MATH Q1. What is the slope formula between two points (x₁,y₁) and (x₂,y₂)?

Answer:

m = (y₂ − y₁) / (x₂ − x₁)

Rise over run — change in y divided by change in x.

Parallel lines: equal slopes. Perpendicular: slopes are negative reciprocals.

MATH Q2. What is the quadratic formula for ax² + bx + c = 0?

Answer:

x = (−b ± √(b²−4ac)) / 2a

The discriminant b²−4ac tells you: >0 two real roots, =0 one root, <0 no real roots.

Memorize this — it appears on almost every ACT Math section!

MATH Q3. What is the area formula for a circle with radius r?

Answer:

A = πr²

Circumference = 2πr

Diameter = 2r

Don’t confuse area (πr²) with circumference (2πr).

MATH Q4. What does SOHCAHTOA stand for in trigonometry?

Answer:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

Only applies to RIGHT triangles.

ACT loves right triangle trig — know all three ratios cold.

MATH Q5. What is the distance formula between points (x₁,y₁) and (x₂,y₂)?

Answer:

d = √[(x₂−x₁)² + (y₂−y₁)²]

Derived from the Pythagorean theorem: a²+b²=c².

Midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)

SCI Q6. What is the difference between a hypothesis and a theory in science?

Answer:

Hypothesis: a testable prediction before an experiment.

Theory: a well-supported explanation backed by extensive evidence.

A theory is NOT a guess — it is a proven framework.

ACT Science loves asking about experimental design and conclusions.

SCI Q7. What is the process by which plants make food using sunlight?

Answer:

Photosynthesis

6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂

Occurs in chloroplasts. Produces glucose and oxygen.

Contrast with cellular respiration which releases energy from glucose.

SCI Q8. What does a control group do in a scientific experiment?

Answer:

A control group receives NO treatment — it is the baseline for comparison.

Without a control, you cannot determine if the independent variable caused the results.

Independent variable = what you change. Dependent variable = what you measure.

SCI Q9. What is the difference between mitosis and meiosis?

Answer:

Mitosis: cell division producing 2 identical daughter cells (growth/repair).

Meiosis: cell division producing 4 genetically unique cells (sex cells/gametes).

Meiosis halves the chromosome number.

MItosis = Makes Identical. MEiosis = Makes Eggs/sperm.

SCI Q10. What is Newton’s Second Law of Motion?

Answer:

F = ma

Force equals mass times acceleration.

If mass doubles and force stays the same, acceleration halves.

Units: Force in Newtons (N), mass in kg, acceleration in m/s².

ENG Q11. When should you use a comma before a coordinating conjunction?

Answer:

Use a comma before FANBOYS (For, And, Nor, But, Or, Yet, So) when joining two INDEPENDENT clauses.

Example: I studied hard, but the test was difficult.

No comma needed if the second part is NOT a complete sentence.

ENG Q12. What is the difference between ‘its’ and ‘it’s’?

Answer:

its = possessive pronoun (belonging to it)

Example: The dog wagged its tail.

it’s = contraction of ‘it is’ or ‘it has’

Example: It’s raining outside.

ACT English tests this constantly. When in doubt, expand: say ‘it is’ aloud.

ENG Q13. What is subject-verb agreement?

Answer:

A singular subject takes a singular verb.

A plural subject takes a plural verb.

Trick: Ignore phrases between subject and verb.

Example: ‘The box of apples IS on the table.’ (box = singular)

Watch for: each, every, either, neither — all take SINGULAR verbs.

ENG Q14. What is a dangling modifier?

Answer:

A modifier that does not logically connect to the subject of the sentence.

Wrong: ‘Running down the street, the rain soaked me.’

Right: ‘Running down the street, I got soaked by the rain.’

The subject right after the comma must be the one doing the action.

ENG Q15. When do you use a semicolon vs. a comma?

Answer:

Semicolon (;): joins two independent clauses WITHOUT a conjunction.

Example: I studied; I passed.

Comma: joins clauses WITH a conjunction OR separates items in a list.

A semicolon = a soft period. Both sides must be complete sentences.

READ Q16. What is the ‘main idea’ of a passage?

Answer:

The central point the author is making — what the WHOLE passage is about.

Not a detail. Not an example. The overarching argument or theme.

Ask: What is the author’s PRIMARY message?

Wrong answers are often too specific (a detail) or too broad (not supported).

READ Q17. What does ‘inference’ mean in ACT Reading?

Answer:

An inference is a conclusion you draw from evidence in the passage — something implied but NOT directly stated.

The answer must be supported by the text. No outside knowledge needed.

Look for ‘most likely suggests,’ ‘implies,’ ‘can be inferred’ — these signal inference questions.

READ Q18. What is the author’s ‘tone’ in a passage?

Answer:

Tone = the author’s attitude toward the subject.

Common tones: admiring, critical, neutral, melancholic, celebratory, skeptical, nostalgic.

Identify tone from word choice (diction).

Look at adjectives and verbs — they carry the emotional weight of tone.

READ Q19. What is a ‘vocabulary in context’ question?

Answer:

It asks what a word means AS USED in the passage — not its dictionary definition.

Strategy: Cover the word, read the sentence, predict your own word, then match to options.

The correct answer fits the passage’s meaning — not just the word’s common meaning.

READ Q20. What is the purpose of a ‘detail’ question in ACT Reading?

Answer:

Detail questions ask you to locate specific information explicitly stated in the passage.

Strategy: Use line references or keywords to find the exact location. Do NOT rely on memory.

The answer is always directly in the text — no inference needed for detail questions.