High School Equivalency
A credential showing academic skills comparable to a high school diploma.
Getting Started: GED Math Exam Overview
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GED Mathematical Reasoning Test — key terms, tricks & tips
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Quantitative Problem Solving
Using numbers and mathematical operations to solve problems.
Getting Started: GED Math Exam Overview
Algebraic Problem Solving
Using variables and equations to represent and solve problems.
Getting Started: GED Math Exam Overview
Geometric Problem Solving
Applying principles of shapes, sizes, and space to solve problems.
Getting Started: GED Math Exam Overview
Rational Numbers
Numbers that can be expressed as a fraction (e.g., integers, fractions, decimals).
Getting Started: GED Math Exam Overview
Ratios
A comparison of two quantities by division.
Getting Started: GED Math Exam Overview
Proportions
An equation stating that two ratios are equal.
Getting Started: GED Math Exam Overview
Percentages
A ratio that compares a number to 100.
Getting Started: GED Math Exam Overview
What is the GED Math Test?
To remember the main content areas, think 'ARPG': Algebra, Ratios/Proportions/Percents, Rational Numbers, Geometry. ARPG is like a video game where you level up your math skills!
Getting Started: GED Math Exam Overview
What is the GED Math Test?
The GED Math test covers four main content areas: Quantitative Problem Solving with Rational Numbers, Quantitative Problem Solving with Ratios, Proportions, and Percents, Algebraic Problem Solving, and Geometric Problem Solving. Algebraic Problem Solving and Ratios, Proportions, and Percents are weighted most heavily.
Getting Started: GED Math Exam Overview
What is the GED Math Test?
Assuming the test is only about memorizing formulas; it's about applying them.
Getting Started: GED Math Exam Overview
What is the GED Math Test?
Neglecting the calculator-prohibited sections; mental math is still important.
Getting Started: GED Math Exam Overview
What is the GED Math Test?
Not understanding the real-world context of problems; read carefully!
Getting Started: GED Math Exam Overview
Scaled Score
Raw score converted to a standard scale (100-200) for fairness.
Getting Started: GED Math Exam Overview
GED College Ready
Score of 165-174, indicating readiness for college-level courses.
Getting Started: GED Math Exam Overview
GED College Ready + Credit
Score of 175-200, potentially earning college credit.
Getting Started: GED Math Exam Overview
On-screen Calculator
Built-in TI-30XS MultiView calculator available on the test.
Getting Started: GED Math Exam Overview
Formula Sheet
Provided reference sheet with common mathematical formulas.
Getting Started: GED Math Exam Overview
GED Math Test Format, Scoring, and Study Strategies
F-O-R-M-A-T: **F**amiliarize, **O**rganize, **R**eview, **M**aster, **A**ssess, **T**est.
Getting Started: GED Math Exam Overview
GED Math Test Format, Scoring, and Study Strategies
The GED Math Test requires a minimum score of 145 to pass. College Ready scores are 165-174, and College Ready + Credit scores are 175-200. Remember these exact score ranges.
Getting Started: GED Math Exam Overview
GED Math Test Format, Scoring, and Study Strategies
Not using the on-screen calculator or formula sheet effectively because of lack of practice.
Getting Started: GED Math Exam Overview
GED Math Test Format, Scoring, and Study Strategies
Spending too much time on a single difficult question, sacrificing easier points later in the exam.
Getting Started: GED Math Exam Overview
GED Math Test Format, Scoring, and Study Strategies
Only memorizing formulas without understanding the underlying mathematical concepts.
Getting Started: GED Math Exam Overview
Place Value
The value of a digit based on its position.
Numbers, Fractions, and Percentages
Whole Number
A non-negative integer (0, 1, 2, 3...). No fractions or decimals.
Numbers, Fractions, and Percentages
Decimal
A number with a fractional part, represented by a decimal point.
Numbers, Fractions, and Percentages
Absolute Value
A number's distance from zero, always non-negative.
Numbers, Fractions, and Percentages
Integer
Any whole number, positive, negative, or zero.
Numbers, Fractions, and Percentages
Number Line
A visual representation of numbers in order.
Numbers, Fractions, and Percentages
Number Sense: Value, Order, and Place Value
Imagine a 'Place Value Party': the further left you are from the decimal point, the 'bigger' your importance (thousands, hundreds). The further right, the 'smaller' your importance (tenths, hundredths).
Numbers, Fractions, and Percentages
Number Sense: Value, Order, and Place Value
On the GED, you'll need to compare and order rational numbers, including positive and negative decimals and fractions. Pay attention to keywords like 'greater than,' 'less than,' 'least to greatest,' and 'greatest to least.'
Numbers, Fractions, and Percentages
Number Sense: Value, Order, and Place Value
Confusing the value of digits (e.g., thinking 0.5 is smaller than 0.05).
Numbers, Fractions, and Percentages
Number Sense: Value, Order, and Place Value
Incorrectly comparing negative numbers (e.g., thinking -10 is greater than -5).
Numbers, Fractions, and Percentages
Number Sense: Value, Order, and Place Value
Forgetting that absolute value always results in a positive number.
Numbers, Fractions, and Percentages
Numerator
The top number in a fraction, indicating parts chosen.
