ACT Mastery: English, Math, Reading & Science · Öffentliche Lernkarten

Frage 1: What is the standard timing and section breakdown for the ACT exam?

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English (45 min, 75 q), Math (60 min, 60 q), Reading (35 min, 40 q), and Science (35 min, 40 q). Writing (40 min) is optional.

Total testing time without Writing is 2 hours 55 minutes. Pacing is fast: Math allows 1 minute per question, Science under 53 seconds per question.

Frage 2: In ACT English, how do you punctuate introductory clauses before an independent clause?

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Use a comma immediately after the introductory dependent clause: 'After the storm passed, the crew inspected the roof.'

Introductory prepositional or adverbial phrases setting up the sentence must be separated from the subject and main verb by a comma.

Frage 3: In ACT Science, what distinguishes an independent variable from a dependent variable?

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The independent variable is manipulated by the researcher (x-axis); the dependent variable is the measured outcome (y-axis).

Controlled variables are held constant across experimental trials to prevent confounding of results.

Frage 4: What is the formula for the $n$ -th term of an arithmetic sequence, and what do the symbols represent?

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$a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term and $d$ is the common difference.

The sum of the first $n$ terms is $S_n = \frac{n}{2}(a_1 + a_n)$ .

Frage 5: What is the formula for the $n$ -th term of a geometric sequence, and the sum of an infinite geometric series ( $|r| < 1$ )?

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$a_n = a_1 \cdot r^{n-1}$ ; Infinite sum $S_\infty = \frac{a_1}{1 - r}$ for $|r| < 1$ .

If $|r| \geq 1$ , the infinite series diverges and has no finite sum.

Frage 6: How is the determinant of a $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ calculated?

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$\det = ad - bc$ .

If the determinant equals zero ( $ad - bc = 0$ ), the matrix has no inverse and the corresponding linear system has no unique solution.

Frage 7: What are the trigonometric reciprocal identities for $\csc(\theta)$ , $\sec(\theta)$ , and $\cot(\theta)$ ?

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$\csc(\theta) = \frac{1}{\sin(\theta)}$ , $\sec(\theta) = \frac{1}{\cos(\theta)}$ , $\cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)}$ .

Remember the SOH CAH TOA framework extended to their reciprocals.

Frage 8: In ACT English, when is a colon (:) used correctly?

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A colon must be preceded by a complete independent clause to introduce a list, quotation, explanation, or dramatic appositive.

Incorrect: 'My favorite subjects are: math and physics.' Correct: 'She had one clear passion: astrophysics.'

Frage 9: How do you identify redundancy/conciseness errors on ACT English?

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Choose the most concise option that preserves grammatical accuracy and intended meaning without repeating synonyms.

Phrases like 'annual anniversary', 'past history', or 'sum total' repeat ideas unnecessarily; prefer shorter phrasing.

Frage 10: In ACT Science conflicting viewpoints passages, how should one approach comparing two student or scientist hypotheses?

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Identify the shared common baseline, then isolate the exact physical mechanism or variable where their assertions diverge.

Create mental or margin notes: What does Scientist 1 say causes X? What does Scientist 2 say causes X?

Frage 11: What is the expected value $E(X)$ of a discrete random variable with outcomes $x_i$ and probabilities $P(x_i)$ ?

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$E(X) = \sum x_i \cdot P(x_i) = x_1 P(x_1) + x_2 P(x_2) + \dots + x_k P(x_k)$ .

Expected value represents the long-term average outcome of a random process repeated many times.

Frage 12: What is the distance formula between two Cartesian points $(x_1, y_1)$ and $(x_2, y_2)$ ?

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$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

The distance formula is a direct algebraic application of the Pythagorean theorem $a^2 + b^2 = c^2$ .

Frage 13: What is the midpoint formula for the segment connecting $(x_1, y_1)$ and $(x_2, y_2)$ ?

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$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ .

The coordinates of the midpoint are the simple arithmetic averages of the endpoints' coordinates.

Frage 14: What is the law of sines for any triangle with sides $a, b, c$ and opposite angles $A, B, C$ ?

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$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$ .

Use the Law of Sines when you know two angles and one side (AAS/ASA) or two sides and a non-included angle (SSA).

Frage 15: What is the law of cosines for a triangle with sides $a, b, c$ and included angle $C$ ?

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$c^2 = a^2 + b^2 - 2ab\cos(C)$ .

Use the Law of Cosines when two sides and the included angle (SAS) are known, or when all three sides (SSS) are known.

Frage 16: What is the relationship between radians and degrees in angle measurement?

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$\pi\text{ radians} = 180^\circ$ ; multiply degrees by $\frac{\pi}{180^\circ}$ to get radians.

Common angles: $30^\circ = \frac{\pi}{6}$ , $45^\circ = \frac{\pi}{4}$ , $60^\circ = \frac{\pi}{3}$ , $90^\circ = \frac{\pi}{2}$ , $360^\circ = 2\pi$ .

Frage 17: In ACT English, how does comma splices occur and how are they repaired?

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A comma splice joins two independent clauses with only a comma. Fix with a comma + coordinating conjunction (FANBOYS), semicolon, or period.

Example: 'She studied diligently, she earned top marks.' (Splice). 'She studied diligently; she earned top marks.' (Correct).

Frage 18: In ACT Reading, what is the best strategy for paired passages (Passage A and Passage B)?

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Read Passage A and answer its specific questions, then read Passage B and answer its questions, then answer synthesis questions comparing both.

This avoids confusing which author made which claim while both passages remain fresh in memory.

Frage 19: How do you calculate combinations $C(n, r)$ and permutations $P(n, r)$ ?

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$C(n, r) = \frac{n!}{r!(n - r)!}$ (order does not matter); $P(n, r) = \frac{n!}{(n - r)!}$ (order matters).

A committee of 3 from 10 is a combination $C(10, 3) = 120$ . Electing President, VP, and Secretary is a permutation $P(10, 3) = 720$ .

Frage 20: In ACT Science, how do you determine if two variables are directly proportional versus inversely proportional?

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Direct: both increase together with constant ratio $\frac{y}{x} = k$ ; Inverse: one increases as the other decreases with constant product $x \cdot y = k$ .

On a Cartesian graph, direct proportionality passes linearly through the origin $(0, 0)$ ; inverse proportionality forms a hyperbola in the first quadrant.