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SAT

Papers, samples and curriculum documents for this course.

Course units and learning goals

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme.

Lessons →Vocabulary practice →

RW.I · Information and Ideas

Identify central ideas and supporting details
Make inferences warranted by the text
Select textual evidence and interpret quantitative evidence

inference: A conclusion supported by stated information
evidence: Information relevant to a particular claim

RW.C · Craft and Structure

Determine words in context
Analyse text structure and purpose
Compare related texts and viewpoints

qualify: To limit or make a claim more precise
contrast: A relationship showing a difference

RW.E · Expression of Ideas

Select transitions expressing logical relationships
Synthesize notes for a stated rhetorical goal

transition: A word or phrase expressing a logical link
synthesis: Combining relevant information for a goal

RW.S · Standard English Conventions

Use sentence boundaries and punctuation
Maintain subject–verb agreement and pronoun clarity
Choose verb forms and modifiers fitting context

clause: A group of words with a subject and a verb
modifier: A phrase describing another word

M.A · Algebra

Solve linear equations and inequalities in one variable
Represent and solve two-variable linear systems
Interpret linear functions and parameters in context

slope: Change in output per unit change in input
intercept: The graph’s value when its input is zero

M.Q · Advanced Math

Transform equivalent polynomial and rational expressions
Solve nonlinear equations and systems
Interpret quadratic and exponential functions

root: An input for which a function equals zero
domain: The allowed input values

M.D · Problem-Solving and Data Analysis

Use ratios, rates and percentages
Interpret distributions and compare centre and spread
Calculate probabilities and assess sample claims

median: The middle value in an ordered data set
random sample: A sample selected using a chance process

M.G · Geometry and Trigonometry

Use area, volume and similarity
Apply right-triangle ratios and the Pythagorean theorem
Use circle equations, arcs and angle relationships

similarity: Equal angles and proportional corresponding lengths
radian: Angle measure defined by arc length divided by radius

ALG-parameters · Linear parameters, solution counts and inequalities

Solve and classify one-variable linear equations with parameters
Interpret two-variable linear equations as sets of ordered pairs
Interpret slope and intercept of a contextual linear function
Classify two-equation linear systems and check their intersections
Represent strict and inclusive inequalities in one or two variables

identity: An equation true for every value in its stated domain
boundary line: The equality separating allowed and excluded pairs in a linear inequality

AM-equivalence · Equivalent expressions and domain restrictions

Factor and expand expressions without changing their values
Simplify rational and radical expressions on the original domain
Use expression structure to identify zeros and coefficients

factor: An expression multiplied by another to form a product
domain restriction: A condition excluding values for which the original expression is undefined

AM-equations · Nonlinear equations and mixed systems

Solve quadratic, absolute-value, rational and radical equations
Reject candidate roots violating the original equation or domain
Find intersections of a line and a nonlinear curve

extraneous root: A transformed-equation solution that fails the original equation
intersection: An ordered pair satisfying both curve equations

AM-functions · Nonlinear functions, transformations and growth

Interpret zeros, vertices and parameters from useful function forms
Distinguish additive linear change from multiplicative exponential change
Transform a graph while tracking its input and output

growth factor: The multiplier applied in one stated interval
vertex form: A quadratic representation a(x-h)²+k exposing its vertex

PSDA-rates · Ratios, unit conversion and successive percentages

Use proportional relationships while preserving units
Convert rates and distinguish direct from inverse relationships
Calculate successive changes and percentage comparisons using the correct base

unit rate: A quantity per one unit of the comparison measure
percentage point: An absolute difference between two percentage values

PSDA-spread · Distributions, transformations and spread

Compare mean, median, range and standard deviation qualitatively
Predict the effect of adding or multiplying every data value
Read frequency information without confusing values and counts

standard deviation: A measure of distances of observations from their mean
frequency: The number of observations having a particular value or category

PSDA-models · Scatterplots, model residuals and predictions

Interpret slope and intercept of a fitted model in context
Calculate a residual and distinguish interpolation from extrapolation
Choose linear or exponential patterns from equal-step data

residual: Observed response minus the model’s predicted response
extrapolation: Prediction outside the range of observed inputs

PSDA-conditional · Probability from a table and a restricted group

Calculate event and complement probabilities from counts
Use the conditioning group as the denominator
Distinguish independence from disjointness

conditional probability: Probability calculated within a stated conditioning event
independent events: Events for which knowing one does not change the probability of the other

PSDA-inference · Sampling, margin of error and causal claims

Interpret a sample estimate and its stated margin of error
Distinguish random sampling from random assignment
Identify the population and causal scope supported by a study

margin of error: A stated sampling-uncertainty allowance around an estimate
random assignment: Allocation of participants to treatment groups by chance

