R&W: Craft and Structure
28%of exam
Words in ContextText StructureAuthor PurposeCross-Text Connections
R&W: Information and Ideas
26%of exam
Central IdeasTextual EvidenceQuantitative EvidenceInferences
R&W: Standard English Conventions
26%of exam
Clause BoundariesVerb AgreementModifier PlacementPossessives
R&W: Expression of Ideas
20%of exam
Rhetorical SynthesisTransitionsRhetorical GoalsLogical Relationships
Math: Algebra
42.5%of exam
Linear EquationsLinear FunctionsLinear SystemsLinear Inequalities
Math: Advanced Math
20%of exam
Equivalent ExpressionsQuadratic EquationsNonlinear FunctionsExponential Models
Math: Problem-Solving and Data Analysis
25%of exam
Ratios and RatesPercentagesData DistributionsConditional Probability
Math: Geometry
12.5%of exam
Area and VolumeLines and AnglesSimilar FiguresRight Triangles
Quick Facts
- Exam
- Digital PSAT 8/9
- Administrator
- College Board
- Total Questions
- 98 items across 4 modules
- Total Time
- 134 minutes total testing
- Score Scale
- 240-1440 total, 120-720 per section
- Adaptive Model
- Two-stage adaptive per section
- Guessing Rule
- No penalty; answer every question
- Calculator
- Permitted all Math; Desmos built-in
- Weight Basis
- Approximate shares within each section
PSAT 8/9 vs PSAT/NMSQT
PSAT 8/9
- For 8th and 9th graders
- Scored 240 to 1440 scale
- Not for National Merit
PSAT/NMSQT
- For 10th and 11th graders
- Scored 320 to 1520 scale
- National Merit eligibility follows program rules
Same standard timing; different score ranges
Reading Question Strategy Picker
- Blank completes meaning in context→Predict from contrast or cause
- Underlined sentence function asked→Check role relative to neighbors
- Text 2 responds to Text 1→Summarize both, test agreement level
- Asked for author's overall rhetorical purpose→Name the action supported by text
Section Logistics and R&W Domain Shares
- R&W Timing
- 64 min, two 32-min modules54 items
- Math Timing
- 70 min, two 35-min modules44 items
- Pretest Items
- 2 unscored items per module
- Craft & Structure
- 13-15 R&W operational items~28% R&W
- Information & Ideas
- 12-14 R&W operational items~26% R&W
- English Conventions
- 11-15 R&W operational items~26% R&W
- Expression of Ideas
- 8-12 R&W operational items~20% R&W
- Math SPR Share
- About 25% student-produced responses
Craft, Structure and Context
- Words in Context
- Match clue words and tone
- Secondary Meaning
- Choose meaning fitting this context
- Main Purpose
- Check author's rhetorical action verb
- Sentence Function
- Role played inside whole paragraph
- Qualify Claim
- Add condition or boundary limit
Choose the Evidence and Inference Method
- Main idea across whole short text→Choose passage-wide claim preserving qualifiers
- Quotation offered to support a claim→Match quote to required relationship
- Table or graph supports a claim→Check values and relevance to claim
- Blank asks for a supported inference→Use stated evidence and cautious implication
Ideas, Evidence and Inferences
- Central Idea
- Covers whole text, no extremes
- Quantitative Evidence
- True data plus supports claim
- Logical Inference
- Choose inference best supported by text
- Textual Evidence
- Quote must support the exact claim
Coordinating Conjunctions (FANBOYS)
For, And, Nor, But, Or, Yet, So join clauses
Comma + FANBOYS = legal joinComma alone = comma spliceHowever is not FANBOYS
Essential vs Nonessential Clauses
Essential Clause
- Needed to identify the noun
- Often begins with 'that'
- No commas enclosing the essential clause
Nonessential Clause
- Removable extra description
- Often begins with 'which'
- Mid-sentence: matching enclosing punctuation
Use matching punctuation for one aside
Clause Boundary Punctuation Picker
