240's GACE Mathematics 6-12 Study Guide Is 97% Test-Aligned
240's GACE 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.
97%
test-aligned
80
Fully covered
6
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.
2001
Practice Questions
338
Flashcards
171
Study Materials
33
Videos
Why Test Alignment Matters for Your GACE 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 GACE Mathematics 6-12 (711) 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 GACE 711 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 · 86 competencies reviewed · 97% 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 (6–12) (DOMAIN 209)
Partially covered
SMR 209.001 Understand mathematical problem-solving, communication, and reasoning in contexts that are familiar to Georgians.
214 Qs15 Materials35 Cards6 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the use of estimation in a variety of situations (e.g., rounding, area, plausibility). | M.Mental Math and Estimation; M.Rounding | Covered | 30 | 2 | 8 | 1 | Covered by 2 topics (30 questions, 2 materials, 8 cards, 1 videos). |
| b. Solve diverse application-based problems involving integers, rational numbers, decimals, and percents. | M.Representations of Fractions in Word Problems; M.Integers in Word Problems; M.Percent Change | Covered | 39 | 3 | 5 | 2 | Covered by 3 topics (39 questions, 3 materials, 5 cards, 2 videos). |
| c. Solve mathematical and diverse application-based problems involving ratios, proportions, and average rates of change. | M.Ratios; M.Unit Rates; M.Proportional Reasoning - Word Problems; M.Ratios, Proportions, Percents | Covered | 100 | 4 | 4 | 3 | Covered by 4 topics (100 questions, 4 materials, 4 cards, 3 videos). |
| d. Translate and analyze multiple representations (e.g., graphs, text, symbols, equations). | M.Variety of Representations for Older Children | Covered | 3 | 1 | 9 | 0 | Covered by 1 topic (3 questions, 1 materials, 9 cards, 0 videos). |
| e. Identify viable arguments based on inductive and deductive reasoning. | M.Inductive vs Deductive Reasoning; M.Reasonableness of Results | Covered | 26 | 2 | 3 | 0 | Covered by 2 topics (26 questions, 2 materials, 3 cards, 0 videos). |
| f. Apply principles of logic to solve problems. | M.Using Logic for Truth; M.Using Logic for Equivalence | Partially covered | 4 | 2 | 4 | 0 | Partial coverage by 2 topics (4 questions, 2 materials, 4 cards, 0 videos); limited supporting content. |
| g. Apply precision and accuracy to solve multistep problems (e.g., irrational numbers, roots of numbers, π). | M.Justify and Prove Number Relationships | Covered | 12 | 1 | 2 | 0 | Covered by 1 topic (12 questions, 1 materials, 2 cards, 0 videos). |
SMR 209.002 Understand numbers and number theory.
166 Qs10 Materials30 Cards7 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 | Covered | 11 | 1 | 5 | 1 | Covered by 1 topic (11 questions, 1 materials, 5 cards, 1 videos). |
| b. Use complex numbers and their operations. | M.Imaginary and Complex Numbers; M.Operations with Complex Numbers; M.Operations with Complex Numbers - Division | Covered | 34 | 3 | 12 | 2 | Covered by 3 topics (34 questions, 3 materials, 12 cards, 2 videos). |
| c. Analyze the properties of numbers and operations. | M.Characteristics of Rational Numbers; M.Operations and Rational and Irrational Numbers; M.Operational Properties | Covered | 55 | 3 | 8 | 1 | Covered by 3 topics (55 questions, 3 materials, 8 cards, 1 videos). |
| d. Apply the principles of basic number theory (e.g., prime factorization, greatest common factor, least common multiple). | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization | Covered | 66 | 3 | 10 | 3 | Covered by 3 topics (66 questions, 3 materials, 10 cards, 3 videos). |
ALGEBRA AND FUNCTIONS (6–12) (DOMAIN 210)
Partially covered
SMR 210.001 Understand linear, quadratic, and higher-order polynomial functions.
