Mathematics
48%of exam
Algebraic IdentitiesFunctions and InversesQuadratic EquationsLogarithm RulesCoordinate GeometryProbability Basics
Reading Comprehension
22%of exam
Economic PassagesExplicit DetailImplicit MeaningAuthor PurposePassage Structure
Numerical Reasoning
12%of exam
Table InterpretationChart ExtractionPercentage ChangeRatio CalculationsSuperfluous Data
Critical Thinking
18%of exam
Deductive ReasoningModus TollensTrue False UnknownData PropositionsHidden Assumptions
Quick Facts
- Exam Format
- 50 questions online
- Time Limit
- 75 minutes continuous
- Scoring
- Plus 1 correct zero blank
- Wrong Penalty
- Minus 0.20 or 0.33
- Exclusion Floor
- Under 17 excluded
- Weighting
- 55 percent test 45 GPA
- Attempt Limit
- Four per type yearly
- Calculators
- Strictly prohibited
Viete Root Formulas
Sum equals negative b/a; product equals c/a
Sum equals negative b over aProduct equals c over aApplies to quadratic equationsSaves time on roots
Permutations vs Combinations
Permutations
- Order is essential
- Rankings or sequences
- Factorial arrangement
Combinations
- Order does not matter
- Committees or groups
- Divide out duplicates
Ordered arrangement versus unordered selection
Mathematics Strategy Picker
- Equation has symmetry→Apply Viete root formulas(Avoid long quadratic solving)
- Rational inequality given→Build sign chart immediately(Exclude denominator roots)
- Compound probability requested→Check for independent events(Multiply separate chances)
- Permutation versus combination→Determine if order counts(Combinations divide duplicates)
- Exponential equation given→Match bases or take logarithms(Check positive bases first)
- Calculations look overwhelming→Look for factoring shortcut(No calculators allowed)
Algebraic Identities
- Difference squares
- a²−b² = (a−b)(a+b)Factor
- Sum of cubes
- a³+b³ = (a+b)(a²−ab+b²)Factor
- Difference cubes
- a³−b³ = (a−b)(a²+ab+b²)Factor
- Quadratic roots
- x = (−b±√(b²−4ac))/(2a)Formula
- Discriminant positive
- Two distinct real rootsRoots
- Discriminant zero
- One repeated real rootRoots
- Discriminant negative
- No real solutions existRoots
- Viete sum
- Minus b divided by aRoots
Logarithm Expansion Rules
Product adds Quotient subtracts Power multiplies forward
Product becomes sumQuotient becomes differencePower drops to frontSame base required
Independent vs Mutually Exclusive
Independent
- Outcomes do not affect
- Product of probabilities
- Can occur together
Mutually Exclusive
- Cannot happen together
- Intersection equals zero
- Sum of probabilities
No influence versus disjoint occurrence
Functions and Exponents
- Invertible function
- Must be strictly bijectiveCore
- Inverse reflection
- Reflect across line y equals xGraph
- Domain of g∘f
- x∈Df; f(x)∈DgRule
- Root principal
- √(x²) = |x|Trap
- Fractional power
- Positive base: exponent means root-powerRule
- Negative power
- a^(−n)=1/a^n; a≠0Rule
- Zero exponent
- a⁰=1; a≠0Rule
Logarithms and Exponentials
- Log product
- log_b(xy)=log_b(x)+log_b(y)Rule
- Log quotient
- Log quotient becomes log differenceRule
- Log power
- log_b(x^k)=k·log_b(x)Rule
- Change of base
- log_b(x)=ln(x)/ln(b)Formula
- Base greater one
- Strictly increasing monotonic functionGrowth
- Base between zero one
- Strictly decreasing functionDecay
- Natural log
- Logarithm with base eBase
Coordinate Geometry
- Distance formula
- d=√((x₂−x₁)²+(y₂−y₁)²)Formula
- Midpoint formula
- Average x-coordinates and y-coordinatesFormula
- Parallel slopes
- Equal slopes for nonvertical parallel linesLines
- Perpendicular slopes
- Nonzero slopes: product equals minus oneLines
- Parabola vertex
- −b/(2a); substitute into quadraticVertex
- Circle equation
- (x−h)²+(y−k)²=r²; r>0Standard
- Vertical line exception
- Horizontal and vertical lines are perpendicularScope
Combinatorics and Probability
- Permutations
- n!/(n−k)!; ordered selectionsOrder
- Combinations
- n!/[k!(n−k)!]; unordered selectionsChoice
- Independent events
- Product of separate probabilitiesRule
- Mutually exclusive
- Probability of intersection is zeroRule
- Complement rule
- One minus event probabilityShortcut
- Conditional probability
- Joint probability ÷ given-event probabilityBayes
- Union probability
- Add probabilities, subtract intersectionUnion
- Conditional denominator
- Given event must have positive probabilityDomain
Explicit vs Implicit Meaning
Explicit Detail
- Directly in text
- Factual statement
- Literal reading
Implicit Meaning
- Logical inference
- Underlying implication
- Author unstated intent
Direct statement versus logical inference
Reading Comprehension Mechanics
- Explicit question
- Fact directly stated in textDirect
- Implicit question
- Requires sound logical deductionInference
- Author tone
- Neutral critical or supportive attitudeTone
- Main purpose
- Overarching argument of passageTheme
- Contextual vocabulary
