Calculus > AP Calculus Exam: How to Justify Answers

## AP Calculus Exam: How to Justify Answers

Advanced Placement (AP) courses are high school courses offered in the United States and Canada that teach material at the same level as undergraduate courses in colleges and universities. Students who test well in **AP calculus** can receive credits for their achievements at participating colleges and universities. The **AP calculus exam** uses short-answer problems. Justify your answers for these problems to receive full credit. If you are asked to justify an answer, it means that you will need to give reasoning for why your answer is correct.

## AP Calculus Exam: How to Justify Answers.

Sample question: If two balls are thrown from the top of a 512 ft tall building with a velocity of 64 feet per second and 102 feet per second, which ball will reach the ground first?

Step 1: Write down the obvious: the second ball will reach the ground first.

Step 2: Justify your answer from Step 1 **using calculus** (remember — this is a calculus test, not basic math!). In other words, figure out how much time it will take for ball 1 and ball 2 to reach the ground.

Step 3: **Record the steps** that you’ve undertaken to calculate your answer in complete detail. For example, in this sample question you need the knowledge that a(t) = -32 ft/sec^{2} (gravity) to answer the question. Recording all steps in the equation demonstrates that you understand how to calculate the answer to the problem even if you are performing the calculations using a calculator.

Step 4: Use your notes and recorded steps to prepare your defense. Mention everything you can think of that led you to the solution. Did you use the power **rule of differentiation**? Or the constant rule? If so, mention what rule you used and why.

*Tip:*

Be neat and organized when writing down your calculations, your notes and your short answers. Not only will this help you keep track of your work and thoughts, it will help prevent confusion on the part of the person marking your exam. You should make sure to space out the steps so that you have room for any notes that you may wish to add and any corrections that you may need to make.

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