264 Qs28 Materials35 Cards4 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.Understanding Linear Functions and Their Properties; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Sketch a Polynomial - From Roots | Covered | 44 | 4 | 6 | 1 | Covered by 4 topics (44 questions, 4 materials, 6 cards, 1 videos). |
| b. Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor). | M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Polynomials; M.Advanced Factoring Polynomials | Covered | 66 | 5 | 16 | 1 | Covered by 5 topics (66 questions, 5 materials, 16 cards, 1 videos). |
| c. Solve linear and quadratic equations and inequalities using a variety of methods, including graphical methods. | M.Solving One-Variable 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 | Covered | 43 | 5 | 3 | 0 | Covered by 5 topics (43 questions, 5 materials, 3 cards, 0 videos). |
| d. Solve systems of linear equations or inequalities using a variety of methods (e.g., substitution, elimination, matrices). | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Equations - Scalar Note; M.Solving Systems of Quadratic Equations; M.Solving Mixed Systems; M.Solving Systems of Linear Inequalities; M.Solving Systems of Quadratic Inequalities | Covered | 46 | 6 | 5 | 1 | Covered by 6 topics (46 questions, 6 materials, 5 cards, 1 videos). |
| e. Solve higher-order polynomial equations and inequalities with a variety of solutions. | M.Solving Linear Inequalities; M.Solving Compound Linear Inequalities; M.Solve Linear Inequalities - Graphically; M.Solve Quadratic Inequalities - Graphically; M.Solve Quadratic Inequalities - Algebraically | Covered | 31 | 5 | 3 | 1 | Covered by 5 topics (31 questions, 5 materials, 3 cards, 1 videos). |
| f. Analyze the characteristics (e.g., degree, parity, values, intercepts, end behavior) of linear, quadratic, and higher-order polynomial equations and their graphs. | M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form; M.Sketch a Polynomial - From Roots; M.Even and Odd Functions | Covered | 42 | 4 | 4 | 1 | Covered by 4 topics (42 questions, 4 materials, 4 cards, 1 videos). |
| g. Solve diverse application-based problems by modeling them with linear, quadratic, and higher-order polynomial functions in contexts that are familiar to Georgians. | M.Advanced Quadratic Equation - Real World Problems; M.Linear Function Word Problems | Covered | 21 | 2 | 0 | 0 | Covered by 2 topics (21 questions, 2 materials, 0 cards, 0 videos). |
SMR 210.002 Understand advanced functions in contexts that are familiar to Georgians.
216 Qs25 Materials41 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Determine inverses and compositions of algebraic functions. | M.Function Inversion; M.Function Composition | Covered | 26 | 2 | 3 | 0 | Covered by 2 topics (26 questions, 2 materials, 3 cards, 0 videos). |
| b. Apply the laws of exponents and logarithms. | M.Properties of Exponents; M.Properties of Logarithms; M.Properties of Exponents - Applying Multiple Properties | Covered | 66 | 3 | 6 | 0 | Covered by 3 topics (66 questions, 3 materials, 6 cards, 0 videos). |
| c. Analyze the relationship between exponential and logarithmic functions. | M.Exponential Functions; M.Logarithmic Functions | Covered | 20 | 2 | 6 | 0 | Covered by 2 topics (20 questions, 2 materials, 6 cards, 0 videos). |
| d. Analyze exponential and logarithmic functions and their graphs. | M.Exponential Functions - Asymptotes; M.Exponential Functions - Reflections; M.Logarithmic Functions - Graph | Covered | 11 | 3 | 2 | 0 | Covered by 3 topics (11 questions, 3 materials, 2 cards, 0 videos). |
| e. Solve diverse application-based problems by modeling them with exponential and logarithmic functions. | M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions - Real World Problems - Annuities | Covered | 32 | 3 | 8 | 0 | Covered by 3 topics (32 questions, 3 materials, 8 cards, 0 videos). |
| f. Manipulate (e.g., simplify, transform, factor) rational, radical, and absolute value expressions, equations, and inequalities. | M.Solving Equations - Logarithmic and Exponential; M.Solving Equations - Rational; M.Absolute Value Inequalities; M.Solving Equations - Radicals and Exponents | Covered | 27 | 4 | 7 | 0 | Covered by 4 topics (27 questions, 4 materials, 7 cards, 0 videos). |
| g. Analyze the relationship of a function (e.g., rational, radical, absolute value, piecewise-defined) and its graph. | M.Absolute Value Functions; M.Piecewise Functions; M.Rational Functions | Covered | 11 | 3 | 8 | 0 | Covered by 3 topics (11 questions, 3 materials, 8 cards, 0 videos). |
| h. Analyze the characteristics (e.g., domain, range, asymptotes, continuity) of rational, radical, absolute value, and piecewise-defined functions. | M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions; M.Advanced Domain and Range of Functions - Piecewise; M.Parent Functions | Covered | 17 | 4 | 11 | 0 | Covered by 4 topics (17 questions, 4 materials, 11 cards, 0 videos). |
| i. Solve diverse application-based problems by modeling them with rational, radical, absolute value, and piecewise-defined functions. | M.Domain and Range - Applications | Partially covered | 6 | 1 | 2 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
MEASUREMENT AND GEOMETRY (6–12) (DOMAIN 211)
Partially covered
SMR 211.001 Understand measurement principles and procedures.