Numbers, Fractions, and Percentages
Denominator
The bottom number in a fraction, indicating total parts.
Numbers, Fractions, and Percentages
Common Denominator
A shared multiple of the denominators of two or more fractions.
Numbers, Fractions, and Percentages
Reciprocal
A number that, when multiplied by another, equals 1 (flipped fraction).
Numbers, Fractions, and Percentages
Decimal Point
Separates the whole part from the fractional part of a number.
Numbers, Fractions, and Percentages
Terminating Decimal
A decimal that has a finite number of digits after the decimal point.
Numbers, Fractions, and Percentages
Repeating Decimal
A decimal with a digit or block of digits that repeats infinitely.
Numbers, Fractions, and Percentages
Fractions and Decimals Operations
For dividing fractions, remember 'KFC': Keep the first, Flip the second, Change to multiply!
Numbers, Fractions, and Percentages
Fractions and Decimals Operations
The GED Math Test often presents problems where you must decide whether to work with fractions or convert to decimals. Look for keywords like 'total amount,' 'difference,' 'product,' or 'quotient' to identify the required operation. Be ready to simplify fractions to their lowest terms.
Numbers, Fractions, and Percentages
Fractions and Decimals Operations
Forgetting to find a common denominator before adding or subtracting fractions.
Numbers, Fractions, and Percentages
Fractions and Decimals Operations
Incorrectly placing the decimal point in multiplication or division of decimals.
Numbers, Fractions, and Percentages
Fractions and Decimals Operations
Not simplifying fractions to their lowest terms as the final step.
Numbers, Fractions, and Percentages
Percentage
A number or ratio expressed as a fraction of 100.
Numbers, Fractions, and Percentages
Fraction
A numerical quantity that is not a whole number (e.g., 1/2).
Numbers, Fractions, and Percentages
Percent Increase
The amount a value has grown, expressed as a percentage of the original value.
Numbers, Fractions, and Percentages
Percent Decrease
The amount a value has shrunk, expressed as a percentage of the original value.
Numbers, Fractions, and Percentages
Original Value
The starting amount before any change or calculation.
Numbers, Fractions, and Percentages
Rate
A ratio comparing two different quantities, often expressed as a percentage.
Numbers, Fractions, and Percentages
Understanding and Applying Percentages
To convert Percent to Decimal, move the decimal point two places Left. To convert Decimal to Percent, move the decimal point two places Right. Think: 'P-D-L, D-P-R' – Pretty Darn Logical, Don't Procrastinate Right!
Numbers, Fractions, and Percentages
Understanding and Applying Percentages
The GED Math test frequently uses percentages in word problems involving financial literacy, such as calculating simple interest, sales tax, tips, and discounts. Look for keywords like 'of', 'is what percent of', 'percent increase', or 'percent decrease'. Remember that 'of' often means multiplication.
Numbers, Fractions, and Percentages
Understanding and Applying Percentages
Forgetting to convert the percentage to a decimal or fraction before multiplying in calculations.
Numbers, Fractions, and Percentages
Understanding and Applying Percentages
Dividing by the new value instead of the original value when calculating percent change.
Numbers, Fractions, and Percentages
Understanding and Applying Percentages
Confusing the discount amount with the final sale price; always read carefully what the question asks for.
Numbers, Fractions, and Percentages
Ratio
Comparison of two or more quantities.
Numbers, Fractions, and Percentages
Proportion
An equation stating two ratios are equal.
Numbers, Fractions, and Percentages
Cross-multiplication
Method to solve proportions by multiplying diagonals.
Numbers, Fractions, and Percentages
Exponent
Indicates how many times to multiply a base by itself.
Numbers, Fractions, and Percentages
Base
The number being multiplied in an exponential expression.
Numbers, Fractions, and Percentages
Square Root
A number that, when squared, equals the given number.
Numbers, Fractions, and Percentages
Cube Root
A number that, when cubed, equals the given number.
Numbers, Fractions, and Percentages
Ratios, Proportions, Exponents, and Roots
Ratios are like Recipes (comparing ingredients). Proportions are like Puzzles (finding the missing piece). Exponents are like Elevators (going up to higher powers). Roots are like Reversing (undoing the power).
Numbers, Fractions, and Percentages
Ratios, Proportions, Exponents, and Roots
The GED exam frequently uses ratios and proportions in word problems involving scale drawings, maps, and percentages. Look for keywords like 'for every,' 'per,' or 'out of' to identify ratios, and 'if...then' or 'is to...as' for proportions. Memorize common perfect squares and cubes to quickly evaluate roots without a calculator.
Numbers, Fractions, and Percentages
Ratios, Proportions, Exponents, and Roots
Not simplifying ratios to their lowest terms, which can make calculations harder.
Numbers, Fractions, and Percentages
Ratios, Proportions, Exponents, and Roots
Incorrectly setting up proportions, especially when units are not aligned (e.g., flour/chips = chips/flour).
Numbers, Fractions, and Percentages
Ratios, Proportions, Exponents, and Roots
Confusing the exponent with multiplication (e.g., 3^2 is 3*3, not 3*2).
Numbers, Fractions, and Percentages
Customary System
Measurement system used in the US (e.g., feet, pounds).