- Two full clauses, no conjunction→Period or semicolon(Never comma alone)
- Two full clauses with FANBOYS→Comma before coordinating conjunction
- Complete clause introduces explanation or list→Colon or single dash
- Extra phrase removable mid-sentence→Matching commas or matching dashes
- However separates two independent clauses→Semicolon or period before however(Comma follows introductory however)
Clause Boundaries & Punctuation
- Period or Semicolon
- Separates two complete independent clauses
- Comma + FANBOYS
- Comma plus conjunction joins independent clauses
- Comma Splice
- Two full clauses, comma only
- Conjunctive Adverb
- Between clauses: semicolon or period first
- Colon Rule
- Full independent clause must precede
- Nonessential Clause
- Mid-sentence: matching commas, dashes, parentheses
- Essential Clause
- Identifies referent; no surrounding aside punctuation
Grammar, Modifiers and Possessives
- Subject-Verb Match
- Ignore intervening prepositional phrases
- Dangling Modifier
- Subject must perform introductory participial action
- Possessive Pronouns
- Its, their, whose take no apostrophe
- Contractions
- It's, they're, who's contain verbs
- Parallel Structure
- Use corresponding grammatical forms in lists
Expression of Ideas Transition Picker
- Second sentence opposes first claim→However or by contrast
- Outcome occurs despite obstacle→Nevertheless or still
- Reason supports a conclusion or outcome→Therefore, consequently, or thus
- Second sentence gives specific case→For instance or specifically
- Second sentence rephrases earlier idea→In other words or that is
Transitions and Rhetorical Goals
- Contrast Transition
- However, nevertheless, by contrast, still
- Result or Inference
- Therefore links supported conclusion or outcome
- Rhetorical Synthesis
- Satisfy prompt's exact goal first
- Restatement
- In other words clarifies earlier meaning
Bluebook SPR Entry Rules
SPR: five positive characters, six negative; fractions or decimals
Fractions or decimals; avoid mixed numbers2/3: .6666, .6667, 0.666, 0.667Omit percent signs, dollars and commas
Evaluating f(4) vs Solving f(x) = 4
Find f(4)
- Input x equals 4
- Plug 4 into formula
- Read y at x = 4
Solve f(x) = 4
- Output y equals 4
- Set expression equal to 4
- Read x where y = 4
Given input x vs output y
Math Solution Strategy Picker
- One variable already isolated→Solve system by substitution
- Linear combination directly produces requested expression→Combine equations, scaling first if needed
- System has messy decimals→Graph both lines in Desmos
- Two genuine lines: count their intersections→Compare equations, including vertical-line cases
Linear Equations, Slope & Systems
- Slope Formula
- Δy/Δx when Δx ≠ 0m
- Slope-Intercept
- Slope m and y-intercept by = mx + b
- Standard Form
- B≠0: slope −A/BAx + By = C
- Parallel Lines
- Nonvertical: equal slopes, different intercepts
- Perpendicular Lines
- Nonvertical: m₁m₂ = −1
- Zero Solutions
- Distinct parallel genuine lines
- Infinite Solutions
- Both equations describe the same line
- Inequality Flip
- Reverse sign when dividing negative
- Vertical and Horizontal
- Undefined slope versus slope zero
- Perpendicular Special Case
- Vertical and horizontal lines are perpendicular
Discriminant Real Solutions Rule
Quadratic a ≠ 0: D counts distinct real roots
D > 0 gives 2 solutionsD = 0 gives 1 solutionD < 0 gives 0 real
Linear vs Exponential Models
Linear Model
- Constant amount added per step
- Constant slope m
- Graph forms straight line
Exponential Model
- Constant multiplier factor per step
- Percent rate growth or decay
- Positive nonconstant exponential curves
Constant difference versus positive multiplicative factor
Choose a Nonlinear Model Method