251 Qs14 Materials31 Cards7 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the use of various units and unit conversions (e.g., imperial and metric systems of measurement, radian and degree angle measures). | M.Choosing Appropriate Units; M.Converting Units - Dimensional Analysis; M.Convert Between Radians and Degrees | Covered | 48 | 3 | 4 | 2 | Covered by 3 topics (48 questions, 3 materials, 4 cards, 2 videos). |
| b. Apply the concepts of similarity, scale factors, and proportional reasoning to solve measurement problems. | M.Proportional Reasoning - 2D Shapes; M.Advanced Similar Shapes; M.Proportional Reasoning - Scale Drawings | Covered | 37 | 3 | 11 | 2 | Covered by 3 topics (37 questions, 3 materials, 11 cards, 2 videos). |
| c. Analyze precision, error, and rounding in measurements and computed quantities. | M.Advanced Measurement Principles | Covered | 9 | 1 | 6 | 0 | Covered by 1 topic (9 questions, 1 materials, 6 cards, 0 videos). |
| d. Apply the concepts of perimeter, circumference, area, surface area, and volume to solve diverse application-based problems in contexts that are familiar to Georgians. | M.Area and Perimeter of Polygons; M.Area and Perimeter of Polygons - Irregular Shapes; M.Measurements in Circles | Covered | 81 | 3 | 5 | 1 | Covered by 3 topics (81 questions, 3 materials, 5 cards, 1 videos). |
| e. Use nets and cross sections to analyze three-dimensional figures. | M.Nets; M.Surface Area in 3D; M.Volume in 3D; M.Proportional Reasoning - 3D Figures | Covered | 76 | 4 | 7 | 2 | Covered by 4 topics (76 questions, 4 materials, 7 cards, 2 videos). |
SMR 211.002 Understand Euclidean geometry in two and three dimensions in contexts that are familiar to Georgians
219 Qs18 Materials43 Cards3 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of the axioms of Euclidean and non-Euclidean geometries in a variety of proofs. | M.Euclidean Versus Non-Euclidean Geometry; M.Proofs | Covered | 12 | 2 | 7 | 0 | Covered by 2 topics (12 questions, 2 materials, 7 cards, 0 videos). |
| b. Use the properties of polygons and circles to solve problems, including problems that involve central, inscribed, and circumscribed angles. | M.Prove Theorems - Triangles; M.Prove Theorems - Parallelograms; M.Prove Properties - Quadrilateral Inscribed in a Circle | Covered | 26 | 3 | 7 | 0 | Covered by 3 topics (26 questions, 3 materials, 7 cards, 0 videos). |
| c. Apply the Pythagorean theorem and its converse in a variety of contexts. | 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.Prove Theorems - Similar Shapes | Partially covered | 7 | 1 | 3 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| e. Analyze two- and three-dimensional figures using coordinate systems. | M.Coordinate Geometry; M.Solving with Points, Lines, Planes, Angles; M.3D Lines and Planes | Covered | 50 | 3 | 7 | 1 | Covered by 3 topics (50 questions, 3 materials, 7 cards, 1 videos). |
| f. Apply concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane. | M.Slope, Midpoint, and Distance | Covered | 16 | 1 | 0 | 1 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 1 videos). |
| g. Determine the effects of geometric transformations on the graph of a function or relation. | 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). |
| h. Analyze and perform transformations and identify symmetries with figures in the coordinate plane. | M.Similarity and Congruence with Transformations; M.Rigid Transformations; M.Non-Rigid Transformations; M.Multiple Transformations | Covered | 40 | 3 | 10 | 0 | Covered by 4 topics (40 questions, 3 materials, 10 cards, 0 videos). |
TRIGONOMETRY AND CALCULUS (6–12) (DOMAIN 212)
Partially covered
SMR 212.001 Understand trigonometric functions.
