MATH Q1. What is the formula for the circumference and area of a circle, and how are they different?

Answer:

Circumference (perimeter) = 2πr or πd

Area = πr²

Circumference measures the distance AROUND the circle.

Area measures the space INSIDE the circle.

Example: r=5 → C=31.4, A=78.5

💡 ACT often mixes up radius and diameter in problems — read carefully. d = 2r always.

MATH Q2. What is a function, and what does f(x) notation mean?

Answer:

A function assigns exactly ONE output to each input.

f(x) means ‘the value of function f at input x.’

Example: If f(x) = 2x + 3, then f(4) = 2(4)+3 = 11

Vertical line test: if a vertical line crosses a graph twice → NOT a function.

💡 Composite functions: f(g(x)) means plug g(x) into f. Work from inside out.

MATH Q3. What are the properties of parallel lines cut by a transversal?

Answer:

When a transversal crosses parallel lines:

• Corresponding angles = equal

• Alternate interior angles = equal

• Alternate exterior angles = equal

• Co-interior (same-side) angles = supplementary (add to 180°)

All acute angles are equal. All obtuse angles are equal.

💡 If you see two parallel lines with a transversal on ACT — only 2 angle sizes exist.

MATH Q4. How do you calculate percentage increase or decrease?

Answer:

% Change = [(New − Old) / Old] × 100

Increase: New > Old → positive %

Decrease: New < Old → negative %

Example: Price goes from $80 to $100

% increase = (20/80)×100 = 25%

💡 Always divide by the ORIGINAL (old) value — not the new one. Common ACT mistake.

MATH Q5. What is the standard form of a circle equation and what does each part mean?

Answer:

(x − h)² + (y − k)² = r²

(h, k) = center of the circle

r = radius

Example: (x−3)² + (y+2)² = 25

Center = (3, −2), Radius = 5

Note: (y+2) means k = −2

💡 If the equation is expanded, complete the square to find center and radius.

SCI Q6. What is the difference between a food chain and a food web?

Answer:

Food chain: a single linear sequence showing who eats whom.

Producer → Primary consumer → Secondary consumer → Tertiary consumer

Food web: multiple interconnected food chains showing the full complexity of an ecosystem.

Energy decreases ~90% at each level (10% rule).

💡 Producers = plants (make own food). Consumers = animals. Decomposers = fungi/bacteria.

SCI Q7. What is the difference between renewable and non-renewable energy sources?

• ACT — Official test information

Answer:

Renewable: naturally replenished — solar, wind, hydro, geothermal, biomass.

Advantage: sustainable, low emissions.

Non-renewable: finite supply — coal, oil, natural gas, nuclear (uranium).

Advantage: high energy density, reliable.

ACT may ask about environmental trade-offs.

💡 Nuclear energy uses uranium (non-renewable) but produces no direct CO₂ emissions.

SCI Q8. What is the difference between a series and parallel circuit?

Answer:

Series circuit: components connected in ONE loop.

• Same current through all components

• If one fails, all fail

• Voltage splits across components

Parallel circuit: components in SEPARATE branches.

• Voltage same across all branches

• If one fails, others continue

• Current splits

💡 Household wiring = parallel (so one light going out doesn’t cut all power).

SCI Q9. What is the difference between prokaryotic and eukaryotic cells?

Answer:

Prokaryotic: no membrane-bound nucleus, no organelles.

Examples: bacteria, archaea.

Smaller and simpler.

Eukaryotic: has a true nucleus and membrane-bound organelles.

Examples: plant, animal, fungal cells.

Larger and more complex.

💡 Pro = before, karyon = nucleus. Prokaryotes came first in evolution.

SCI Q10. What is the greenhouse effect and how does it relate to climate change?

Answer:

Natural greenhouse effect: CO₂, water vapor, and methane trap heat from the sun, keeping Earth warm enough for life.

Enhanced greenhouse effect: excess CO₂ from burning fossil fuels traps MORE heat → global temperatures rise → climate change.

Key gases: CO₂, CH₄, N₂O, water vapor.

💡 ACT Science may show temperature/CO₂ graphs — rising CO₂ correlates with rising temperatures.

ENG Q11. What is the difference between a phrase and a clause?

Answer:

Phrase: a group of words WITHOUT a subject + verb.

Examples: ‘in the morning,’ ‘running fast,’ ‘the tall man’

Clause: a group of words WITH a subject + verb.

