Standardized Test Preparation

GED

Math

Assessment Exam - GED Mathematical Reasoning

Quantitative problem solving	eTAP Lesson
Apply number sense concepts, including ordering rational numbers, absolute value, multiples, factors, and exponents
Order fractions and decimals, including on a number line GED.Q.1.a	Number Lines with Decimals, Fractions, Whole Numbers Order of Decimals
Apply number properties involving multiples and factors, such as using the least common multiple, greatest common factor, or distributive property to rewrite numeric expressions GED.Q.1.b	Factors and Greatest Common Factors (GCF) Solving Rational Equations
Apply rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents GED.Q.1.c	Rules of Exponents
Identify absolute value or a rational number as its distance from 0 on the number line and determine the distance between two rational numbers on the number line, including using the absolute value of their difference GED.Q.1.d	Absolute Value Inequalities
Add, subtract, multiply, divide, and use exponents and roots of rational, fraction and decimal numbers
Perform addition, subtraction, multiplication, and division on rational numbers GED.Q.2.a	Rational & Irrational Numbers
Perform computations and write numerical expressions with squares and square roots of positive, rational numbers GED.Q.2.b	Finding Square Roots and Other Roots
Apply number sense concepts, including ordering rational numbers, absolute value, multiples, factors, and exponents
Perform computations and write numerical expressions with cubes and cube roots of rational numbers GED.Q.2.c	Roots and Radicals
Add, subtract, multiply, divide, and use exponents and roots of rational, fraction and decimal numbers
Determine when a numerical expression is undefined GED.Q.2.d
Solve one-step or multi-step arithmetic, real world problems involving the four operations with rational numbers, including those involving scientific notation GED.Q.2.e	Word Problems of Measurements & Four Operations
Calculate and use ratios, percents and scale factors
Compute unit rates. Examples include but are not limited to: unit pricing, constant speed, persons per square mile, BTUs per cubic foot GED.Q.3.a	Word Problems of Ratios & Rates
Use scale factors to determine the magnitude of a size change. Convert between actual drawings and scale drawings GED.Q.3.b	Properties of Isometrics
Solve multistep, arithmetic, real-world problems using ratios or proportions including those that require converting units of measure GED.Q.3.c	Measurement Conversions
Solve two-step, arithmetic, real world problems involving percents. Examples include but are not limited to: simple interest, tax, markups and markdowns, gratuities and commissions, percent increase and decrease GED.Q.3.d
Calculate dimensions, perimeter, circumference, and area of two-dimensional figures
Compute the area and perimeter of triangles and rectangles. Determine side lengths of triangles and rectangles when given area or perimeter. GED.Q.4.a	Triangle Areas Area & Perimeter Measurements of Rectangles
Compute the area and circumference of circles. Determine the radius or diameter when given area or circumference GED.Q.4.b	Definition - Circles Circumference/Diameter Ratio Areas of Circles
Calculate dimensions, perimeter, circumference, and area of two-dimensional figures
Compute the perimeter of a polygon. Given a geometric formula, compute the area of a polygon. Determine side lengths of the figure when given the perimeter or area GED.Q.4.c	Areas of Regular Polygons
Compute perimeter and area of 2-D composite geometric figures, which could include circles, given geometric formulas as needed GED.Q.4.d
Use the Pythagorean theorem to determine unknown side lengths in a right triangle GED.Q.4.e	The Theorem of Pythagoras
Calculate dimensions, surface area, and volume of three-dimensional figures
When given geometric formulas, compute volume and surface area of rectangular prisms. Solve for side lengths or height, when given volume or surface area GED.Q.5.a	Surface Area Rectangular Prism Volume
Calculate dimensions, surface area, and volume of three-dimensional figures
When given geometric formulas, compute volume and surface area of cylinders. Solve for height, radius, or diameter when given volume or surface area GED.Q.5.b	Cylinders
Calculate dimensions, surface area, and volume of three-dimensional figures
When given geometric formulas, compute volume and surface area of right prisms. Solve for side lengths or height, when given volume or surface area GED.Q.5.c	Polyhedrons, Prisms and Pyramids
Calculate dimensions, surface area, and volume of three-dimensional figures
When given geometric formulas, compute volume and surface area of right pyramids and cones. Solve for side lengths, height, radius, or diameter when given volume or surface area GED.Q.5.d	Cones
