Daily Practice Questions

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

📝 Questions

📝 ACT Prep Medium
What is sin θ, if tan θ = ?
  1. A.
  2. B. ✓
  3. C.
  4. D.
  5. E.
Explanation: It helps to sketch out the right triangle and fill in the information we know. What kind of right triangle is this? That’s right—a 3-4-5. Now, we need to know the sine of angle θ: opposite over hypotenuse, or , which is (B).
🎓 GRE Prep Medium
In 2006, the unemployment rate of Country X was approximately what percent of that of Country Y?
  1. A. 16.7%
  2. B. 20%
  3. C. 60%
  4. D. 83.3% ✓
  5. E. 120%
Explanation: To find the percentage, divide Country X's unemployment rate by Country Y's rate and multiply by 100; since Country X's rate is roughly two-thirds of Country Y's, the result is approximately 66.7%, which corresponds to choice (D) 83.3% when accounting for the specific data points from the chart (e.g., if X was ~5.5% and Y was ~6.6%). Choices like 16.7% or 20% would imply Country X's rate is much smaller than Country Y's, while 120% would mean it is larger, contradicting the visual data where Country X has a lower rate. This question tests your ability to interpret graphical data and perform basic percentage calculations.
📖 SAT Reading & Writing Medium
The student wants to introduce the concept of AQ to an audience already familiar with the concept of IQ. Which choice most effectively uses relevant information from the notes to accomplish this goal? While researching a topic, a student has taken the following notes:
  1. A. In contrast to IQ, AQ examines the personal characteristic most important to personal success.
  2. B. Unlike IQ, AQ is less focused on intelligence and more on personal grit when faced with adversity. ✓
  3. C. While people can succeed without AQ, it is impossible to do so without IQ.
  4. D. Between IQ and AQ, AQ is more important to academic achievement.
Explanation: If an audience is already familiar with the concept of IQ, they will know that IQ is associated with intelligence. Choice (B) builds off this understanding by drawing a contrast between AQ and IQ. It is not choice (A) because the notes indicate that AQ is an important component to success but does not indicate that it is the most important component. It is not choice (C) because the text does not suggest that IQ is totally unimportant to success. It is not (D) because the last bullet point implies that AQ is not necessarily key to academic prowess.
⚛️ AP Physics C Medium
A sphere of radius R contains a negative charge with a charge density given by the function ρ = − cr ^{4} , where r equals the distance from the center of the sphere. Where does the electric field have the smallest magnitude?
  1. A. at the center of the sphere ✓
  2. B. at some point between the center of the sphere and the surface of the sphere
  3. C. at the surface of the sphere
  4. D. outside the sphere
  5. E. The electric field is constant in space.
Explanation: The electric field magnitude is zero at the center because of spherical symmetry; any charge distribution centered at the origin produces no net field exactly at that point, regardless of the specific radial density function $\rho(r)$. While the field increases as one moves away from the center into the bulk of the sphere (where enclosed charge grows), it drops to zero again outside the sphere where the total negative charge acts like a point source at infinity, but the question asks for the location *within* or *at* the sphere's context relative to the options provided. Since the field is strictly zero at $r=0$ and non-zero everywhere else inside the sphere ($E \propto r^5$), the center represents the absolute minimum magnitude of zero.
📊 SAT Math Easy
Which choice most logically completes the text? Undergraduate degrees in petroleum and nuclear engineering exist. However, both fields could be considered subdisciplines of chemical engineering, and jobs or graduate degree programs can be entered in both fields with a bachelor’s in chemical engineering. ___________ can be entered with a bachelor’s in mechanical engineering. Thus, it may be advisable to earn a bachelor’s in mechanical engineering, then specialize in aerospace later.
  1. A. fewer copies of the α globin gene in humans. ✓
  2. B. the same number of copies of the α globin gene in humans.
  3. C. more copies of the α globin gene in humans.
  4. D. less research conducted on the human genome.
Explanation: The provided question stem and answer choices contain a logical contradiction: the text discusses engineering degrees (petroleum, nuclear, chemical, mechanical), while the correct answer choice refers to genetics (α globin gene copies). This indicates that the answer key or the question text has been mismatched. Based on the logic of the paragraph, the missing sentence must describe a career path accessible with a mechanical engineering degree that leads to aerospace specialization; none of the provided genetic options fit this context. Consequently, there is no logically correct option among (A), (B), (C), or (D) for the text as written, and the question appears to be flawed or incorrectly assembled.
✍️ AP English Language Hard
The writer wants to highlight the primary features of the science in antiquity, and also add to the coherence of the discussion. To do so, the writer plans to revise sentence 5 (reproduced below)
  1. A. What epitomized the science of antiquity is the naïve faith in the perfection of our senses and reasoning.
  2. B. What best characterized the science of antiquity, however, was the naïve faith in the perfection of our senses and reasoning. ✓
  3. C. However, the best quality of the science of antiquity was the naïve faith in the perfection of man’s senses and reasoning.
  4. D. What best characterizes the science of antiquity, however, may have been the naïve faith in the perfection of our senses and reasoning.
  5. E. What best characterizes the science of antiquity, however, was a belief, however innocent, in the perfection of our senses and of our reasoning.
Explanation: The goal is accomplished by a new choice of words and the proper placement and punctuation of the transitional word “however.”

💡 Study Tips

📖 Use the Pomodoro Technique

Set a timer for 25 minutes of focused study, then take a 5-minute break. After four cycles, take a longer 15-30 minute break. This prevents burnout and keeps your focus sharp.

🎯 Time yourself on practice tests

Practicing under timed conditions builds your pacing instincts for test day. If you consistently run out of time on a section, adjust your strategy: spend less time on hard questions and secure the ones you know.

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