Daily Practice Questions

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

📝 Questions

⚛️ AP Physics C Easy
If the angular position of a disk is given by the equation θ ( t ) = 2 + 4 t − 3 t ^{2} , what is the angular velocity of the disk as a function of time?
  1. A. 4 − 6 t
  2. B. 6 t − 4
  3. C. 2 t + 2 t ^{2} − 3 t ^{3} ✓
  4. D. 3 t ^{3} − 2 t ^{2} − 2 t
  5. E. 3 t ^{3} − 2 t ^{2} − 2 t + C
Explanation: The angular velocity $\omega(t)$ is the time derivative of the angular position function $\theta(t)$. Differentiating the given equation $\theta(t) = 2 + 4t - 3t^2$ term by term using the power rule ($\frac{d}{dt}at^n = nat^{n-1}$) yields $0 + 4 - 6t$, which simplifies to $4 - 6t$. This corresponds to choice (A), making the provided correct answer (C) incorrect based on standard calculus rules. The underlying concept tested is the relationship between angular position and angular velocity, where velocity is the rate of change of position over time.
🧬 AP Biology Medium
Which cell comes from an organism that is more likely to be dependent on pollinators for reproduction?
  1. A. I ✓
  2. B. II
  3. C. III
  4. D. IV
Explanation: Plants depend on pollinators for reproduction, and plants have chloroplasts. Choices (B), (C), and (D) are incorrect because they do not have chloroplasts.
🎓 GRE Prep Medium
h Quantity A Quantity B
  1. A. Quantity A is greater.
  2. B. Quantity B is greater.
  3. C. The two quantities are equal.
  4. D. The relationship cannot be determined from the information given. ✓
Explanation: The correct answer is (D) because there is insufficient information to compare Quantity A and Quantity B; without specific values or constraints linking the two variables, their relative sizes could vary depending on the inputs. This question tests the ability to recognize when a relationship is indeterminate rather than assuming equality or picking an arbitrary side. Since multiple scenarios exist where either quantity is greater, no definitive conclusion can be drawn from the given data alone.
🧪 AP Chemistry Medium
Which of the following is a solution with an initial KCOOH concentration of 1 M and an initial K _{2} HPO _{2} concentration of 1 M ?
  1. A. a solution with a pH > 7, which is a buffer
  2. B. a solution with a pH < 7, which is not a buffer
  3. C. a solution with a pH < 7, which is a buffer
  4. D. a solution with a pH > 7, which is not a buffer ✓
Explanation: D —The two substances are not a conjugate acid–base pair, so this is not a buffer, which eliminates answers A and C. Both compounds are salts of a strong base and a weak acid; such salts are basic (pH > 7).
📊 SAT Math Hard
6. If 2 x ^{2} + x ^{2} y − 2 xy − 4 x − 15 y − 30 = 0, and x > 5, what is the value of y ?
  1. A. −5
  2. B. −2 ✓
  3. C. 2
  4. D. The value cannot be determined from the information given.
Explanation: Getting to the Answer: The first two terms have a common factor of x ^{2} , the next two terms have a common factor of −2 x , and the last two terms are divisible by 15. So rewrite the equation as x ^{2} (2 + y ) − 2 x ( y + 2) − 15( y + 2) = 0. Combine the factors of (2 + y ) to get ( x ^{2} − 2 x − 15)( y + 2) = 0. Factor the quadratic: ( x − 5)( x + 3)( y + 2) = 0. Since x > 5, neither of the first two terms can be 0, so y must be −2 in order for the last term to be 0. Choice (B) is correct.
✍️ AP English Language Medium
In sentence 18 (reproduced below), which of the following versions best supports the writer’s position on the main argument of the passage?
  1. A. (as it is now)
  2. B. But Dr. Greene tells patients they can still get the same benefits by taking a long walk on one day and making a trip to a recreational area on a weekend. ✓
  3. C. But a long walk on one day and a trip to a recreational area on weekends has the same effect.
  4. D. Irregardless, Dr. Greene claims they can still get the same benefits from a long walk on one day and a trip to a recreational area on a weekend.
  5. E. However, the benefits available to them by taking a long walk on one day or making a trip to a recreational area on a weekend.
Explanation: is the best choice because it relates directly to the exigence of the passage and avoids writing errors found among the others, including faulty diction, verb choice, pronoun person, pronoun reference, sentence fragment, and parallel structure.

💡 Study Tips

🎯 Eliminate before you guess

On multiple-choice questions, crossing out answers you know are wrong before guessing dramatically improves your odds. Even eliminating one option on a four-choice question raises your chance from 25% to about 33%.

📖 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.

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