Daily Practice Questions

6 questions across multiple subjects, with detailed explanations and study tips.

📝 Questions

📊 SAT Math Hard
3. In the xy ‑plane above, a point (not shown) with coordinates ( a , b ) lies on the graph of the linear function h . If a and b are positive integers, what is the ratio of a to b ?
  1. A. 2:3
  2. B. 3:2
  3. C. 5:6
  4. D. 6:5 ✓
Explanation: Getting to the Answer: Using the point (6, 5), the slope is 5:6, but this is the trap choice (C) since the question asks for the ratio of a : b rather than b : a . Therefore, (D), 6:5 is correct.
🎓 GRE Prep Medium
Mount Godwin-Austen, more commonly known as K2, is the second highest mountain in the world, with its peaks reaching more than 28,000 feet high.
  1. A. famous ✓
  2. B. bombastic
  3. C. critical
  4. D. prolific
  5. E. eclectic
Explanation: The sentence describes K2 as 'the second highest mountain in the world, with its peaks reaching more than 28,000 feet high'—a description that emphasizes its fame and recognition due to its extreme height and status. 'Famous' fits best as it means widely known, which aligns with K2's renowned status among mountaineers and the public. The other options (bombastic = overly dramatic, critical = essential or judgmental, prolific = productive, eclectic = diverse) do not describe the mountain's renown.
📝 ACT Prep Easy
If the area of circle A is 16π, then what is the circumference of circle B if its radius is 1/2 that of circle A?
  1. A. 2π
  2. B. 4π ✓
  3. C. 6π
  4. D. 8π
  5. E. 16π
Explanation: The area of circle A is 16π, so πr² = 16π, which gives r = 4. The radius of circle B is 1/2 of that, so r = 2. The circumference of circle B is 2πr = 2π(2) = 4π.
📖 SAT Reading & Writing Hard
Which choice completes the text so that it conforms to the conventions of Standard English? While hiking has always been known to be a good form of exercise, current research ___________ that its added mental benefits have a significant impact on the physical health of those who hike.
  1. A. cornfields; and Arizona it’s majestic Grand Canyon.
  2. B. cornfields: Arizona its majestic Grand Canyon.
  3. C. cornfields; and Arizona, its majestic Grand Canyon. ✓
  4. D. cornfields, and Arizona, it’s majestic Grand Canyon.
Explanation: The correct answer is (C) because the semicolon properly joins two independent clauses, while the comma after "Arizona" correctly sets off the nonrestrictive appositive phrase "its majestic Grand Canyon." Additionally, "its" is the possessive pronoun needed to show that the canyon belongs to Arizona, whereas "it's" in choices (A) and (D) incorrectly uses the contraction for "it is." Choice (B) is incorrect because a colon cannot be used before an appositive phrase.
📐 AP Calculus Easy
The motion of a particle in a plane is given by the pair of equations x = cos 2 t , y = sin 2 t . The magnitude of its acceleration at any time t equals
  1. A. 1
  2. B. 2
  3. C. 4 ✓
  4. D. 16
Explanation: To find the magnitude of acceleration, first determine the velocity components by differentiating position: $v_x = -2\sin(2t)$ and $v_y = 2\cos(2t)$. Differentiating again gives the acceleration components $a_x = -4\cos(2t)$ and $a_y = -4\sin(2t)$. The magnitude is $\sqrt{(-4\cos(2t))^2 + (-4\sin(2t))^2} = \sqrt{16(\cos^2(2t) + \sin^2(2t))} = 4$, using the identity $\cos^2\theta + \sin^2\theta = 1$.
✍️ AP English Language Medium
Keeping in mind the main purpose in the passage, which of the following versions of the underlined text of sentence 13 (reproduced below) is most supportive of the writer’s main concern in the passage?
  1. A. (as it is now)
  2. B. reward dedicated workers with regular cost-of-living pay increases
  3. C. whether supervisors treated employees with respect
  4. D. encourage employees to participate in making decisions that improve customer satisfaction
  5. E. the extent to which employees knew exactly how their job contributed to the restaurant’s success ✓
Explanation: 30. (E) Because Whyte focused his research on why some restaurants are more successful than others, he studied the roles of staff members—in particular, whether employees understood how their specific jobs made a difference in determining the restaurant’s success or failure.

💡 Study Tips

📖 Teach concepts using diagrams

Drawing concept maps, flowcharts, or diagrams helps you see relationships between ideas that aren't obvious in linear notes. This approach works for everyone and strengthens conceptual thinking.

🎯 Read the question before the passage

On reading-heavy sections like the ACT and AP English exams, skim the questions first. Knowing what you're looking for turns passive reading into active searching, saving time and improving accuracy.

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