Algebraic Reasoning
55-60%of exam
Quantitative Reasoning
25-30%of exam
Geometric Reasoning
15-20%of exam
Quick Facts
- Exam
- PERT Math
- Questions
- 30 (25 scored)
- Time
- Untimed
- Format
- Adaptive MCQ
- Elective
- Score 114
- Gen-Ed
- Score 123
- Scale
- 50-150
- Fee
- Free
- Calculator
- On-screen only
Order of Operations
Please Excuse My Dear Aunt Sally
P: parenthesesE: exponentsMD: multiply/divideAS: add/subtract
Expression vs Equation
Expression
- No equals sign
- Simplify only
- Cannot solve
Equation
- Has equals sign
- Solve for variable
- Find a value
Simplify vs solve
Which Factoring Method
- Common factor all terms→GCF first(Always start)
- Two perfect squares→Difference of squares(a²-b²)
- Trinomial, a is 1→Find two numbers(Sum b, product c)
- Trinomial, a not 1→AC method(Then group)
- Four terms→Grouping(Common binomial)
- Middle twice product→Perfect square((a±b)²)
Linear Equations
- Isolate variable
- Inverse operation both sides
- Multi-step order
- Distribute, combine, move, divide
- Clear fractions
- Multiply all by LCD
- Variables both sides
- Collect variables one side
- Check solution
- Substitute into original
- Literal equation
- Solve for one variable
Multiply Two Binomials
First, Outer, Inner, Last
First termsOuter termsInner termsLast terms
Factoring vs Formula
Factoring
- Fast when factorable
- Integer roots
- Zero product
Quadratic Formula
- Always works
- Any roots
- Uses discriminant
Nice roots vs any
Solving a Quadratic
- Not equal to zero→Set to zero(Standard form)
- Factors easily→Factoring(Zero product)
- No linear term→Square root method(x²=k)
- Will not factor→Quadratic formula(Always works)
- Need root count→Discriminant(b²-4ac)
- Need vertex→Vertex form(y=a(x-h)²+k)
Inequalities
- Flip sign
- When negative multiply/divideKey rule
- Compound 'and'
- Overlap; connected segment
- Compound 'or'
- Union; two rays
- Open circle
- Strict < or >
- Closed circle
- ≤ or ≥ included
- Solution set
- All values satisfying
Quadratic Formula
x equals negative b plus/minus root
a,b,c from standard formDiscriminant b²-4acTwo ± solutions
Cancel Factor vs Term
Factor
- Multiplied piece
- Can cancel
- After factoring
Term
- Added piece
- Never cancel
- Common mistake
Multiply vs add
Systems of Equations
- Substitution
- Replace one variable
- Elimination
- Add to cancel variable
- One solution
- Lines intersect once
- No solution
- Parallel distinct lines
- Infinite solutions
- Same line overlap
- Graphing
- Intersection point solves
Divide Fractions
Keep, Change, Flip
Keep first fractionChange to multiplyFlip second fraction
Algebraic Expressions
- Like terms
- Same variable and power
- Distribute
- a(b+c)=ab+ac
- FOIL
- First Outer Inner Last
- PEMDAS
- Order of operations
- Combine terms
- Add matching coefficients
- Evaluate
- Substitute then simplify
Factoring Patterns
- GCF first
- Pull common factor outAlways start
- Difference of squares
- a²-b²=(a+b)(a-b)
- Perfect square
- (a±b)² trinomial
- AC method
- When leading coefficient ≠1
- Grouping
- Four terms, shared binomial
- Zero product
- Set each factor zero
Quadratic Equations
- Standard form
- ax²+bx+c=0
- By factoring
- Then zero product
- Square root method
- For x²=k form
- Quadratic formula
- x=(-b±√(b²-4ac))/2a
- Discriminant
- b²-4ac tells roots
- Vertex form
- Vertex at (h,k)
Rational Expressions
- Simplify
- Factor then cancel factors
- Add or subtract
- Need common LCD
- Multiply