- Need real roots of a quadratic→Factor or use quadratic formula(Quadratic coefficient a≠0)
- Asked for unrestricted quadratic maximum/minimum→Find vertex, checking sign of a
- Equal intervals show constant positive multiplier→Use positive-base exponential model
- Need equivalent nonlinear expressions→Apply identities; preserve original domain
Quadratics & Exponential Functions
- Vertex Form
- For a ≠ 0: vertex (h,k)a(x-h)²+k
- Axis of Symmetry
- a≠0: x = −b/(2a)
- Discriminant
- For quadratic a ≠ 0: b²−4acD
- Sign of D
- Real roots: positive2, zero1, negative0
- Sum of Roots
- Quadratic a ≠ 0: −b/a
- Product of Roots
- Quadratic a ≠ 0: c/a
- Exponential Growth
- Positive initial quantity; growth factor >1
- Exponential Decay
- Positive quantity; 0<factor<1
Mean vs Median With Outliers
Mean
- Sum divided by count n
- Pulled toward extreme outliers
- Useful center when mean fits context
Median
- Middle value when sorted
- Resistant to extreme outliers
- Often useful with skew or outliers
Resistance does not guarantee unchanged median
Choose the Probability Denominator
- Question conditions on a named group→Positive total for that group
- Question asks share of entire population→Grand total of that population
- Question compares rates in two groups→Compute each group's own denominator
- Conditioning group contains zero observations→Conditional probability is undefined
Ratios, Percents & Data Analysis
- Part-to-Whole
- Exhaustive disjoint groups: a/(a+b)
- Average Speed
- Total distance over total time
- Original Before %
- Divide new value by factor
- Successive Percents
- Multiply change factors together
- Outlier Effect
- Median resists magnitude; can still change
- Residual
- Actual y minus predicted y
- Conditional P
- Given group must have positive total
Part-to-Part vs Part-to-Whole Ratio
Part-to-Part
- Compares subgroup A to B
- Written as ratio a to b
Part-to-Whole
- Compares subgroup A to total
- Divide a by a plus b
Summing parts requires disjoint exhaustive groups
Geometric Scale Factor Powers
Similar figures: lengths k, areas k², volumes k³
Perimeter or side times kSurface or area times k²3D prism volume times k³
Geometry, Angles & Right Triangles
- Triangle Area
- Half base times perpendicular height
- Prism or Cylinder Volume
- Base area times perpendicular heightV = Bh
- Scale Factor k
- Similar figures: area k², volume k³
- Triangle Angles
- Interior angles sum to 180°
- Exterior Angle
- Equals sum of remote interiors
- Pythagorean Theorem
- Right triangle: legs a²+b² = c²
- Pythagorean Triples
- Common sets 3-4-5 and 5-12-13
Common Traps
However Between Independent Clauses
Comma alone cannot join independent clauses ≠ Semicolon or period can separate them
Possessive Pronoun vs Contraction
Its and whose express possession ≠ It's and who's: is or has
Reverse Percent Recovery Trap
Divide by nonzero original change factor ≠ Equal percentage increase need not restore
Vertex Form Sign Trap
Inside x minus h flips sign ≠ Outside plus k keeps sign
True Data Wrong Claim Trap
Graph numbers can be accurate ≠ Still wrong if claim unsupported
Prepositional Phrase Verb Trap
Cross out 'of the samples' ≠ Match verb to head noun
Last Minute
- 1.98 questions in 134 total minutes
- 2.Module 1 routes Module 2 difficulty
- 3.No guessing penalty; answer every item
- 4.Read Rhetorical Synthesis goal before notes
- 5.Colon requires complete clause before it
- 6.Use matching punctuation around one aside
- 7.Flip inequality sign dividing by negative
- 8.Use Desmos intersections for tough systems
- 9.Enter improper fractions, never mixed numbers
- 10.Residual equals actual minus predicted y
- 11.Median resists extremes; not necessarily unchanged
- 12.Check units and axis labels first
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