Quantitative: Rational Numbers
25%of exam
Number OpsFractions & DecimalsRatios & PercentsStatisticsProbability
Quantitative: Measurement
20%of exam
Algebraic: Equations
30%of exam
ExpressionsLinear EquationsInequalitiesQuadraticsSystems
Algebraic: Graphs & Functions
25%of exam
SlopeGraphing LinesFunctionsDomain & RangeNonlinear
Quick Facts
- Exam
- GED Mathematical Reasoning
- Items
- About 46 questions
- Item types
- MC, drag-drop, hot spot, fill-in
- Time
- 115 minutes
- Pass score
- 145 out of 200
- College Ready
- 165 or higher
- College Ready + Credit
- 175 or higher
- Calculator
- TI-30XS Multiview onscreen
- No-calc items
- First 5 questions only
Order of Operations
Please Excuse My Dear Aunt Sally
Parens firstExponents nextMultiply/divide left-rightAdd/subtract left-right
Mean vs Median
Mean
- Sum ÷ count
- Pulled by outliers
Median
- Middle sorted value
- Ignores outliers
Average vs middle value
Order of Operations & Signs
- PEMDAS
- P-E-MD-AS order
- Two negatives multiplied
- Positive product
- Negative times positive
- Negative product
- Absolute value
- Distance from zero
- Reciprocal
- Flip numerator, denominator
- Keep-Change-Flip
- Divide fractions method
Keep-Change-Flip
Keep first, change sign, flip second
Keep: first fractionChange: ÷ to ×Flip: second fraction
Fractions, Decimals & Percents
- Fraction to decimal
- Divide top by bottom
- Decimal to percent
- Multiply by 100
- Percent to decimal
- Divide by 100
- Unit rate
- Amount per one unit
- Proportion
- Equal ratios, cross multiply
- Percent change
- Difference over original ×100Common trap
- Percent of whole
- Part divided by percent
- Markup
- Price × (1 + rate)
- Discount
- Price × (1 − rate)
Percent Trap Reminder
Always divide by the original value
New minus originalDivide by originalMultiply by 100
Statistics & Probability
- Mean
- Sum divided by count
- Median
- Middle value, sorted data
- Mode
- Most frequent value
- Range
- Max minus min
- Weighted average
- Values times their frequencies
- Probability
- Favorable over total outcomes
- Probability range
- Between 0 and 1
- Frequency table
- Counts data value occurs
Formula Sheet Reminder
Formula sheet given; know when to use it
Given: all formulasMissing: when to applyPractice: word-problem cues
Area vs Circumference
Area
- Space inside shape
- Square units
Circumference
- Distance around circle
- Linear units
Inside vs around
Formula Picker
- Need enclosed space→Area formula(Square units)
- Need distance around→Perimeter or circumference(Linear units)
- Need space inside solid→Volume formula(Cubic units)
- Need outside covering→Surface area formula(Square units)
- Right triangle side→Pythagorean theorem(a²+b²=c²)
- Irregular shape→Split into simple shapes(Add or subtract)
- Scaled drawing given→Set up proportion(Cross multiply)
Area Formulas
- Square area
- A = s²
- Rectangle area
- A = lw
- Parallelogram area
- A = bh
- Triangle area
- A = 1/2 bh
- Trapezoid area
- Half height times base sum
- Circle area
- A = πr²
Volume vs Surface Area
Volume
- Space inside solid
- Cubic units
Surface Area
- Material covering outside
- Square units
Fill vs cover
Perimeter & Circumference
- Square perimeter
- P = 4s
- Rectangle perimeter
- P = 2l + 2w
- Triangle perimeter
- Sum of three sides
- Circumference (radius)
- C = 2πr
- Circumference (diameter)
- C = πd
- Composite figure area
- Add or subtract shapes
Volume & Surface Area
- Rectangular prism volume
- V = lwh
- Rectangular prism surface
- SA = 2lw+2lh+2wh
- Cylinder volume
- V = πr²h
- Cylinder surface
- SA = 2πrh + 2πr²
- Cone volume
- V = 1/3 πr²h
- Sphere volume
- V = 4/3 πr³
- Sphere surface
- SA = 4πr²
Pythagorean, Scale & Units
- Pythagorean theorem
- a² + b² = c²Right triangles only
- Hypotenuse
- Longest side, right triangle
- Scale factor use
- Set up, cross multiply
- Distance formula
- d = rt
- Simple interest
- I = Prt
- Total cost
- Units times price each
- Unit conversion
- Match units before solving
Substitution vs Elimination
Substitution
- One equation solved
- Plug into other
Elimination
- Standard form equations
- Add or subtract
Solved variable vs matching terms
Equation Method Picker