- Factor, cancel, multiply across
- Divide
- Multiply by reciprocal
- Excluded values
- Denominator cannot be zero
- Extraneous check
- Reject zero-denominator roots
Product vs Power Rule
Product Rule
- Multiplying like bases
- Add exponents
- aᵐ·aⁿ
Power Rule
- Power of power
- Multiply exponents
- (aᵐ)ⁿ
Add vs multiply
Exponent Rules
- Product rule
- Add exponents, like base
- Quotient rule
- Subtract exponents dividing
- Power of power
- Multiply the exponents
- Negative exponent
- Reciprocal, positive power
- Zero exponent
- Equals one
- Fractional exponent
- Root from denominator
Radicals
- Simplify radical
- Remove perfect-square factor
- Rationalize
- Clear radical denominator
- Add radicals
- Combine like radicands
- Multiply radicals
- Multiply under one root
- Radical product
- √a·√b=√ab
- Conjugate
- Flip middle sign
Percent + Proportion
- Proportion
- Cross-multiply to solve
- Percent of
- Multiply by decimal
- Percent change
- Difference over original
- Is over of
- Part over whole
- Direct variation
- y=kx, constant ratio
- Unit rate
- Quantity per one
Word Problem Keywords
- Define variable
- State what x is
- 'of'
- Means multiply
- 'is'
- Means equals
- 'per'
- Means divide
- 'less than'
- Reverses subtraction order
- Consecutive integers
- n, n+1, n+2
Reading Slope
Rise over run
Rise: vertical changeRun: horizontal changePositive: uphill rightNegative: downhill right
Parallel vs Perpendicular
Parallel
- Equal slopes
- Never intersect
- Same steepness
Perpendicular
- Negative reciprocal
- Meet at 90°
- Product is -1
Equal vs opposite reciprocal
Coordinate Geometry Picker
- Slope from two points→Slope formula(Rise over run)
- Distance between points→Distance formula(Pythagorean based)
- Halfway point→Midpoint formula(Average coordinates)
- Slope and intercept→y=mx+b(Slope-intercept)
- Line parallel to given→Same slope(Equal m)
- Line perpendicular→Negative reciprocal(Flip and negate)
- Right-triangle side→Pythagorean theorem(a²+b²=c²)
Coordinate Geometry
- Slope
- (y2-y1)/(x2-x1)
- Slope-intercept
- y=mx+b
- Distance
- √(Δx²+Δy²)
- Midpoint
- Average both coordinates
- Parallel
- Equal slopes
- Perpendicular
- Negative reciprocal slope
Distance vs Midpoint
Distance
- Length between points
- Uses subtraction, squares
- Square root
Midpoint
- Halfway point
- Average coordinates
- Uses addition
Length vs middle
Area + Volume
- Pythagorean
- a²+b²=c²
- Rectangle area
- length × width
- Triangle area
- ½ base × height
- Circle area
- πr²
- Box volume
- length × width × height
- Circumference
- 2πr or πd
Common Traps
Simplify vs solve
Expression simplifies ≠ Equation solves value
Cancel factors not terms
Cancel common factors ≠ Never cancel terms
Inequality sign flip
Flip for negative multiply ≠ Keep for positive
Percent base
Base is original ≠ Not the new amount
Negative exponent
Means reciprocal ≠ Not a negative number
Parallel vs perpendicular
Parallel equal slopes ≠ Perpendicular negative reciprocal
Last Minute
- 1.Factor GCF before anything else
- 2.Set quadratic to zero first
- 3.Flip inequality for negative only
- 4.Cancel factors, never terms
- 5.Percent base is original amount
- 6.Parallel slopes equal
- 7.Perpendicular slopes negative reciprocal
- 8.Negative exponent means reciprocal
- 9.Check extraneous rational solutions
- 10.Clear fractions using LCD
- 11.Score 114 elective, 123 gen-ed
- 12.Distance is Pythagorean theorem
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