📖 AP Calculus

AP Calculus Practice

AP Calculus practice questions with explanations

246 Practice questions
3 Difficulty levels
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📝 Sample Questions

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Hard
If y = e ^{– x ^{2}} , then y ″(0) equals
  1. A. 2
  2. B. 1
  3. C. 0
  4. D. –2 ✓
Explanation: Since y ′ = –2 xe ^{– x ^{2}} , therefore y ″ = –2( x · e ^{– x ^{2}} · (–2 x ) + e ^{– x ^{2}} ). Replace x by 0.
Hard
A particle is moving in the xy -plane. The position of the particle is given by x ( t ) = t ^{2} + ln ( t ^{2} + 1) and y ( t ) = 2 t + 5cos( t ^{2} ). What is the speed of the particle when t = 3.1?
  1. A. 3.641
  2. B. 3.807
  3. C. 10.269 ✓
  4. D. 12.041
Explanation: The speed of the particle is the magnitude of the velocity vector. At t = 3.1, the velocity vector is 〈6.784,7.709〉 and the magnitude is \sqrt{6.784^2 + 7.709^2} = 10.269 .

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