101 Qs11 Materials9 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze characteristics and relationships between sine, cosine, and tangent functions and their inverses. | M.Trigonometric Ratios; M.Inverse Trigonometric Ratios | Covered | 20 | 2 | 0 | 1 | Covered by 2 topics (20 questions, 2 materials, 0 cards, 1 videos). |
| b. Apply trigonometric functions to solve problems involving distance and angles. | M.Trigonometric Ratios | Covered | 12 | 1 | 0 | 1 | Covered by 1 topic (12 questions, 1 materials, 0 cards, 1 videos). |
| c. 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). |
| d. Manipulate trigonometric expressions and equations (e.g., by applying trigonometric identities and reciprocals of trigonometric functions). | M.Advanced Trigonometric Identities - Special Triangles; M.Advanced Trigonometric Identities - Quotient and Reciprocal; M.Advanced Trigonometric Identities - Pythagorean Identities | Covered | 14 | 3 | 0 | 0 | Covered by 3 topics (14 questions, 3 materials, 0 cards, 0 videos). |
| e. Analyze the relationship between a trigonometric function and its graph. | M.Trigonometric Ratio Graphs | Covered | 19 | 1 | 3 | 0 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 0 videos). |
| f. Use trigonometric functions to model periodic relationships. | M.Trigonometric Ratio Graphs - Real Word Problems; M.Analyze and Solve Trigonometric Functions | Covered | 18 | 2 | 0 | 0 | Covered by 2 topics (18 questions, 2 materials, 0 cards, 0 videos). |
| g. Apply the laws of sine and cosine. | M.Laws of Sines and Cosines | Covered | 11 | 1 | 2 | 0 | Covered by 1 topic (11 questions, 1 materials, 2 cards, 0 videos). |
| h. Analyze conic sections algebraically. | M.Conic Sections | Covered | 10 | 1 | 4 | 0 | Covered by 1 topic (10 questions, 1 materials, 4 cards, 0 videos). |
SMR 212.002 Understand essential concepts in calculus in contexts that are familiar to Georgians.
124 Qs17 Materials34 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Evaluate limits with and without bound. | M.Limits and Continuity | Covered | 24 | 1 | 5 | 0 | Covered by 1 topic (24 questions, 1 materials, 5 cards, 0 videos). |
| b. Identify and classify points of discontinuity within a graph. | M.Limits and Continuity | Covered | 24 | 1 | 5 | 0 | Covered by 1 topic (24 questions, 1 materials, 5 cards, 0 videos). |
| c. Analyze the derivative as the slope of a tangent line and as the limit of the difference quotient and interpret the derivative as the instantaneous rate of change of a function. | M.Derivatives and Slopes | Covered | 15 | 1 | 7 | 0 | Covered by 1 topic (15 questions, 1 materials, 7 cards, 0 videos). |
| d. Calculate the derivatives of functions (e.g., polynomial, exponential, logarithmic, trigonometric) using various techniques (e.g., quotient rule, product rule, power rule, chain rule). | M.Derivatives and Trigonometric Functions; M.Derivatives and Exponential Functions; M.Derivatives and Logarithmic Functions | Partially covered | 5 | 2 | 2 | 0 | Partial coverage by 3 topics (5 questions, 2 materials, 2 cards, 0 videos); limited supporting content. |
| e. Apply differentiation to analyze the graphs of functions. | M.Derivatives and Slopes | Covered | 15 | 1 | 7 | 0 | Covered by 1 topic (15 questions, 1 materials, 7 cards, 0 videos). |
| f. Apply differentiation to solve diverse application-based problems involving rates of change and optimization. | M.Calculus - Rates; M.Calculus - Velocity and Acceleration | Covered | 13 | 2 | 4 | 0 | Covered by 2 topics (13 questions, 2 materials, 4 cards, 0 videos). |
| g. Relate the area under a curve to the limit of a Riemann sum. | M.Riemann Sums; M.Approximating Area; M.Riemann Sum - Integral Calculations | Covered | 14 | 3 | 4 | 0 | Covered by 3 topics (14 questions, 3 materials, 4 cards, 0 videos). |
| h. Calculate the integrals of functions (e.g., polynomial, exponential, logarithmic, trigonometric) using basic integration techniques. | 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). |
| i. Apply integration to analyze the graphs of functions and solve diverse application-based problems | M.Areas by Integration; M.Volumes by Integration; M.Distance by Integration | Covered | 22 | 3 | 4 | 0 | Covered by 3 topics (22 questions, 3 materials, 4 cards, 0 videos). |
STATISTICS AND PROBABILITY (6–12) (DOMAIN 213)
Partially covered
SMR 213.001 Understand principles and techniques of statistics in contexts that are familiar to Georgians.
