ACT · ACT

ACT

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 →

E.P · English: purpose, organisation and style

Determine relevance and rhetorical purpose
Organise sentences and paragraphs
Choose precise, concise language consistent with tone

relevance: How information serves the stated purpose
register: The style appropriate to a situation

E.C · English: conventions and punctuation

Control clause boundaries and punctuation
Maintain agreement, tense and pronoun reference
Place modifiers and parallel structures correctly

parallelism: Matching grammatical forms in a series
agreement: Matching grammatical number or person

M · Mathematics: models, functions and higher maths

Apply number and quantity, algebra and functions
Use coordinate and Euclidean geometry and trigonometry
Interpret statistics, probability and essential-skill models

composition: Applying one function to the output of another
independent: One outcome does not change the other’s probability

R · Reading: details, structure and integration

Find key ideas, details and warranted inferences
Analyse author craft, viewpoint and structure
Compare passages and integrate textual or visual evidence

viewpoint: The position from which something is described
tone: An attitude conveyed by wording

S · Optional Science: data, investigations and models

Interpret data and graphical relationships
Evaluate experimental methods and variables
Compare scientific arguments and predictions against evidence

control variable: A factor kept the same in a comparison
interpolation: Estimating between observed values

W · Optional Writing: perspectives and argument

Analyse multiple perspectives and develop a position
Support reasoning with relevant examples
Organise and express an argument clearly

perspective: A way of interpreting an issue
counterargument: A reason challenging your position

N-real-complex · Real numbers, rational powers and complex arithmetic

Distinguish rational and irrational numbers without assuming their sums retain type
Apply exponent and radical rules on the permitted domain
Calculate with complex numbers using i²=-1 and conjugates

conjugate: The number a-bi paired with a+bi
rational exponent: An exponent m/n interpreted using powers and roots on the stated domain

N-vectors-matrices · Vectors and matrices as organised quantitative models

Add and scale vectors component by component
Multiply a matrix and vector with matching dimensions
Interpret entries and units in a quantitative model

dot product: The sum of products of corresponding components
matrix dimension: The ordered number of rows and columns

A-polynomial · Linear, quadratic and polynomial relationships

Choose equivalent expanded, factored or vertex forms for a task
Solve linear and polynomial equations using structure
Determine quadratic inequality regions from signs rather than roots alone

sign interval: A region between roots on which an expression keeps one sign
polynomial degree: The highest variable power with a nonzero coefficient after simplification

A-radical-systems · Rational equations, radical branches and systems

Record denominator and radical restrictions before solving
Check transformed-equation candidates in the original
Find and interpret simultaneous solutions or allowed regions

extraneous solution: A transformed-equation root that does not satisfy the source equation
feasible region: The set satisfying all simultaneous inequality conditions

F-compose · Functions, composition, transformations and inverses

Evaluate and convert between function rules, tables and graphs
Track input order and domain through composition
Find an inverse after choosing a one-to-one domain

composition: Applying an inner function before an outer function
one-to-one: A function in which distinct allowed inputs have distinct outputs

F-series-logs · Sequences, finite sums, exponentials and logarithms

Distinguish arithmetic difference from geometric ratio
Find a term or finite sum while keeping indexing consistent
Convert logarithmic equations to exponential form on the valid domain

common ratio: The fixed multiplier between consecutive geometric terms
logarithm: The exponent needed to obtain an argument from a stated base

F-trigonometry · Trigonometric graphs, identities and general triangles

Interpret amplitude, period and vertical shift in a sinusoidal rule
Use unit-circle signs and basic identities
Choose a sine, cosine or area relation for a general triangle

amplitude: The distance from a sinusoid’s midline to a peak
included angle: The angle between the two specified sides

G-plane · Plane transformations, coordinate reasoning and proof

Transform coordinates while distinguishing rigid motions from dilation
Use distance, midpoint and slope as geometric evidence
Use valid congruence and angle relationships rather than a diagram’s appearance

rigid motion: A transformation preserving distances and angles
perpendicular bisector: The perpendicular line through a segment’s midpoint

G-conics · Conics, circle relationships and geometric measurement

Identify and interpret standard circle, ellipse, parabola and hyperbola forms
Use circle angle, tangent and secant relationships under their conditions
Calculate area, surface area or volume with the correct dimension and units

semiaxis: Half of an ellipse’s full principal-axis length
secant: A line crossing a circle at two points