When given geometric formulas, compute volume and surface area of spheres. Solve for radius or diameter when given the surface area GED.Q.5.e	Solids with Curved Surfaces
Compute surface area and volume of composite 3-D geometric figures, given geometric formulas as needed GED.Q.5.f	Surface Area of 3-D Polygons
Interpret and create data displays
Represent, display, and interpret categorical data in bar graphs or circle graphs GED.Q.6.a	Comparing Categories with Bar Graphs
Represent, display, and interpret data involving one variable plots on the real number line including dot plots, histograms, and box plots GED.Q.6.b	Showing Orderly Data with Histograms Probability Data Plots
Represent, display, and interpret data involving two variables in tables and the coordinate plane including scatter plots and graphs GED.Q.6.c	Paired Data Sets and Scatterplots
Calculate and use mean, median, mode and weighted average
Calculate the mean, median, mode and range. Calculate a missing data value, given the average and all the missing data values but one, as well as calculating the average, given the frequency counts of all the data values, and calculating a weighted average GED.Q.7.a	Basic Methods of Describing Data
Utilize counting techniques and determine probabilities
Use counting techniques to solve problems and determine combinations and permutations GED.Q.8.a	Permutation and Combination
Determine the probability of simple and compound events GED.Q.8.b	Probability of Events
Algebraic problem solving	eTAP Lesson
Write, evaluate, and compute with expressions and polynomials
Add, subtract, factor, multiply and expand linear expressions with rational coefficients GED.A.1.a	Solving Equations When Several Terms and Procedures are Involved Solving Equations by Addition and Subtraction
Evaluate linear expressions by substituting integers for unknown quantities GED.A.1.b	Solving Equations Using Several Operations
Write linear expressions as part of word-to-symbol translations or to represent common settings GED.A.1.c	Changing Words into Math
Add, subtract, multiply polynomials, including multiplying two binomials, or divide factorable polynomials GED.A.1.d	Adding and Subtracting Polynomials Dividing Polynomials
Evaluate polynomial expressions by substituting integers for unknown quantities GED.A.1.e	Polynomials
Factor polynomial expressions GED.A.1.f	Factoring by Grouping
Write polynomial expressions as part of word-to-symbol translations or to represent common settings GED.A.1.g
Add, subtract, multiply and divide rational expressions GED.A.1.h	Simplifying Rational Expressions
Evaluate rational expressions by substituting integers for unknown quantities GED.A.1.i	Simplifying Rational Expressions
Write rational expressions as part of word-to-symbol translations or to represent common settings GED.A.1.j
Write, manipulate, and solve linear equations
Solve one-variable linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms or equations with coefficients represented by letters GED.A.2.a	Graphing Systems of Inequalities Factoring with the Distributive Property
Solve real-world problems involving linear equations GED.A.2.b
Write one-variable and multi-variable linear equations to represent context GED.A.2.c
Solve a system of two simultaneous linear equations by graphing, substitution, or linear combination. Solve real-world problems leading to a system of linear equations GED.A.2.d	Why Do We Need Two Equations?
Write, manipulate, solve, and graph linear inequalities
Solve linear inequalities in one variable with rational number coefficients GED.A.3.a	Solving Inequalities by Addition and Subtraction
Identify or graph the solution to a one variable linear inequality on a number line GED.A.3.b	Graphing Systems of Equations
Solve real-world problems involving inequalities GED.A.3.c
Write linear inequalities in one variable to represent context GED.A.3.d
Write, manipulate, and solve quadratic equations
Solve quadratic equations in one variable with rational coefficients and real solutions, using appropriate methods. (e.g., quadratic formula, completing the square, factoring, inspection) GED.A.4.a	Quadratic Formula Completing the Square
Write one-variable quadratic equations to represent context GED.A.4.b	Sum and Product of Roots
Connect and interpret graphs and functions
Locate points in the coordinate plane GED.A.5.a	Graphing in Four Quadrants
Determine the slope of a line from a graph, equation, or table GED.A.5.b	Slope of a Line
Interpret unit rate as the slope in a proportional relationship GED.A.5.c	Slope Intercept Form of Equations
Graph two-variable linear equations GED.A.5.d	Slope Intercept Form of Equations

