ACT Practice Test: Video 1 Answers (25 Questions) — Questions and Answers

Question 1: If f(x) = 3x² - 5x + 2, what is the value of f(-3)?

-40
14
-10
44 (Correct answer)

Correct answer: 44

To find f(-3), substitute -3 for every instance of x in the function f(x) = 3x² - 5x + 2. The calculation is f(-3) = 3(-3)² - 5(-3) + 2 = 3(9) + 15 + 2 = 27 + 15 + 2 = 44. Be careful with the signs, especially when squaring a negative number.

Question 2: A function f is defined as f(x) = |x − 3|. For what value(s) of x does f(x) = 5?

x = −2 only
x = 2 and x = 8
x = 8 and x = −2 (Correct answer)
x = 8 only

Correct answer: x = 8 and x = −2

Set up the absolute value equation: |x − 3| = 5. This gives two cases: x − 3 = 5 → x = 8, OR x − 3 = −5 → x = −2. Always check both cases when solving absolute value equations.

Question 3: Which of the following represents the inverse function of f(x) = 2x + 6?

f⁻¹(x) = (x − 6)/2 (Correct answer)
f⁻¹(x) = 2x − 6
f⁻¹(x) = (x + 6)/2
f⁻¹(x) = x/2 + 6

Correct answer: f⁻¹(x) = (x − 6)/2

To find the inverse, swap x and y, then solve for y. Starting with y = 2x + 6: swap to get x = 2y + 6, then solve: x − 6 = 2y, so y = (x − 6)/2. Therefore f⁻¹(x) = (x − 6)/2.

Question 4: The function f(x) = x² − 4x + 3 has zeros at x = 1 and x = 3. What is the x-coordinate of the vertex of this parabola?

x = 2 (Correct answer)
x = 4
x = 1
x = 3

Correct answer: x = 2

The vertex of a parabola lies on the axis of symmetry, which is the vertical line exactly halfway between the two zeros. Midpoint of x = 1 and x = 3: (1 + 3)/2 = 4/2 = 2. Alternatively, use the vertex formula x = −b/2a = −(−4)/(2·1) = 4/2 = 2.

Question 5: Which of these represents a function?

{(0,1),(0,2),(0,3)}
{(1,2),(2,3),(3,4)} (Correct answer)
{(1,2),(1,3),(2,4)}
{(2,1),(2,2),(3,3)}

Correct answer: {(1,2),(2,3),(3,4)}

Each x-value maps to exactly one y-value only in the first set.

Question 6: An author uses first-person narration to recount a frightening childhood event in vivid detail. The purpose is primarily to:

Report statistics
Tell a story and engage emotionally (Correct answer)
Compare products
Instruct a skill

Correct answer: Tell a story and engage emotionally

First-person vivid recounting serves a narrative, emotionally engaging purpose.

Question 7: An editorial repeatedly uses phrases like 'we must act now' and 'the choice is clear.' This signals the author intends to:

Describe neutrally
Persuade (Correct answer)
Define terms
Entertain

Correct answer: Persuade

Calls to action and definitive language are hallmarks of persuasive writing.

Question 8: An author writes a parody of a famous fairy tale, twisting the plot for laughs. The purpose is to:

Entertain through parody (Correct answer)
Educate about history
Persuade voters
Document research

Correct answer: Entertain through parody

A humorous twist on a known story is parody meant to entertain.

Question 9: The author's point of view is that the debate between digital and traditional art should NOT be about:

The future evolution of creativity.
Which medium is inherently superior to the other. (Correct answer)
The skills required for each medium.
The history of art.

Correct answer: Which medium is inherently superior to the other.

The final sentence of the passage explicitly states, 'The debate is not about which medium is superior, but about recognizing digital art as a legitimate and distinct evolution...' The author is trying to shift the conversation away from a simple comparison of which is 'better' and toward an appreciation of digital art's unique place.

Question 10: An author ends a memoir chapter reflecting on lessons learned from a personal loss. The purpose is primarily to:

Advertise a service
Reflect and share personal experience (Correct answer)
Report breaking news
Instruct a procedure

Correct answer: Reflect and share personal experience

Personal reflection on lived experience characterizes reflective, expressive writing.

Question 11: If sin θ = 5/13 and θ is in the first quadrant, what is cos θ?

8/13
12/13 (Correct answer)
5/12
13/12

Correct answer: 12/13

Using the Pythagorean identity: cos²θ = 1 − sin²θ = 1 − 25/169 = 144/169. cos θ = 12/13 (positive in Q1).

Question 12: A car travels 240 miles in 4 hours. At this rate, how far will it travel in 7 hours?

420 miles (Correct answer)
400 miles
380 miles
480 miles

Correct answer: 420 miles

Rate = 240 ÷ 4 = 60 mph. Distance in 7 hours = 60 × 7 = 420 miles.

Question 13: What is the slope of a line that passes through (−3, 4) and (5, −2)?