S-data · Data displays, normal distributions and association

Read centre, spread and shape from labelled data displays
Interpret a normal model using mean and standard deviation
Distinguish two-variable association from causal evidence

normal distribution: A symmetric bell-shaped model determined by a mean and standard deviation
residual: Observed response minus the model’s predicted response

S-inference-probability · Sampling inference, expected value and counting

Interpret a population estimate and simulation evidence without claiming proof
Calculate conditional, compound and expected-value quantities
Choose permutations or combinations according to whether order matters

expected value: A probability-weighted average of possible outcomes
combination: An unordered selection of distinct objects

IES-models · Essential skills in a multi-step practical model

Build a model connecting quantities, rates and geometric measures
Interpret parameters and test the model’s assumptions
Evaluate predictions and adjust a parameter using new evidence

model parameter: A quantity setting a rule’s rate, scale or fixed contribution
model assumption: A condition under which the representation is intended to work

E-purpose · English: purpose, focus and argumentative support

Infer a paragraph’s purpose from the passage before judging an addition
Select evidence that directly supports the writer’s particular claim
Evaluate a counterclaim without mistaking relevance for agreement

relevance: A detail’s direct contribution to the stated purpose or claim
counterclaim: A competing claim that an argument can acknowledge and address

E-cohesion · English: paragraph order, cohesion and introductions

Order sentences according to references and logical dependence
Choose transitions expressing the relationship actually present
Write an introduction or conclusion fitting the whole passage

cohesion: Connections that let a reader follow relationships between sentences
antecedent: The earlier referent to which a pronoun or referring expression points

E-language · English: precision, concision and consistent style

Remove redundancy while retaining necessary qualifications
Select precise words suited to the meaning in context
Maintain a passage’s tone and level of formality

redundancy: Unnecessary repetition of meaning
register: A level and style of language suited to an audience and purpose

E-conventions · English: sentence formation, agreement and punctuation

Distinguish complete clauses, fragments and comma splices
Locate the grammatical subject despite intervening phrases
Punctuate boundaries and modifiers according to structure

independent clause: A subject–verb group that can stand as a complete sentence
dangling modifier: A modifier whose intended subject is absent or wrongly attached

R-details · Reading: explicit detail, inference and relationships

Separate directly stated details from supported inferences
Track causes, contrasts and chronological relationships
Reject conclusions requiring information outside the passage

inference: A conclusion supported by textual evidence rather than stated verbatim
causal relationship: A supported connection in which one condition contributes to another

R-craft · Reading: contextual meaning, structure and point of view

Infer a word’s local sense from surrounding evidence
Explain how a passage’s structure shapes its effect
Distinguish narrator perspective, quoted views and author purpose

connotation: An association or emotional colouring beyond a word’s basic reference
narrative perspective: The position from which events and knowledge are presented

R-integration · Reading: arguments, paired texts and graphic evidence

Evaluate whether evidence supports a specific argument
Compare agreement and disagreement across paired texts
Integrate a graph or table without replacing the passage’s claim

synthesis: Connecting ideas across sources while preserving their distinct claims
denominator: The reference total used when interpreting a proportion

S-investigation · Science: research summaries, controls and engineering tests

Identify independent, dependent and controlled variables across experiments
Choose a follow-up that isolates the proposed explanation
Apply engineering criteria and constraints to a design comparison

controlled variable: A relevant condition held fixed to support a fair comparison
constraint: A required limit that an acceptable design must satisfy

S-models · Science: conflicting viewpoints and evidence that separates models

Represent each model’s assumptions and predictions separately
Select observations that discriminate between competing explanations
Evaluate a model or design without claiming more than the evidence warrants

discriminating test: A test under conditions where competing models predict different outcomes
model assumption: A condition or relationship taken as given when deriving predictions

S-data-representation · Science: data representation and defensible extrapolation

Read values with correct axes, units and conditions
Translate a table into a trend and interpolate within a measured interval
Evaluate an extrapolation against the model’s assumptions

interpolation: An estimate between observed input values using an explicit assumption
extrapolation: An estimate beyond the measured range that relies on model extension

Preparing for this qualification

English 50/35 min; Math 45/50 min; Reading 36/40 min. Science optional 40/40 min; Writing optional 1/40 min. Composite uses English, Math and Reading. Official keys exclude field-test items from raw-score conversion.

Teaching coverage still needed

All 48 Math, 7 English, 8 Reading and 11 Science skill areas have explicit teaching crosswalks. Original targeted passage/data cases are not full-length forms. Larger complete-form variants and broader sustained passage practice remain. Native passage parsing applies to English/Reading/Science; Math is standalone, with field-test exclusions required.