GT-scale · Scale factors, angle relationships and triangles

Apply length, area and volume scaling to similar figures
Use parallel-line angles and triangle sums to find unknowns
Distinguish similarity from congruence and adequate information

similarity: Matching shape with proportional corresponding lengths
perpendicular height: The shortest perpendicular distance used with a chosen base

GT-circles · Circle equations, arcs and unit-circle trigonometry

Recover circle centre and radius by completing the square
Convert central angles and calculate arc length and sector area
Use tangent, inscribed-angle and unit-circle relationships

radian: An angle measure equal to arc length divided by radius
tangent: A line meeting a circle at a point and perpendicular to its radius there

RW-central · Central ideas, details and the scope of a claim

Distinguish the passage’s central claim from a supporting example
Interpret details without widening their stated scope
Choose an accurate summary covering the whole passage

central idea: The controlling point developed across a passage
scope: The people, objects or circumstances to which a claim applies

RW-evidence · Choose evidence for a precise textual or numerical claim

Choose a detail that directly supports or challenges a stated claim
Use a table’s labels, quantities and comparison base correctly
Separate relevance from evidence that discriminates between explanations

supporting evidence: Information bearing directly on the claim being evaluated
comparison base: The reference group or starting quantity used in a comparison

RW-inferences · Complete a passage with a warranted inference

Combine stated facts to draw a supported conclusion
Distinguish necessary support from a plausible outside explanation
Preserve uncertainty and avoid causal overstatement

warranted inference: A conclusion supported by the passage’s stated and implied information
unsupported assumption: A necessary extra claim not established by the available evidence

RW-words · Words in context: meaning, polarity and collocation

Infer a word’s intended meaning from its sentence and nearby logic
Use contrast and explanation to determine a missing word
Choose a word fitting syntax, degree and collocation

contextual meaning: A word’s intended sense within its surrounding sentence
collocation: A conventional combination of words fitting a particular use

RW-structure · Text structure, sentence function and rhetorical purpose

Identify how a passage develops its central point
Explain a sentence’s role in the larger argument
Distinguish a text’s purpose from its subject matter

rhetorical purpose: The action a text performs for its reader
qualification: A restriction that narrows or conditions a claim

RW-cross-text · Compare two texts without merging their claims

Identify each author’s claim and degree of certainty separately
Explain agreement, disagreement or qualification on the same issue
Predict one author’s response using their stated reasoning

cross-text relationship: How claims in two texts support, challenge or qualify one another
interpretation: The meaning or conclusion assigned to an observation

RW-synthesis · Use research notes for the requested rhetorical goal

Translate a rhetorical goal into a specific information requirement
Select relevant accurate details from notes
Combine notes without inventing a relationship or including irrelevant material

rhetorical goal: The specific communicative action requested for the response
synthesis: Combining selected information into a purposeful accurate statement

RW-transitions · Transitions: choose the logical relationship first

Identify contrast, consequence, example and continuation relationships
Choose a transition that preserves the argument’s logic
Distinguish logical linking from punctuation requirements

concession: Acknowledging a point while maintaining a contrasting conclusion
consequence: An outcome presented as following from a preceding fact or reason

RW-boundaries · Sentence boundaries, colons and nonessential information

Distinguish independent and dependent clauses before choosing punctuation
Join complete clauses without a comma splice
Place colons and paired punctuation according to sentence structure

independent clause: A subject–predicate structure that can stand as a sentence
comma splice: Joining two independent clauses with only a comma

RW-form · Agreement, verb forms, modifiers and logical parallelism

Match verbs and pronouns to their actual referents
Choose tense and verb form from the passage’s time relationship
Place modifiers and parallel elements so their logical subject is clear

antecedent: The noun or referent to which a pronoun points
parallel structure: Compatible grammatical forms expressing comparable ideas

Preparing for this qualification

Reading and Writing: 54 items, 64 minutes; Math: 44 items, 70 minutes. Two modules per section. Paper practice is nonadaptive and may have extra items (paper Test 11: 66 Reading/Writing, 54 Math). Use its own instructions and scoring ranges; use Bluebook for an adaptive rehearsal.

Teaching coverage still needed

All nineteen Math and ten Reading/Writing testing points have task-level crosswalks, dedicated teaching and original examples. Larger complete-form item variants and reviewed whole-form bank/crop integration remain; current adaptive rehearsal uses official Bluebook. Original tasks here are formative; paper mock scores cannot simulate digital routing.