Independent clause: complete thought (can stand alone).

Dependent clause: incomplete thought (cannot stand alone).

💡 A sentence must have at least one independent clause. Dependent clauses alone = fragments.

ENG Q12. What are transitional words and how are they tested on the ACT?

Answer:

Transitions show relationships between ideas:

• Addition: furthermore, moreover, also

• Contrast: however, nevertheless, on the other hand

• Cause/Effect: therefore, consequently, as a result

• Example: for instance, specifically

• Sequence: first, then, finally

ACT asks: which transition best fits the logical relationship?

💡 Read the sentence BEFORE and AFTER the blank — identify the relationship first, then pick.

ENG Q13. What is the difference between ‘lay’ and ‘lie’?

Answer:

Lay: to place something (needs an object)

Present: lay | Past: laid

Example: I lay the book on the table.

Lie: to recline (no object needed)

Present: lie | Past: lay

Example: I lie down. Yesterday I lay down.

Trick: Lay = place. Lie = recline.

💡 Past tense of ‘lie’ is ‘lay’ — this is the most confusing part. Memorize it!

ENG Q14. What is a sentence fragment and how do you identify one?

Answer:

A fragment is an incomplete sentence — missing a subject, verb, or complete thought.

Examples of fragments:

• ‘Running through the park.’ (no subject)

• ‘Because she was tired.’ (dependent clause only)

• ‘The tall, mysterious stranger.’ (no verb)

Fix: add missing element or attach to another sentence.

💡 On ACT, fragments often appear as answer choices — eliminate any that can’t stand alone.

ENG Q15. What does ‘relevance’ mean in ACT English writing strategy questions?

Answer:

Relevance = does the sentence/detail support the paragraph’s main idea?

ACT asks: Should this sentence be added/kept/deleted?

If the sentence:

• Supports the main idea → keep/add it

• Introduces off-topic information → delete it

• Repeats what was already said → delete it (redundant)

💡 Always identify the paragraph’s PURPOSE first — then judge whether the detail serves that purpose.

READ Q16. What is the difference between ‘tone’ and ‘mood’ in a literary passage?

Answer:

Tone: the AUTHOR’S attitude toward the subject.

Example: The author writes with admiration about jazz.

Mood: the READER’S emotional response to the passage.

Example: The passage creates a melancholic mood.

Tone is created by the author. Mood is felt by the reader.

💡 ACT usually asks about TONE (author’s attitude) — identify through word choice and diction.

READ Q17. What is a ‘counterargument’ and why do authors include one?

Answer:

A counterargument presents the opposing view to the author’s main argument.

Authors include counterarguments to:

• Show awareness of other perspectives

• Strengthen their own argument by refuting the opposition

• Appear fair and credible to readers

ACT may ask: why does the author mention this opposing view?

💡 After a counterargument, look for ‘however,’ ‘but,’ ‘nevertheless’ — the author’s rebuttal follows.

READ Q18. What is the difference between ‘summarizing’ and ‘paraphrasing’ a passage?

Answer:

Summary: a brief overview of the MAIN points — shorter than the original, captures the big picture.

Paraphrase: restating specific content in your OWN words — same length, different wording.

ACT main idea questions require summarizing.

ACT detail questions require paraphrasing specific lines.

💡 Wrong answer traps: too broad (not supported), too narrow (just one detail), or distorted meaning.

READ Q19. What is ‘evidence-based reasoning’ in ACT Reading science passages?

Answer:

Evidence-based reasoning = conclusions must be supported by data or observations in the passage.

ACT tests whether you can:

• Identify what the data actually shows

• Distinguish between what IS stated vs. what is assumed

• Recognize when a conclusion goes beyond the evidence

Never bring in outside knowledge.

💡 ‘The data suggests’ ≠ ‘the data proves.’ ACT rewards careful, limited conclusions.

READ Q20. What is the best strategy for eliminating wrong answer choices on ACT Reading?

Answer:

4 types of wrong answers to eliminate:

1. Too extreme: uses ‘always,’ ‘never,’ ‘only,’ ‘all’

2. Out of scope: introduces ideas not in the passage

3. Opposite: says the reverse of what the passage states

4. Too narrow: focuses on one detail, misses the big picture

The correct answer is always supported by the text.

💡 If you can’t find evidence in the passage for an answer — it’s wrong. Period.