1. If and are integers and and are real numbers, which of the following statements is incorrect? can be simplified to which of the following choices?

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1 Answer Key The Calculus Pre-Exam is a tool for evaluating whether a student is ready to take the AP Calculus AB Course offered by Patrick Henry College Preparatory Academy. After taking the exam, students or their parents may download the Pre-Exam Answer Key to grade the exam. A student should be able to score at least 80% on the exam before signing up for the course. This test covers (1) basic algebraic skills, (2) basic skills involving functions, and (3) basic trigonometric skills. A student should be able to effectively use mathematical skills in all three of these areas before taking AP Calculus AB. For each of the following questions, choose the best response. Problems (1) (10) test basic algebraic skills: 1. If and are integers and and are real numbers, which of the following statements is incorrect? Correct answer 2. The expression can be simplified to which of the following choices? Correct answer

2 3. which of the following choices? Correct answer 4. Which of the following is a correct factoring of the expression 24 25? Correct answer If 4 54, what is the value of y when 2? Correct answer 6. If Correct answer 0, cannot be evaluated for what value of?

3 7. What are the values of for which the following is it true: 2 1 0? 2,1,and 1 2,1,and1 Correct answer 1 and 2 1 and 2 0, 1, and 2 8. The solution of the equation 4 is which of the following? Correct answer 9. One number is 5 more than another and the sum of the two numbers is 25. What is the smaller of the two numbers? 5 10 Correct answer Let 24. For what value or values of is 0? Correct answer 0 0

4 Problems (11) (20) test basic skills involving the concept of functions: 11. Suppose 1 and 3. What is as a function of? Correct answer Suppose and. Which of the following is not true? when 1 when 0 Correct answer when 0 when Suppose and. Which of the following is not true? is not defined at 0. when 1 when Correct answer when Suppose 2 and 1. For what value is it true that 0? Correct answer

5 15. Suppose and. For what values is it true that? and 1 Correct answer 3 and 1 no values satisfy the condition 16. Consider the function 4. For what is it true that 0? 2 and 2 Correct answer 2 and 2 all values of no values of Let 2 3 Correct answer ; is not defined for which of the following values of? 18. Suppose 2 1. For which of the following x values is it true that 0? and 1 1 and 1 Correct answer no values of

6 19. Suppose and 4. For what value do these functions map into the same value? Correct answer 20. A rectangle has a height, width, and a perimeter of length 30. Express as a function of. 15 Correct answer Problems (21) (30) test basic skills involving trigonometry: Problems 21, 22, and 23 refer to the following figure showing triangle with angles,, and ; sides,, and ; and the line which is perpendicular to side. We will indicate length of lines with a pair of vertical lines. Thus, is the length of side. B A a D c C 21. Which of the following is sin? sin sin sin Correct answer sin sin

7 22. Which of the following is cos? cos Correct answer cos cos cos cos 23. Which of the following is tan? tan tan tan tan Correct answer tan 24. For which angle is tan not defined? Correct answer 360 tan is defined for all. 25. Let be some angle for which cos sin45. For which of the following θ values is this true? Correct answer 225 none of the above.

8 26. It is known that tan45 1. For which of the following values is it also true that tan 1? Correct answer none of the above. 27. What is the minimum value of cos 45? Correct answer 28. Which of the following is not true? tan sincos sin cos 1 cos sin90 cos 90 sin cos cos Correct answer 29. Suppose cos and is an integer. Which of the following is true? Correct answer

9 30. Consider the function cos3. For which of the following values is this function equal to 0? Correct answer 45 none of the above