- One variable, linear→Isolate the variable
- Fractions in equation→Multiply by LCD
- Two equations, one solved→Substitution method
- Two equations, standard form→Elimination method
- Equals zero, factors easily→Factor, zero product
- Quadratic won't factor→Quadratic formula
- Dividing by a negative→Flip inequality sign
Expressions & Polynomials
- Like terms
- Same variable, same exponent
- Distributive property
- Multiply outside term, every term
- Adding polynomials
- Combine like terms only
- Multiplying polynomials
- Distribute every term (FOIL)
- Translating phrases
- Key words to operations
- 'Less than' phrase
- Reverses subtraction orderCommon trap
- Evaluating expressions
- Substitute value, every instance
Linear Equations & Inequalities
- Multi-step equation order
- Distribute, combine, isolate variable
- Equations with fractions
- Multiply every term, LCD
- Systems: substitution
- Solve one, sub into other
- Systems: elimination
- Add or subtract, cancel variable
- Inequality sign flip
- Flip when × or ÷ negativeCommon trap
- Open vs closed circle
- Strict open, equal closed
- Graphing inequality
- Shade direction, mark boundary
Quadratics & Factoring
- Factor x²+bx+c
- Two numbers: multiply c, add b
- Zero product property
- One factor must be zero
- Difference of squares
- Factors into sum, difference
- Quadratic graph shape
- U-shaped parabola curve
- Positive leading coefficient
- Opens upward, has minimum
- Negative leading coefficient
- Opens downward, has maximum
- Quadratic formula
- Solves any quadratic equation
Slope-Intercept Memory
m is slope, b is start
m: rate of changeb: y-intercept valuex=0 finds b
Domain vs Range
Domain
- Input values
- x-axis values
Range
- Output values
- y-axis values
Input vs output
Graph Reading Picker
- Line crosses y-axis→Read y-intercept(Set x=0)
- Line crosses x-axis→Read x-intercept(Set y=0)
- Need rate of change→Calculate slope
- Graph curves, not straight→Nonlinear function
- Vertical line crosses twice→Not a function
- Comparing two lines→Compare slope values
Slope & Linear Graphing
- Slope formula
- Change in y over x
- Positive slope
- Line rises left to right
- Negative slope
- Line falls left to right
- Slope-intercept form
- y = mx + b
- y-intercept meaning
- Starting value, where x is 0
- x-intercept
- Set y to 0, solve x
- Parallel lines slope
- Same slope value
- Perpendicular lines slope
- Negative reciprocal slope
- Rate of change (table)
- Change in y over x
Parallel vs Perpendicular Slope
Parallel
- Same slope
- Never intersect
Perpendicular
- Negative reciprocal slope
- Right angle meet
Same vs flipped-negative slope
Functions & Graph Features
- Function notation f(x)
- Output for input x
- Evaluating f(3)
- Substitute 3 for x
- Vertical line test
- One crossing per input
- Domain
- Set of input values
- Range
- Set of output values
- Linear vs nonlinear
- Constant vs varying rate
- Function table check
- Same input, one output
- Reading graph context
- Match features to meaning
Linear vs Nonlinear Function
Linear
- Constant rate of change
- Straight line graph
Nonlinear
- Varying rate of change
- Curved graph shape
Constant vs varying rate
Common Traps
Area vs volume units
Area = square units ≠ Volume = cubic units
Percent change base
Divide by original ≠ Not by new value
Negative divide flip
Flip inequality sign ≠ Only for negative ÷/×
Slope sign order
Same order both times ≠ Not mismatched x, y
Radius vs diameter
Use radius in formulas ≠ Diameter = 2× radius
Mean vs median pull
Mean shifts with outliers ≠ Median stays put
Function vs relation
One output per input ≠ Vertical line test
Last Minute
- 1.Test: about 46 questions, 115 min
- 2.Part 1: 5 questions, no calculator
- 3.Part 2: TI-30XS Multiview calculator allowed
- 4.Pass score: 145 out of 200
- 5.165+ = College Ready status
- 6.175+ = College Ready + Credit
- 7.Formula sheet given for whole test
- 8.Quantitative Problem Solving = 45% weight
- 9.Algebraic Problem Solving = 55% weight
- 10.Percent change: divide by original value
- 11.Flip inequality sign when dividing negative
- 12.Area: square units. Volume: cubic units
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