Measurement, Data, and Probability
Metric System
Decimal-based measurement system used globally (e.g., meters, grams).
Measurement, Data, and Probability
Unit Conversion
Changing a measurement from one unit to another.
Measurement, Data, and Probability
Conversion Factor
A ratio used to convert between units (e.g., 12 inches/foot).
Measurement, Data, and Probability
Prefixes (Metric)
Indicators of magnitude in metric units (e.g., kilo-, centi-).
Measurement, Data, and Probability
Length
Measurement of distance (e.g., meter, foot).
Measurement, Data, and Probability
Mass/Weight
Measurement of quantity of matter (e.g., gram, pound).
Measurement, Data, and Probability
Capacity/Volume
Measurement of how much a container holds (e.g., liter, gallon).
Measurement, Data, and Probability
Units of Measurement and Conversions
King Henry Died By Drinking Chocolate Milk: Kilo, Hecto, Deka, Base, Deci, Centi, Milli. This helps remember metric prefixes in order!
Measurement, Data, and Probability
Units of Measurement and Conversions
The GED Math test expects you to know common conversions within both the Customary and Metric systems. Pay attention to keywords like 'how many feet are in a mile' or 'convert liters to milliliters' to identify conversion problems. A reference sheet with some conversions is provided on the test, but knowing common ones saves time.
Measurement, Data, and Probability
Units of Measurement and Conversions
Confusing multiplication and division: Always remember to multiply when going from a larger unit to a smaller unit, and divide when going from a smaller unit to a larger unit.
Measurement, Data, and Probability
Units of Measurement and Conversions
Ignoring units in the final answer: Make sure your answer is expressed in the unit requested by the problem.
Measurement, Data, and Probability
Units of Measurement and Conversions
Mixing Customary and Metric systems: Do not try to convert directly between systems unless a specific conversion factor is provided (e.g., 1 inch = 2.54 cm). Stick to within one system per problem unless explicitly told otherwise.
Measurement, Data, and Probability
Mean
The average of a data set; sum of values divided by count.
Measurement, Data, and Probability
Median
The middle value in an ordered data set.
Measurement, Data, and Probability
Mode
The value that appears most frequently in a data set.
Measurement, Data, and Probability
Range
The difference between the highest and lowest values.
Measurement, Data, and Probability
Data Set
A collection of numbers or values.
Measurement, Data, and Probability
Outlier
An extreme value that significantly differs from others.
Measurement, Data, and Probability
Data Analysis: Mean, Median, Mode, Range
To remember them: 'Mean' is 'mean' because you have to do all that adding and dividing. 'Median' is the 'middle' of the road. 'Mode' is 'most often'. 'Range' is how far you can 'roam' from low to high.
Measurement, Data, and Probability
Data Analysis: Mean, Median, Mode, Range
On the GED Math test, you will need to interpret these measures in context. Look for keywords like 'average' (mean), 'middle value' (median), 'most common' (mode), and 'spread' or 'difference' (range). You may be given a data set and asked to calculate one or more of these, or interpret a graph that displays them.
Measurement, Data, and Probability
Data Analysis: Mean, Median, Mode, Range
Forgetting to order the data set before finding the median.
Measurement, Data, and Probability
Data Analysis: Mean, Median, Mode, Range
Confusing the mean with the median or mode.
Measurement, Data, and Probability
Data Analysis: Mean, Median, Mode, Range
Incorrectly calculating the range by adding instead of subtracting.
Measurement, Data, and Probability
Data Display
Visual representation of data.
Measurement, Data, and Probability
Bar Graph
Compares quantities across categories.
Measurement, Data, and Probability
Line Graph
Shows trends or changes over time.
Measurement, Data, and Probability
Circle Graph
Shows parts of a whole (percentages).
Measurement, Data, and Probability
Histogram
Frequency distribution of numerical data in intervals.
Measurement, Data, and Probability
Box-and-Whisker Plot
Summarizes data distribution, showing median, quartiles.
Measurement, Data, and Probability
Scatter Plot
Shows relationship between two variables.
Measurement, Data, and Probability
Truncated Axis
An axis that does not start at zero.
Measurement, Data, and Probability
Statistics: Interpreting Data Displays
To remember the purpose of different graphs, think: 'BLiCS HS'. **B**ar for comparisons, **L**ine for trends, **C**ircle for parts of a whole, **S**catter for relationships, **H**istograms for frequencies, **S**tem-and-leaf for individual data.
Measurement, Data, and Probability
Statistics: Interpreting Data Displays
On the GED exam, pay close attention to the labels and scales of graphs. Questions often ask you to find specific values, calculate differences, or identify trends. Keywords like 'highest,' 'lowest,' 'increase,' 'decrease,' or 'average' are common in data display questions.
Measurement, Data, and Probability
Statistics: Interpreting Data Displays
Misreading the scale on an axis, especially if it doesn't start at zero or uses unusual increments.
Measurement, Data, and Probability
Statistics: Interpreting Data Displays
Confusing a bar graph with a histogram; bar graphs compare categories, histograms show frequency distribution of continuous data.
Measurement, Data, and Probability
Statistics: Interpreting Data Displays
Not checking if percentages in a circle graph add up to 100%, which can indicate missing data or errors.