3/4
-3/4 (Correct answer)
-4/3
4/3

Correct answer: -3/4

Slope = (y₂ − y₁)/(x₂ − x₁) = (−2 − 4)/(5 − (−3)) = −6/8 = −3/4.

Question 14: A rectangle has a perimeter of 54 cm. If the length is twice the width, what is the area of the rectangle?

108 cm²
162 cm² (Correct answer)
81 cm²
243 cm²

Correct answer: 162 cm²

Let width = w, length = 2w. Perimeter: 2(w + 2w) = 54 → 6w = 54 → w = 9. Length = 18. Area = 9 × 18 = 162 cm².

Question 15: Two sides of a triangle have sides 4 and 8. The length of the third side must be greater than_ and less than.

2, 3
4, 8
4,12 (Correct answer)
0, 12

Correct answer: 4,12

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For sides 4 and 8, the third side must be greater than their difference (8 - 4 = 4) and less than their sum (4 + 8 = 12). Therefore, the length of the third side must be greater than 4 and less than 12.

Question 16: What is the exact value of tan(5π/4) on the unit circle?

-1
1 (Correct answer)
√2/2
undefined

Correct answer: 1

The angle 5π/4 is in the third quadrant of the unit circle. The reference angle is π/4. In the third quadrant, both sine and cosine are negative. Since tan(θ) = sin(θ)/cos(θ), the value will be (-√2/2) / (-√2/2), which simplifies to 1.

Question 17: Which identity is always true for any angle θ?

tanθ = sinθ + cosθ
sin²θ - cos²θ = 1
sinθ + cosθ = 1
sin²θ + cos²θ = 1 (Correct answer)

Correct answer: sin²θ + cos²θ = 1

The Pythagorean identity sin²θ + cos²θ = 1 holds for all angles.

Question 18: What is the period of the function f(x) = 3sin(4x)?

2π
3
4π
π/2 (Correct answer)

Correct answer: π/2

The period of a sine or cosine function of the form y = Asin(Bx + C) + D is given by the formula 2π/|B|. In this function, B = 4. Therefore, the period is 2π/4, which simplifies to π/2.

Question 19: In which quadrant is sine positive but cosine negative?

Quadrant IV
Quadrant III
Quadrant I
Quadrant II (Correct answer)

Correct answer: Quadrant II

In Quadrant II, y is positive (sine +) and x is negative (cosine −).

Question 20: In a right triangle, the side opposite a 30° angle has length 5. What is the length of the hypotenuse?

10 (Correct answer)
2.5
5√3
5√2

Correct answer: 10

sin(30°) = opposite/hypotenuse = 1/2, so hypotenuse = 5 / (1/2) = 10.

Question 21: A passage presents three theories on dinosaur metabolism. A question asks which theory is UNIQUE in claiming warm-bloodedness. You should:

Choose the shortest theory
Choose all three theories
Pick any theory that mentions temperature
Find the single theory that asserts warm-bloodedness (Correct answer)

Correct answer: Find the single theory that asserts warm-bloodedness

A 'unique' claim belongs to only one theory, so isolate the one making that specific assertion.

Question 22: A Conflicting Viewpoints question asks which new evidence would WEAKEN Scientist 2's hypothesis. The best answer is one that:

Is irrelevant to either viewpoint
Restates Scientist 2's claim
Supports Scientist 2's prediction
Contradicts a key assumption Scientist 2 relies on (Correct answer)

Correct answer: Contradicts a key assumption Scientist 2 relies on

Evidence weakens a hypothesis when it conflicts with one of that hypothesis's necessary assumptions or predictions.

Question 23: To answer 'Which viewpoint would be most weakened if Assumption X is false?', you should first:

Ignore Assumption X
Pick the viewpoint with more data
Pick the viewpoint mentioned first
Determine which viewpoint depends on Assumption X (Correct answer)

Correct answer: Determine which viewpoint depends on Assumption X

A false assumption hurts the viewpoint that relies on it, so identify which one depends on X.

Question 24: A question asks how Scientist 2 would respond to a fact cited only by Scientist 1. The best approach is to:

Apply Scientist 2's reasoning to that new fact (Correct answer)
Quote Scientist 1's response instead
Choose the longest answer
Ignore Scientist 2's framework

Correct answer: Apply Scientist 2's reasoning to that new fact

Predicting a response requires extending the chosen scientist's logic and assumptions to the new information.

Question 25: Scientist 1 predicts temperature will rise; Scientist 2 predicts it will stay constant. An experiment shows a sharp rise. This result:

Supports Scientist 2 only
Is consistent with neither
Supports both equally
Supports Scientist 1 and challenges Scientist 2 (Correct answer)

Correct answer: Supports Scientist 1 and challenges Scientist 2

A sharp rise matches Scientist 1's prediction while contradicting Scientist 2's claim of no change.

ACT Practice Test: Video 1 Answers (25 Questions)

If f(x) = 3x² - 5x + 2, what is the value of f(-3)?

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