135 Qs5 Materials28 Cards2 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Use visual representations (e.g., bar graphs, pie charts, histograms, scatterplots) for organizing and displaying data. | M.Graphs and Plots | Covered | 32 | 1 | 9 | 1 | Covered by 1 topic (32 questions, 1 materials, 9 cards, 1 videos). |
| b. Analyze data in a variety of representations (e.g., frequency tables, contingency tables, Venn diagrams, tree diagrams). | M.Diagrams | Covered | 16 | 1 | 2 | 0 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 0 videos). |
| c. Analyze the use of measures of central tendency and variability. | M.Measures of Center and Range; M.Advanced Measures of Center and Range | Covered | 75 | 2 | 12 | 1 | Covered by 2 topics (75 questions, 2 materials, 12 cards, 1 videos). |
| d. Analyze the effects of bias and sampling techniques. | M.Sampling Methods | Covered | 12 | 1 | 5 | 0 | Covered by 1 topic (12 questions, 1 materials, 5 cards, 0 videos). |
SMR 213.002 Understand principles and techniques of probability in contexts that are familiar to Georgians
170 Qs14 Materials44 Cards3 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Use counting principles to calculate probabilities. | M.Fundamental Counting Principle; M.Probability | Covered | 57 | 2 | 9 | 2 | Covered by 2 topics (57 questions, 2 materials, 9 cards, 2 videos). |
| b. 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). |
| c. Apply set theory to solve problems. | M.Set Notation | Partially covered | 0 | 0 | 0 | 0 | Partial coverage by 1 topic (0 questions, 0 materials, 0 cards, 0 videos); limited supporting content. |
| d. Determine probabilities of simple and compound events and conditional probabilities. | M.Simple and Compound Events; M.Compound Probabilities (OR); M.Tables to Determine Independence | Covered | 23 | 3 | 4 | 1 | Covered by 3 topics (23 questions, 3 materials, 4 cards, 1 videos). |
| e. Use a variety of representations to calculate probabilities (e.g., frequency tables, contingency tables, graphs). | M.Data Analysis - Frequency | Covered | 8 | 1 | 10 | 0 | Covered by 1 topic (8 questions, 1 materials, 10 cards, 0 videos). |
| f. Select simulations that model diverse application-based 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. |
| g. Analyze uniform, binomial, and normal probability distributions. | M.Probability Distributions; M.Comparing to Probability Distribution; M.Normal Distribution; M.Using Distributions; M.Uniform Distributions; M.Probability Distributions - Expected Value | Covered | 55 | 6 | 21 | 0 | Covered by 6 topics (55 questions, 6 materials, 21 cards, 0 videos). |
FINANCIAL LITERACY (501) (DOMAIN 501)
Covered
SMR 501.001 Apply principles of financial responsibility, decision-making, and planning.
50 Qs5 Materials2 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of financial decision-making strategies (e.g., considering opportunity costs, comparing marginal costs and marginal benefits) for achieving short-term and long-term goals. | M.Financial Strategies | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| b. Demonstrate knowledge of the personal decisions and situational factors that affect people's purchasing power and earning potential as employees and as entrepreneurs. | M.Financial Strategies | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| c. Analyze sources of earned and unearned income and the relationships between gross pay, deductions and withholdings, and net or spendable pay. | M.Income | Covered | 10 | 1 | 0 | 0 | Covered by 1 topic (10 questions, 1 materials, 0 cards, 0 videos). |
| d. Apply knowledge of the development of a personal budget, distinctions between expense types (e.g., fixed, discretionary, variable, intermittent), and the effects of spending decisions on budgeting. | M.Budgeting | Covered | 10 | 1 | 0 | 0 | Covered by 1 topic (10 questions, 1 materials, 0 cards, 0 videos). |
| e. Analyze the effects of local, state, and federal taxes on budgets, including the effects of tax credits and deductions on total tax liability and the uses of federal tax forms (e.g., Form W-2, Form W-4, Form 1040, Form 1099). | M.Taxes | Covered | 10 | 1 | 0 | 0 | Covered by 1 topic (10 questions, 1 materials, 0 cards, 0 videos). |
| f. Apply knowledge of methods of funding and financing postsecondary educational and career choices. | M.Post-Secondary Financing | Covered | 10 | 1 | 0 | 0 | Covered by 1 topic (10 questions, 1 materials, 0 cards, 0 videos). |
SMR 501.002 Apply knowledge of tools for informing consumers and managing risk.