Measurement, Data, and Probability
Probability
Measure of how likely an event is to occur.
Measurement, Data, and Probability
Experiment
A process with uncertain results or outcomes.
Measurement, Data, and Probability
Outcome
A single possible result of an experiment.
Measurement, Data, and Probability
Sample Space
The set of all possible outcomes for an experiment.
Measurement, Data, and Probability
Event
A specific outcome or set of outcomes of interest.
Measurement, Data, and Probability
Theoretical Probability
Expected probability based on mathematical reasoning.
Measurement, Data, and Probability
Experimental Probability
Probability based on actual results from trials.
Measurement, Data, and Probability
Introduction to Probability Concepts
Think 'FOT': Favorable Over Total. This reminds you that the number of Favorable outcomes goes on top of the fraction, and the Total possible outcomes goes on the bottom when calculating probability.
Measurement, Data, and Probability
Introduction to Probability Concepts
The GED Math test expects you to calculate the probability of simple events, often presented as fractions, decimals, or percentages. Look for keywords like 'what is the probability' or 'likelihood' and identify the total possible outcomes and the specific favorable outcomes.
Measurement, Data, and Probability
Introduction to Probability Concepts
Confusing favorable outcomes with total outcomes, leading to an inverted fraction.
Measurement, Data, and Probability
Introduction to Probability Concepts
Forgetting to simplify fractions to their lowest terms when expressing probability.
Measurement, Data, and Probability
Introduction to Probability Concepts
Mixing up theoretical probability (what should happen) with experimental probability (what did happen).
Measurement, Data, and Probability
Perimeter
The total distance around the outside of a 2D shape.
Geometry: Perimeter, Area, and Volume
Circumference
The perimeter of a circle.
Geometry: Perimeter, Area, and Volume
Polygon
A closed 2D shape with straight sides.
Geometry: Perimeter, Area, and Volume
Radius
Distance from a circle's center to any point on its edge.
Geometry: Perimeter, Area, and Volume
Diameter
Distance across a circle through its center; d = 2r.
Geometry: Perimeter, Area, and Volume
Pi (π)
Mathematical constant, approx. 3.14159, used in circle formulas.
Geometry: Perimeter, Area, and Volume
Linear units
Units for measuring length, e.g., feet, meters, inches.
Geometry: Perimeter, Area, and Volume
Perimeter and Circumference Calculations
To remember the circumference formulas: 'Cherry Pies Delicious' (C = πd) or 'Apple Pies Are Too' (C = 2πr).
Geometry: Perimeter, Area, and Volume
Perimeter and Circumference Calculations
The GED exam often presents perimeter and circumference problems in real-world contexts, requiring you to identify the correct formula and apply it. Look for keywords like 'distance around,' 'fence,' 'border,' or 'lap' to indicate perimeter or circumference. Be prepared to use the π button on your calculator or approximate π as 3.14 as specified in the question.
Geometry: Perimeter, Area, and Volume
Perimeter and Circumference Calculations
Confusing perimeter with area (perimeter is distance around, area is space inside).
Geometry: Perimeter, Area, and Volume
Perimeter and Circumference Calculations
Using the radius instead of the diameter (or vice versa) in circumference formulas.
Geometry: Perimeter, Area, and Volume
Perimeter and Circumference Calculations
Forgetting to include all sides when calculating the perimeter of an irregular polygon.
Geometry: Perimeter, Area, and Volume
Area
The measure of the 2D space a shape occupies.
Geometry: Perimeter, Area, and Volume
Square Unit
A unit of area, e.g., square feet (ft²).
Geometry: Perimeter, Area, and Volume
Length (L)
The longer side of a rectangle.
Geometry: Perimeter, Area, and Volume
Width (W)
The shorter side of a rectangle.
Geometry: Perimeter, Area, and Volume
Base (b)
Any side of a triangle used for area calculation.
Geometry: Perimeter, Area, and Volume
Height (h)
Perpendicular distance from base to opposite vertex.
Geometry: Perimeter, Area, and Volume
Radius (r)
Distance from circle's center to its edge.
Geometry: Perimeter, Area, and Volume
Diameter (d)
Distance across circle through its center.
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
For a triangle, think: 'A triangle is a TRICKY rectangle, so you have to DIVIDE IT BY TWO!'
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
The GED Math Test will provide a formula sheet, but you must know when and how to apply each formula. Keywords like 'surface covered,' 'space inside,' or 'amount of material needed' indicate an area problem.
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
Confusing area with perimeter: Area is inside, perimeter is around.
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
Forgetting to square the units: Area is always in square units (e.g., m²).
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
Using diameter instead of radius for circle area: Always use r, where r = d/2.
Geometry: Perimeter, Area, and Volume
Area of 2D Shapes (Rectangles, Triangles, Circles)
Not using the perpendicular height for triangle area.
Geometry: Perimeter, Area, and Volume
Surface Area
Total area of all faces of a 3D object.
Geometry: Perimeter, Area, and Volume
Rectangular Prism
A 3D shape with six rectangular faces.
Geometry: Perimeter, Area, and Volume
Cylinder
A 3D shape with two circular bases and a curved side.
