Numbers + Ratios
25%of exam
IntegersFractionsPercentsRatiosUnits
Equations + Expressions
25%of exam
LinearInequalitiesSystemsExponentsPolynomials
Functions + Graphs
25%of exam
SlopeInterceptsDomainRangeQuadratics
Advanced Readiness
25%of exam
Quick Facts
- Assessment
- ALEKS PPL
- Format
- Adaptive open response
- Questions
- 25 or fewer
- Time
- About 90 minutes
- Score
- Institution mapped
- Calculator
- School policy
- Goal
- Course placement
Order
Groups, exponents, multiply divide, add subtract.
GroupsExponentsMultiplyDivideAddSubtract
Exact vs Decimal
Exact
- Fractions radicals pi
- Preferred often
Decimal
- Approximate value
- Round carefully
Follow entry format
Number Rules
- Negative minus
- Add opposite
- Absolute value
- Distance from zero
- Fraction sum
- Match denominators
- Percent change
- Use original base
- Ratio
- Compare same units
- Proportion
- Cross multiply
- Estimate
- Catch impossible answers
Expression vs Equation
Expression
- Simplify only
- No equals sign
Equation
- Solve variable
- Has equals sign
Simplify before solving
Equation Picker
- Fractions appear→Clear denominators
- Parentheses appear→Distribute first
- Like terms appear→Combine terms
- Variable both sides→Collect variable
- Inequality negative→Reverse symbol
- Quadratic equals zero→Factor first
- Denominator has x→Check restrictions
- Root equation→Check extraneous
Linear Tools
- Distribute
- Multiply every term
- Like terms
- Same variable power
- One step
- Undo operation
- Multi step
- Simplify first
- Inequality
- Flip for negative
- System
- Eliminate or substitute
- Check
- Substitute result
Factor vs Expand
Factor
- Create products
- Helps solve
Expand
- Remove parentheses
- Helps combine
Match next step
Polynomial Rules
- Degree
- Greatest exponent
- GCF
- Factor first
- Difference squares
- Two conjugates
- Trinomial
- Product and sum
- Product rule
- Add exponents
- Power rule
- Multiply exponents
- Zero exponent
- Nonzero base one
Domain Checks
No zero denominators; no negative even roots.
DenominatorEven rootLog input
Slope vs Intercept
Slope
- Rate of change
- m value
Intercept
- Axis crossing
- Set variable zero
Identify the ask
Graph Picker
- Find slope→Rise over run
- Find x-intercept→Set y zero
- Find y-intercept→Set x zero
- Input restricted→State domain
- Output bounded→State range
- Parabola asked→Find vertex
- Parallel line→Reuse slope
- Perpendicular line→Negative reciprocal
Graph Basics
- Slope
- Rise over run
- y-intercept
- Set x zero
- x-intercept
- Set y zero
- Parallel
- Same slope
- Perpendicular
- Negative reciprocal
- Vertex
- Parabola turning point
- Transform
- Shift stretch reflect
Function Rules
- f(a)
- Substitute a
- Domain
- Allowed inputs
- Range
- Possible outputs
- Composition
- Inside first
- Inverse
- Swap x y
- Increasing
- Outputs rise
- Decreasing
- Outputs fall
Trig
Sine opposite; cosine adjacent; tangent opposite.
SOHCAHTOA
Radical vs Exponent
Radical
- Root symbol
- Check domain
Exponent
- Power notation
- Use exponent rules
Convert if useful
Rational Rules
- Restriction
- Denominator not zero
- Simplify
- Factor then cancel
- Multiply
- Cancel common factors
- Divide
- Flip second fraction
- Add
- Use common denominator
- Equation
- Clear denominators
- Extraneous
- Reject zero denominator
Radicals + Logs
- Square root
- Principal nonnegative root
- Even root
- Radicand nonnegative
- Rational exponent
- Root then power
- Log
- Exponent question
- Log product
- Add logs
- Log quotient
- Subtract logs
- Log power
- Bring exponent down
Geometry + Trig
- Area rectangle
- length times width
- Area triangle
- half base height
- Circle area
- pi r squared
- Pythagorean
- a2 plus b2 c2
- SOH
- Sine opposite hypotenuse
- CAH
- Cosine adjacent hypotenuse
- TOA
- Tangent opposite adjacent
Common Traps
Sign Errors
Distribute negative signs ≠ Flip inequality signs
Fraction Errors
Use common denominator ≠ Do not cancel terms
Function Notation
Substitute input ≠ Not multiplication
Domain Loss
Track original restrictions ≠ Reject impossible inputs
Open Response
Practice exact entry ≠ Avoid answer recognition
Last Minute
- 1.Memorize exponent rules
- 2.Review slope forms
- 3.Practice factoring patterns
- 4.Check denominator restrictions
- 5.Check radical domains
- 6.Use original percent base
- 7.Substitute final answers
- 8.Read school score table
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