44 Qs4 Materials0 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Demonstrate knowledge of organizations and advocacy groups that provide information to consumers and protect them from fraud (e.g., AARP, Better Business Bureau, Consumer Reports). | M.Consumer Protection | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| b. Demonstrate knowledge of state and federal laws and regulatory agencies that protect consumers from fraud and loss. | M.Consumer Protection | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| c. Apply knowledge of the differences between the list price and indirect costs associated with a purchase (e.g., taxes, shipping costs, handling fees, delivery charges). | M.Indirect Costs | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| d. Demonstrate knowledge of liability lawsuits, warranties, and service plans used to protect consumers from the loss of personal and business assets and income. | M.Consumer Protection | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| e. Demonstrate knowledge of the sources of vulnerability to identity theft, the effects of disclosing personal information, and actions to limit losses and restore information security. | M.Protecting Personal Information | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| f. Demonstrate knowledge of various insurance products used to transfer risk (e.g., health, life, disability, auto, homeowners, renters, liability) and analyze factors that influence the choice of insurance coverage (e.g., occupation, lifestyle, age, premiums, government requirements, risk tolerance). | M.Insurance | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
SMR 501.003 Apply principles of investing and the management of credit and debt.
47 Qs5 Materials31 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Apply knowledge of key investing concepts, principles, and strategies to increase net worth (e.g., assets, liabilities, compound interest, the time value of money and the cost of delay, diversification). | M.Net Worth | Covered | 9 | 1 | 3 | 0 | Covered by 1 topic (9 questions, 1 materials, 3 cards, 0 videos). |
| b. Demonstrate knowledge of the variety of financial institutions and the products and services they offer. | M.Financial Institutions | Covered | 11 | 1 | 11 | 0 | Covered by 1 topic (11 questions, 1 materials, 11 cards, 0 videos). |
| c. Analyze options among financial products (e.g., checking and savings accounts, certificates of deposit, bonds, stocks, mutual funds, 401(k) plans, individual retirement accounts, real estate, digital assets) in terms of costs and fees, tax implications, time horizons, liquidity, expected rates of return, and various types of risk. | M.Financial Products | Covered | 9 | 1 | 12 | 0 | Covered by 1 topic (9 questions, 1 materials, 12 cards, 0 videos). |
| d. Demonstrate knowledge of state and federal laws and regulatory agencies that oversee financial institutions and protect investors and debtors. | M.Financial Institutions | Covered | 11 | 1 | 11 | 0 | Covered by 1 topic (11 questions, 1 materials, 11 cards, 0 videos). |
| e. Apply knowledge of the legal and financial implications of the contractual terms and conditions of lending services (e.g., timing of payments, interest rate, service fees, late penalties, consequences of default) and the costs and benefits associated with loans from financial institutions and payday lenders. | M.Loans | Covered | 9 | 1 | 3 | 0 | Covered by 1 topic (9 questions, 1 materials, 3 cards, 0 videos). |
| f. Apply knowledge of the effective balancing of credit and debt to achieve financial goals, risks arising from the use of credit and debt (e.g., struggling to afford payments, establishing repayment plans, filing for bankruptcy), and factors that affect a person's credit score. | M.Financial Goals | Covered | 9 | 1 | 5 | 0 | Covered by 1 topic (9 questions, 1 materials, 5 cards, 0 videos). |
How 240 Creates The GACE Mathematics 6-12 (711) 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 GACE 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 GACE 711 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 GACE Mathematics 6-12 Study Guide
The questions teacher candidates ask us most often about the GACE Mathematics 6-12 study guide.
1
Is 240 a good study guide for GACE 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 GACE 711 exam?
This guide is 97% 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 GACE 711 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.