Geometry: Perimeter, Area, and Volume
Face
A flat surface of a 3D object.
Geometry: Perimeter, Area, and Volume
Net
A 2D pattern that folds into a 3D shape.
Geometry: Perimeter, Area, and Volume
Lateral Surface Area
Area of the sides, excluding the bases.
Geometry: Perimeter, Area, and Volume
Surface Area of 3D Figures
Think of 'SA' as 'Siding All Around' – you're covering every side of the shape!
Geometry: Perimeter, Area, and Volume
Surface Area of 3D Figures
The GED exam often includes questions where you need to calculate the surface area of composite figures (shapes made of two or more simpler shapes). Remember to break down the complex figure into its basic components, calculate the surface area of each exposed part, and then sum them up, being careful not to double-count or miss any surfaces.
Geometry: Perimeter, Area, and Volume
Surface Area of 3D Figures
Forgetting to multiply by two for opposite faces of a rectangular prism.
Geometry: Perimeter, Area, and Volume
Surface Area of 3D Figures
Confusing surface area with volume; surface area is square units, volume is cubic units.
Geometry: Perimeter, Area, and Volume
Surface Area of 3D Figures
Incorrectly identifying whether to include the bases (e.g., for an open-top box or a label).
Geometry: Perimeter, Area, and Volume
Volume
The amount of 3D space an object occupies.
Geometry: Perimeter, Area, and Volume
Cubic Units
Units used to measure volume, e.g., cm³, m³.
Geometry: Perimeter, Area, and Volume
Pyramid
A 3D shape with a polygonal base and triangular sides.
Geometry: Perimeter, Area, and Volume
Base Area (B)
The area of the bottom face of a 3D figure.
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
For 'Volume of a Pyramid,' remember 'Pyramid has a P, and P is for PARTIAL.' It's only 1/3 of a full prism!
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
The GED Math test expects you to use the provided formula sheet accurately. Keywords like 'capacity,' 'how much it holds,' or 'space inside' usually indicate a volume problem. For cylinders, be careful if a diameter is given; you must divide it by 2 to get the radius before using the formula.
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
Confusing volume with surface area or perimeter.
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
Forgetting to use cubic units for volume answers.
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
Using diameter instead of radius in cylinder formulas (or vice versa).
Geometry: Perimeter, Area, and Volume
Volume of 3D Figures
Not dividing by 3 for pyramids.
Geometry: Perimeter, Area, and Volume
Right Triangle
A triangle with one 90-degree angle.
Advanced Geometry and Scale
Hypotenuse
The longest side of a right triangle, opposite the right angle.
Advanced Geometry and Scale
Legs
The two shorter sides of a right triangle adjacent to the right angle.
Advanced Geometry and Scale
Pythagorean Theorem
a² + b² = c², relating sides of a right triangle.
Advanced Geometry and Scale
Pythagorean Triple
Three integers (a, b, c) satisfying a² + b² = c².
Advanced Geometry and Scale
Pythagorean Theorem and its Applications
ABC: Always Be Calculating (a² + b² = c²)! And remember 'C' is for 'Corner-opposite' (hypotenuse).
Advanced Geometry and Scale
Pythagorean Theorem and its Applications
The GED Math test often presents Pythagorean Theorem problems in word problems that require you to visualize or sketch a right triangle. Look for keywords like 'ladder against a wall,' 'ramp,' 'diagonal,' or 'distance between two points' that imply a right angle. Remember that the distance formula is derived from the Pythagorean Theorem.
Advanced Geometry and Scale
Pythagorean Theorem and its Applications
Confusing a leg with the hypotenuse, especially when solving for a missing side.
Advanced Geometry and Scale
Pythagorean Theorem and its Applications
Forgetting to take the square root as the final step, leaving the answer as c² instead of c.
Advanced Geometry and Scale
Pythagorean Theorem and its Applications
Applying the theorem to triangles that are not right triangles.
Advanced Geometry and Scale
Coordinate Plane
A 2D surface with x and y axes for plotting points.
Advanced Geometry and Scale
Origin
The point (0,0) where the x-axis and y-axis intersect.
Advanced Geometry and Scale
Ordered Pair
A set of two numbers (x, y) that specifies a point's location.
Advanced Geometry and Scale
X-axis
The horizontal number line on a coordinate plane.
Advanced Geometry and Scale
Y-axis
The vertical number line on a coordinate plane.
Advanced Geometry and Scale
Distance Formula
A formula to find the straight-line distance between two points.
Advanced Geometry and Scale
Distance Formula on the Coordinate Plane
Remember 'X-difference squared, plus Y-difference squared, all under the square root!' It's like finding the hypotenuse of a hidden triangle!
Advanced Geometry and Scale
Distance Formula on the Coordinate Plane
The GED exam often presents distance formula problems in a word problem context, requiring you to first identify the coordinates from the description or a given graph, then apply the formula. Look for keywords like 'distance between', 'length of a segment', or 'how far apart'.
Advanced Geometry and Scale
Distance Formula on the Coordinate Plane
Forgetting to square the differences before adding them.
Advanced Geometry and Scale
Distance Formula on the Coordinate Plane
Incorrectly handling negative signs when subtracting coordinates, especially (x₂ - (-x₁)).