For a function that models a linear or nonlinear relationship between two quantities, interpret key features of graphs and tables in terms of quantities, and sketch graphs showing key features of graphs and tables in terms of quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior, and periodicity GED.A.5.e	Graphing Quadratic Functions Functions as Graphs in the Coordinate System
Connect coordinates, lines, and equations
Write the equation of a line with a given slope through a given point GED.A.6.a	Slope of a Line
Write the equation of a line passing through two given distinct points GED.A.6.b
Use slope to identify parallel and perpendicular lines and to solve geometric problems GED.A.6.c
Compare, represent, and evaluate functions
Compare two different proportional relationships represented in different ways. Examples include but are not limited to: compare a distance-time graph to a distance-time equation to determine which of two moving objects has a greater speed GED.A.7.a	Simultaneous Equations
Represent or identify a function in a table or graph as having exactly one output (one element in the range) for each input (each element in the domain) GED.A.7.b	Functions as Graphs in the Coordinate System
Compare, represent, and evaluate functions
Evaluate linear and quadratic functions for values in their domain when represented using function notation GED.A.7.c	Simple Quadratic Functions
Compare properties of two linear or quadratic functions each represented in a different way (algebraically, numerically in tables, graphically or by verbal descriptions). Examples include but are not limited to: given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change GED.A.7.d	Linear Parametric equations
Mathematical practices	eTAP Lesson
Building Solution Pathways and Lines of Reasoning
Search for and recognize entry points for solving a problem GED.MP.1.a	Setting Up and Solving Equations
Plan a solution pathway or outline a line of reasoning GED.MP.1.b	Changing Words into Math
Select the best solution pathway, according to given criteria GED.MP.1.c	Postulates of Geometry
Recognize and identify missing information that is required to solve a problem GED.MP.1.d

Select the appropriate mathematical technique(s) to use in solving a problem or a line of reasoning GED.MP.1.e	Finding Answers to Questions
Abstracting Problems
Represent real world problems algebraically GED.MP.2.a	Open Sentences
Represent real world problems visually GED.MP.2.b	Methods of Collecting, Representing, and Displaying Data
Recognize the important and salient attributes of a problem GED.MP.2.c	Geometric Proofs
Furthering Lines of Reasoning
Build steps of a line of reasoning or solution pathway, based on previous step or givens GED.MP.3.a	Symbols of Logic
Complete the lines of reasoning of others GED.MP.3.b
Improve or correct a flawed line of reasoning GED.MP.3.c
Mathematical Fluency
Manipulate and solve arithmetic expressions GED.MP.4.a	Variables and Expressions
Transform and solve algebraic expressions GED.MP.4.b	Solving Rational Equations
Display data or algebraic expressions graphically GED.MP.4.c	Graphing Data
Evaluating Reasoning and Solution Pathways
Recognize flaws in others' reasoning GED.MP.5.a	Conditional Proof
Recognize and use counterexamples GED.MP.5.b	Law of Contraposition Write Persuasive Compositions
Identify the information required to evaluate a line of reasoning GED.MP.5.c	Direct Proofs