M.Statistical Experiments; M.Statistics of One-Variable Data | Covered | 25 | 4 | 4 | 0 | Covered by 4 topics (25 questions, 4 materials, 4 cards, 0 videos). |
| 6. Identify appropriate processes used to design statistical experiments, including the use of randomized trials and proper sampling methods to reduce possible sources of bias. | M.Surveys; M.Sampling Methods; M.Statistical Questions | Covered | 33 | 3 | 8 | 0 | Covered by 3 topics (33 questions, 3 materials, 8 cards, 0 videos). |
| 9. Use a variety of methods (e.g., permutations, combinations, tables, tree diagrams, addition and multiplication rules) to determine the probabilities and conditional probabilities of events in probability experiments (e.g., complements of events and unions, intersections of independent and dependent events). | M.Probability; M.Simple and Compound Events; M.Diagrams; M.Fundamental Counting Principle; M.Combinations and Permutations; M.Tables to Determine Independence; M.Geometric Probability | Covered | 115 | 7 | 14 | 4 | Covered by 7 topics (115 questions, 7 materials, 14 cards, 4 videos). |
| 10. Analyze 2-way frequency tables and relative frequency tables summarizing real-world bivariate categorical data, using the data or conditional, marginal, or joint relative frequencies from the data, and interpret the quantities in such a table within a context. | M.Data Analysis - Frequency | Covered | 8 | 1 | 10 | 0 | Covered by 1 topic (8 questions, 1 materials, 10 cards, 0 videos). |
| 11. Determine an appropriate sample space for a simple experiment (e.g., rolling a die, drawing an object randomly from a bag, spinning a spinner) or a repeated simple experiment (e.g., repeatedly tossing a coin, rolling several dice, drawing an object repeatedly from a bag with replacement). | M.Probability Models; M.Probability Simulations; M.Expressing Probabilities; M.Sample Spaces to Determine Probabilities | Covered | 25 | 4 | 7 | 1 | Covered by 4 topics (25 questions, 4 materials, 7 cards, 1 videos). |
| 12. Compare experimental and theoretical probabilities to make predictions and draw conclusions about real-world situations. | M.Observations, Conclusions, and Relationships | Covered | 11 | 1 | 10 | 0 | Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos). |
| 13. Calculate the expected value and standard deviation of a random variable to solve real-world problems (e.g., compare the expected payoffs and risks of different decisions). | M.Probability Distributions; M.Payoff; M.Fairness | Covered | 11 | 3 | 11 | 0 | Covered by 3 topics (11 questions, 3 materials, 11 cards, 0 videos). |
KNOWLEDGE OF STUDENT REASONING AND INSTRUCTIONAL PRACTICES (DOMAIN 6)
Covered
253 Qs25 Materials49 Cards7 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identify appropriate methods to facilitate instruction in using mathematical strategies, concepts, and procedures with fluency to solve problems in various real-world or mathematical contexts. | M.Selecting Appropriate Solution Strategies; M.Using Structure to Analyze Complex Problems; M.Backward Design | Covered | 27 | 3 | 3 | 1 | Covered by 3 topics (27 questions, 3 materials, 3 cards, 1 videos). |
| 3. Identify patterns to make connections between mathematical and real-world problems across subject areas, and analyze a sequence of concepts for mathematical continuity. | M.Major Math Instructional Theories; M.Real-World Applications; M.Mathematical Connections; M.Interdisciplinary Connections | Covered | 32 | 4 | 5 | 1 | Covered by 4 topics (32 questions, 4 materials, 5 cards, 1 videos). |
| 2. Identify opportunities for students to evaluate the reasonableness of their results, and assess the validity of students’ mathematical arguments. | M.Reasonableness of Results; M.Evaluating Truth of Statements; M.Teaching Mathematical Reasoning; M.Teaching Mathematical Reasoning for Older Children | Covered | 30 | 4 | 2 | 0 | Covered by 4 topics (30 questions, 4 materials, 2 cards, 0 videos). |
| 4. Select appropriate mathematical representations (e.g., verbal statements, tables, algebraic expressions) and instructional tools for teaching mathematical concepts to all students. | M.Alternate Representations of Problems; M.Multiple Interpretations of Math Concepts; M.Teaching Mathematical Vocabulary; M.Manipulatives for Older Children; M.Variety of Representations for Older Children; M.Modeling and Evaluating Real-World Situations | Covered | 40 | 5 | 13 | 0 | Covered by 6 topics (40 questions, 5 materials, 13 cards, 0 videos). |
| 5. Analyze learning progressions to demonstrate how students’ mathematical knowledge and skills develop over time among concrete, representational, and abstract modes of understanding. | M.Learning Progressions in Math; M.Learning Progressions in Geometry | Covered | 26 | 2 | 8 | 1 | Covered by 2 topics (26 questions, 2 materials, 8 cards, 1 videos). |
| 6. Analyze and interpret individual student mathematics assessment data using a variety of assessment formats to guide instructional decisions and differentiate instruction. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction; M.Authentic Assessment; M.Assessment Terminology; M.Fair Assessment; M.Use Variety in Problem Structure | Covered | 58 | 6 | 20 | 3 | Covered by 6 topics (58 questions, 6 materials, 20 cards, 3 videos). |
| 7. Analyze students' mathematical misconceptions, errors, and gaps in knowledge and choose instructional approaches to promote student achievement. | M.Evaluate Student Solutions | Covered | 40 | 1 | 0 | 1 | Covered by 1 topic (40 questions, 1 materials, 0 cards, 1 videos). |
How 240 Creates The FTCE Mathematics 6-12 (026) 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 FTCE Mathematics 6-12.
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 FTCE 026 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 FTCE Mathematics 6-12 Study Guide
The questions teacher candidates ask us most often about the FTCE Mathematics 6-12 study guide.
1
Is 240 a good study guide for FTCE Mathematics 6-12?
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 FTCE 026 exam?
This guide is 98% 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.
4
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 FTCE 026 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.