Advanced Geometry and Scale
Distance Formula on the Coordinate Plane
Forgetting to take the final square root of the sum.
Advanced Geometry and Scale
Scale Factor
Ratio describing enlargement or reduction of a figure.
Advanced Geometry and Scale
Similar Figures
Figures with the same shape but different sizes.
Advanced Geometry and Scale
Corresponding Sides
Sides in the same relative position in similar figures.
Advanced Geometry and Scale
Enlargement
When a figure is made larger by a scale factor > 1.
Advanced Geometry and Scale
Reduction
When a figure is made smaller by a scale factor < 1.
Advanced Geometry and Scale
Understanding and Applying Scale Factor
Scale Factor: 'New over Old' – always put the 'new' or 'image' dimension on top of the fraction, and the 'original' or 'pre-image' on the bottom.
Advanced Geometry and Scale
Understanding and Applying Scale Factor
The GED exam often presents scale factor problems in a practical context, such as maps, blueprints, or photographs. Look for keywords like 'scale,' 'ratio,' 'similar,' or 'model.' Be prepared to convert units (e.g., inches to feet, centimeters to kilometers) as part of the problem-solving process.
Advanced Geometry and Scale
Understanding and Applying Scale Factor
Mixing up which figure is the 'new' and which is the 'original' when calculating the ratio.
Advanced Geometry and Scale
Understanding and Applying Scale Factor
Forgetting to convert units when working with real-world problems like maps or models.
Advanced Geometry and Scale
Understanding and Applying Scale Factor
Applying the scale factor incorrectly (e.g., adding instead of multiplying/dividing).
Advanced Geometry and Scale
Composite Figure
A shape made up of two or more basic geometric shapes.
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
For Area vs. Perimeter: 'Area' is like an 'Are-a-rug' (covers a surface). 'Perimeter' is like 'Per-around-the-meter' (distance around).
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
The GED Math test frequently includes problems where you need to find the area or volume of composite figures. Look for keywords like 'total area,' 'how much space,' or 'capacity' to identify these problems. Remember that the formulas for basic shapes are provided on the test.
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
Confusing area with perimeter or volume with surface area.
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
Using the wrong formula for a given shape.
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
Forgetting to include units or using incorrect units (e.g., square feet instead of cubic feet for volume).
Advanced Geometry and Scale
Solving Problems with Geometric Concepts
Not breaking down composite figures correctly or missing parts of the shape.
Advanced Geometry and Scale
Algebraic Expression
A mathematical phrase with numbers, variables, and operation symbols.
Algebraic Foundations: Expressions
Variable
A letter or symbol representing an unknown numerical value.
Algebraic Foundations: Expressions
Constant
A numerical value that does not change within an expression.
Algebraic Foundations: Expressions
Coefficient
The numerical factor multiplied by a variable in a term.
Algebraic Foundations: Expressions
Term
Parts of an algebraic expression separated by addition or subtraction.
Algebraic Foundations: Expressions
Evaluate
To find the numerical value of an expression by substituting given values.
Algebraic Foundations: Expressions
Order of Operations
Rules for the sequence of performing calculations (PEMDAS).
Algebraic Foundations: Expressions
Substitute
To replace a variable with a specific numerical value.
Algebraic Foundations: Expressions
Writing and Evaluating Algebraic Expressions
PEMDAS: Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). This helps you remember the order of operations!
Algebraic Foundations: Expressions
Writing and Evaluating Algebraic Expressions
The GED exam often presents real-world scenarios requiring you to 'write an expression' or 'evaluate an expression' given specific values. Look for keywords indicating operations (e.g., 'sum of', 'product of', 'less than').
Algebraic Foundations: Expressions
Writing and Evaluating Algebraic Expressions
Incorrectly translating 'less than': '5 less than x' is x - 5, not 5 - x.
Algebraic Foundations: Expressions
Writing and Evaluating Algebraic Expressions
Ignoring the order of operations (PEMDAS) when evaluating, leading to incorrect results.
Algebraic Foundations: Expressions
Writing and Evaluating Algebraic Expressions
Forgetting to use parentheses when substituting negative numbers, especially when squaring them.
Algebraic Foundations: Expressions
Expression
A combination of numbers, variables, and operations.
Algebraic Foundations: Expressions
Like Terms
Terms with the same variable parts and exponents.
Algebraic Foundations: Expressions
Simplify
To rewrite an expression in a more compact form.
Algebraic Foundations: Expressions
Distributive Property
a(b + c) = ab + ac.
Algebraic Foundations: Expressions
Simplifying Algebraic Expressions
Remember 'DL C': **D**istribute, then **L**ook for like terms, then **C**ombine them!
Algebraic Foundations: Expressions
Simplifying Algebraic Expressions
The GED exam often includes questions where you must simplify expressions before you can solve for a variable or evaluate a formula. Look for keywords like 'simplify,' 'combine,' or 'rewrite in simplest form.'
Algebraic Foundations: Expressions
Simplifying Algebraic Expressions
Forgetting to distribute the term outside the parentheses to ALL terms inside.
Algebraic Foundations: Expressions
Simplifying Algebraic Expressions
Incorrectly combining unlike terms (e.g., adding 3x and 2y).