- Meaning defined by surrounding sentenceContext
- Structural markers
- Contrast transition shifts argumentStructure
Economic Passage Concepts
- GDP growth
- Change in specified output measureMacro
- Fiscal deficit
- Government spend exceeds revenuesFiscal
- Inflation rate
- General price-level percentage changePrices
- Monetary policy
- Central-bank rates and other instrumentsPolicy
- Trade balance
- Exports minus import total valueTrade
- Supply demand shift
- Price equilibrium response to shockMicro
Editorial Pacing Aid
Average ninety seconds per item across the whole test
Three questions per screenVariable time by difficultyNo backward screen returnNo fixed screen timer
Percent vs Percentage Point
Percentage Change
- Relative growth rate
- Change over base
- Multiplied by hundred
Percentage Points
- Absolute difference
- Arithmetic subtraction
- Direct point difference
Relative change versus absolute difference
Numerical Reasoning Workflow
- Dense table presented→Identify requested variable first(Ignore extraneous columns)
- Percentage change asked→Divide change by original(Do not divide final)
- Comparing two percentages→Distinguish points from percent(Subtraction yields points)
- Answer options widely spaced→Round values for speed(Eliminate distant distractors)
- Overall time running low→Choose using remaining evidence(No separate screen timer)
- Zero options eliminable→Consider positive expected guessing(Five-option blind EV: +0.04)
Numerical Reasoning Essentials
- Percent change
- 100×(new−old)/old; old≠0Core
- Percentage points
- Arithmetic difference between two ratesTrap
- Ratio scaling
- Maintain equal fraction multipliersRatio
- Weighted average
- Σ(wᵢxᵢ)/Σwᵢ; nonzero denominatorMean
- Superfluous data
- Ignore unneeded table rows columnsFilter
- Estimation filter
- Round numbers to eliminate choicesSpeed
Critical Thinking Decision Criteria
True matches False conflicts Cannot Say lacks data
True: stated or implied supportFalse: direct contradictionCannot say: incomplete evidenceIgnore external facts
False vs Cannot Say
False
- Contradicts stated or implied facts
- Text entails its opposite
- Definitive conflict
Cannot Say
- Neither verdict follows
- Plausible but unproven
- Missing crucial information
Contradiction versus missing evidence
Critical Thinking Decision Flow
- Text entails the claim→Select True verdict(Explicit or implicit support)
- Text entails the opposite→Select False verdict(Explicit or implicit contradiction)
- Neither claim nor opposite follows→Select Cannot Say(Unmentioned may still be implied)
- Claim contains extreme absolutes→Verify text supports absolute(Often Cannot Say)
- Conditional premise affirmed→Conclude consequence validly(Modus ponens rule)
- Two options firmly eliminated→Choose among remaining options(Positive expected value)
Deductive Logic Mechanics
- Modus ponens
- Affirm premise conclude consequenceValid
- Modus tollens
- Deny consequence conclude negated premiseValid
- Affirming consequent
- Invalid fallacy cannot conclude premiseFallacy
- Denying antecedent
- Invalid fallacy consequence might holdFallacy
- Syllogism rule
- Conclusion must follow strictlyValidity
- Contrapositive
- Logically equivalent to original conditionalIdentity
Modus Ponens vs Tollens
Modus Ponens
- Affirm the antecedent
- Derive the consequent
- Valid conditional inference
Modus Tollens
- Deny the consequent
- Deny the antecedent
- Valid contrapositive logic
Forward affirmation versus backward negation
Three Option Critical Thinking
- True verdict
- Entailed by stated or implied factsTrue
- False verdict
- Passage entails the claim is falseFalse
- Cannot say
- Insufficient text facts to decideNeutral
- Extreme wording
- Check exact quantifier supportTrap
- Negative penalty
- Three-option critical errors: −0.33Scoring
- Prior knowledge trap
- Rely solely on provided factsRule
Common Traps
Cannot Say vs False
Neither verdict follows: cannot say ≠ False: explicit or implicit contradiction
Sequential Navigation Trap
Once submitted screen is locked ≠ Never plan to revisit questions
Blind Guessing vs Elimination
Penalty does not imply negative EV ≠ Five-option blind guess averages +0.04
Percent vs Percentage Point
Points subtract two rates directly ≠ Percent divides by baseline
Denominator Zero Exclusion
Rational inequalities must exclude zeros ≠ Denominator must remain nonzero
Prior Knowledge in Logic
External facts invalidate answers ≠ Base conclusions strictly on passage
Last Minute
- 1.Fifty questions seventy five minutes total
- 2.Forward navigation: cannot return backwards
- 3.Plus one correct zero blank
- 4.Minus point twenty wrong standard
- 5.Minus point thirty three wrong logic
- 6.Score under seventeen excludes applicant
- 7.No calculators allowed in exam
- 8.Guessing has positive expected points
- 9.Test counts fifty five percent
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