Daily Practice Questions

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

📝 Questions

📊 SAT Math Medium
A cylindrical tank has base with a diameter of 10 feet and a volume of 300 π cubic feet. What is the height of this tank in feet?
  1. A. 8
  2. B. 10
  3. C. 12 ✓
  4. D. 16
Explanation: Use the volume formula for a cylinder, V = π r ^{2} h , in which r is the radius and h is the height. Note that this formula is provided in the formulas at the beginning of the section, so refer to it if you do not remember the formula. Since the tank has a base with a diameter of 10 feet, the radius will be 5. Plug in the volume and the radius into the formula to solve for height:
🧪 AP Chemistry Easy
CS _{2} (l) + 3 O _{2} (g) → CO _{2} (g) + 2 SO _{2} (g) How many moles of O _{2} (g) must react to form 6.30 moles of gaseous products?
  1. A. 2.10
  2. B. 4.20
  3. C. 6.30 ✓
  4. D. 9.45
Explanation: Three moles of O2gas produce three moles of gaseous products ∴ the number of moles of oxygen gas that reacts is equal to the number of moles of gas the reaction produces.
📖 SAT Reading & Writing Hard
Which choice completes the text so that it conforms to the conventions of Standard English? Music is a combination of specific sound waves started and stopped at specific times. Some waves align nicely with one another or contrast nicely with one another, ___________ others are neither regularly contrasting nor matching.
  1. A. from the two mens’ works directly derive.
  2. B. from the works of these two men directly derive.
  3. C. derive directly from the works of these two men. ✓
  4. D. come directly from this.
Explanation: Choice (C) is correct because it uses the active verb "derive" to agree with the plural subject "others," whereas choices (A) and (B) incorrectly use the passive construction "from... derive." Choice (D) is vague and fails to specify the necessary antecedent. The sentence requires a standard English structure where the subject performs the action of deriving from the works mentioned earlier.
📐 AP Calculus Hard
Write an equation for the line tangent to the curve defined by F ( t ) = 〈 t ^{2} + 1,2 ^{t} 〉 at the point where y = 4.
  1. A. y – 4 = (ln 2)( x – 2)
  2. B. y – 4 = (4 ln 2)( x – 2)
  3. C. y – 4 = (ln 2)( x – 5) ✓
  4. D. y – 4 = (4 ln 2)( x – 5)
Explanation: To find the tangent line, first determine the $t$-value where $y = 2^t = 4$, which gives $t = 2$. At this point, the $x$-coordinate is $x = 2^2 + 1 = 5$, so the point of tangency is $(5, 4)$. Next, calculate the slope using the derivative $\frac{dy}{dx} = \frac{y'(t)}{x'(t)} = \frac{2^t \ln 2}{2t}$; evaluating at $t=2$ yields a slope of $\ln 2$. Substituting the point $(5, 4)$ and the slope $\ln 2$ into the point-slope form results in the equation $y - 4 = (\ln 2)(x - 5)$.
💻 AP Computer Science A Easy
A large sorted array containing about 30,000 elements is to be searched for a value key using an iterative binary search algorithm. Assuming that key is in the array, which of the following is closest to the smallest number of iterations that will guarantee that key is found? Note: 10 ^{3} ≈ 2 ^{10} .
  1. A. 15 ✓
  2. B. 30
  3. C. 100
  4. D. 300
  5. E. 3000
Explanation: 30,000 = 1000 × 30 ≈ 2 ^{10} × 2 ^{5} = 2 ^{15} . Since a successful binary search in the worst case requires log _{2} n iterations, 15 iterations will guarantee that key is found. (Note that 30,000 < 2 ^{10} × 2 ^{5} = 32,768.) Shortcut: 30,000 < 2 ^{15} . Therefore, the maximum (worst case) number of comparisons that guarantees the key is found is equal to the exponent, 15.
🧬 AP Biology Medium
A molecule is analyzed and found to contain carbon, hydrogen, oxygen, nitrogen, and phosphorus. This molecule is most likely to be a __________.
  1. A. carbohydrate
  2. B. lipid
  3. C. nucleic acid ✓
  4. D. protein
Explanation: Nucleic acids contain carbon, hydrogen, oxygen, nitrogen, and phosphorus. Choice (A) is incorrect because carbohydrates do not usually contain nitrogen or phosphorus. Lipids usually do not contain nitrogen, so choice (B) is incorrect. Choice (D) is incorrect because proteins usually do not contain phosphorus.

💡 Study Tips

🎯 Review your mistakes, not just your score

After a practice test, spend more time analyzing the questions you got wrong than celebrating the ones you got right. Understanding your error patterns reveals exactly what to study next.

📖 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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