Algebraic Foundations: Expressions
Simplifying Algebraic Expressions
Making sign errors, especially when distributing a negative number.
Algebraic Foundations: Expressions
Polynomial
Algebraic expression with non-negative integer exponents.
Algebraic Foundations: Expressions
Degree
Highest exponent of the variable in a polynomial.
Algebraic Foundations: Expressions
GCF
Greatest Common Factor; largest monomial dividing all terms.
Algebraic Foundations: Expressions
Factoring
Breaking down a polynomial into a product of simpler expressions.
Algebraic Foundations: Expressions
Binomial
A polynomial with exactly two terms.
Algebraic Foundations: Expressions
Trinomial
A polynomial with exactly three terms.
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
FOIL: First, Outer, Inner, Last – for multiplying two binomials. Remember to 'FOIL' your way to polynomial multiplication success!
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
The GED Mathematical Reasoning Test frequently includes questions that require you to add, subtract, or multiply polynomials, especially binomials. Look for keywords like 'simplify,' 'expand,' or 'factor.' You must be able to factor out the GCF and recognize common factoring patterns like the difference of squares (a^2 - b^2) and perfect square trinomials (a^2 +/- 2ab + b^2).
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
Forgetting to distribute the negative sign when subtracting polynomials.
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
Incorrectly combining unlike terms (e.g., adding 3x^2 and 2x).
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
Not finding the *greatest* common factor when factoring out the GCF.
Algebraic Foundations: Expressions
Polynomials: Operations and Factoring Basics
Making arithmetic errors when multiplying coefficients or adding exponents.
Algebraic Foundations: Expressions
Keywords
Words that indicate specific mathematical operations (e.g., sum, product).
Algebraic Foundations: Expressions
Translate
To convert words or phrases into mathematical symbols.
Algebraic Foundations: Expressions
Real-World Problems with Expressions
Think 'VDOK': Variables, Define, Operations, Keywords. First, identify the Variables. Then, Define what they represent. Next, find the Operations. Finally, look for Keywords to guide you.
Algebraic Foundations: Expressions
Real-World Problems with Expressions
The GED exam often uses keywords like 'per,' 'each,' 'total,' 'difference,' 'sum,' 'product,' and 'quotient' to signal operations. Memorize these associations to quickly set up expressions. Always define your variables clearly.
Algebraic Foundations: Expressions
Real-World Problems with Expressions
Incorrectly interpreting keywords (e.g., 'less than' often means subtraction in reverse order).
Algebraic Foundations: Expressions
Real-World Problems with Expressions
Forgetting to define variables, leading to confusion about what each letter represents.
Algebraic Foundations: Expressions
Real-World Problems with Expressions
Not using parentheses when necessary to maintain the correct order of operations.
Algebraic Foundations: Expressions
Real-World Problems with Expressions
Confusing an expression with an equation (expressions do not have an equals sign).
Algebraic Foundations: Expressions
Linear Equation
Equation where variable's highest power is 1.
Solving Linear Equations and Inequalities
Inverse Operations
Operations that undo each other (e.g., add/subtract).
Solving Linear Equations and Inequalities
Isolate the Variable
To get the variable by itself on one side.
Solving Linear Equations and Inequalities
Combine Like Terms
Add or subtract terms with the same variable and exponent.
Solving Linear Equations and Inequalities
Solving One-Step and Multi-Step Linear Equations
Don't Call Me After Midnight: Distribute, Combine like terms, Move variable terms, Add/Subtract constants, Multiply/Divide.
Solving Linear Equations and Inequalities
Solving One-Step and Multi-Step Linear Equations
The GED exam often presents linear equations within word problems. Look for keywords like 'total,' 'sum,' 'difference,' 'product,' and 'quotient' to help translate the problem into an algebraic equation. Remember to define your variable clearly.
Solving Linear Equations and Inequalities
Solving One-Step and Multi-Step Linear Equations
Forgetting to perform an operation on BOTH sides of the equation.
Solving Linear Equations and Inequalities
Solving One-Step and Multi-Step Linear Equations
Incorrectly applying inverse operations (e.g., adding when you should subtract).
Solving Linear Equations and Inequalities
Solving One-Step and Multi-Step Linear Equations
Making arithmetic errors when combining terms or simplifying.
Solving Linear Equations and Inequalities
Inequality
A mathematical statement comparing two expressions using <, >, ≤, or ≥.
Solving Linear Equations and Inequalities
Solution Set
The range of values that make an inequality true.
Solving Linear Equations and Inequalities
Open Circle
Indicates an endpoint is not included in the solution set (<, >).
Solving Linear Equations and Inequalities
Closed Circle
Indicates an endpoint is included in the solution set (≤, ≥).
Solving Linear Equations and Inequalities
Reverse Sign
Rule for multiplying/dividing an inequality by a negative number.
Solving Linear Equations and Inequalities
Linear Inequality
An inequality where the highest power of the variable is one.
Solving Linear Equations and Inequalities
Solving Linear Inequalities
N.E.G.A.T.I.V.E. Flip! When you multiply or divide by a NEGATIVE number, you must FLIP the inequality sign!
Solving Linear Equations and Inequalities
Solving Linear Inequalities
GED test questions on inequalities often involve translating word problems into algebraic inequalities. Look for keywords like 'at least,' 'at most,' 'no more than,' 'minimum,' and 'maximum' to determine the correct inequality symbol.
Solving Linear Equations and Inequalities
Solving Linear Inequalities
Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
Solving Linear Equations and Inequalities
Solving Linear Inequalities
Incorrectly using open vs. closed circles when graphing solutions on a number line.
Solving Linear Equations and Inequalities
Solving Linear Inequalities
Misinterpreting keywords in word problems (e.g., 'at least' means ≥, not just >).
Solving Linear Equations and Inequalities
System of Linear Equations
Two or more linear equations with the same variables.
Solving Linear Equations and Inequalities
Solution to a System
The point (x, y) that satisfies all equations in the system.
Solving Linear Equations and Inequalities
Intersection Point
The point where the graphs of two lines cross on a coordinate plane.
Solving Linear Equations and Inequalities
Substitution Method
Solving one equation for a variable, then plugging into the other.
Solving Linear Equations and Inequalities
No Solution
A system where the lines are parallel and never intersect.
Solving Linear Equations and Inequalities
Infinitely Many Solutions
A system where both equations represent the same line.
Solving Linear Equations and Inequalities
Graphing Method
Finding the solution by plotting both lines and identifying their intersection.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Graphing/Substitution)
GRAPH for 'Get Ready And Plot Heavily' to remember to graph both lines carefully. SUBSTITUTE for 'Solve Until Both Equations Take Everything' to recall isolating a variable and plugging it in.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Graphing/Substitution)
On the GED Math Test, look for keywords like 'when are they equal,' 'find the common point,' or 'solve for both variables.' These often indicate a system of equations. Be prepared to interpret graphs of lines to find solutions.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Graphing/Substitution)
Incorrectly graphing lines, leading to an inaccurate intersection point.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Graphing/Substitution)
Making algebraic errors when isolating a variable or substituting an expression.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Graphing/Substitution)
Forgetting to find the value of the second variable after solving for the first.
Solving Linear Equations and Inequalities
System of Equations
Two or more equations with the same variables.
Solving Linear Equations and Inequalities
Elimination Method
Adding or subtracting equations to remove a variable.
Solving Linear Equations and Inequalities
Standard Form
A linear equation written as Ax + By = C.
Solving Linear Equations and Inequalities
Consistent System
A system with at least one solution.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Elimination)
ELIMINATE: E-qualize L-ike I-tems, M-ultiply if needed, I-ntegrate (add/subtract), N-arrow down to one variable, A-nswer, T-ry it again (check), E-very time!
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Elimination)
The GED exam often presents system of equations problems as word problems requiring you to set up the equations before solving. Look for keywords indicating two different totals or relationships between two quantities.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Elimination)
Forgetting to multiply ALL terms in an equation when scaling it up for elimination.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Elimination)
Incorrectly adding or subtracting equations, especially with negative signs.
Solving Linear Equations and Inequalities
Solving Systems of Linear Equations (Elimination)
Not checking the solution by substituting values back into BOTH original equations.
Solving Linear Equations and Inequalities
Quadratic Equation
A polynomial equation of the second degree.
Quadratic Equations and Functions
Constant Term
The term in an algebraic expression that has no variable.
Quadratic Equations and Functions
Parabola
The U-shaped graph of a quadratic equation.
Quadratic Equations and Functions
Introduction to Quadratic Equations
ABC: Always Be Careful! 'A' cannot be zero, 'B' is with x, 'C' is the constant.
Quadratic Equations and Functions
Introduction to Quadratic Equations
On the GED Math test, you must be able to identify quadratic expressions and equations. Look for the highest exponent of 2 on a variable (like x²). Equations that can be rewritten as ax² + bx + c = 0 are quadratic.
Quadratic Equations and Functions
Introduction to Quadratic Equations
Forgetting to set the equation to zero before identifying a, b, and c.
Quadratic Equations and Functions
Introduction to Quadratic Equations
Confusing the 'b' term with the 'c' term, especially if one is missing.
Quadratic Equations and Functions
Introduction to Quadratic Equations
Assuming an equation is quadratic without simplifying it first to check the highest exponent.
Quadratic Equations and Functions
Zero Product Property
If A * B = 0, then A = 0 or B = 0.
Quadratic Equations and Functions
Solutions (Roots)
The values of x that satisfy a quadratic equation.
Quadratic Equations and Functions
Solving Quadratic Equations by Factoring
ZAP! Zero Product Property: If anything equals ZERO, one of the PARTS must be ZERO!
Quadratic Equations and Functions
Solving Quadratic Equations by Factoring
The GED exam often presents quadratic equations in real-world contexts, requiring you to set up the equation first, then solve it. Look for keywords like 'area', 'product', or 'height' that lead to quadratic models.
Quadratic Equations and Functions
Solving Quadratic Equations by Factoring
Forgetting to set the equation to zero before factoring.
Quadratic Equations and Functions
Solving Quadratic Equations by Factoring
Incorrectly factoring the quadratic expression (e.g., wrong signs or numbers).
Quadratic Equations and Functions