Honors AP Calculus / Mr. Hansen

Name: _________________________ Start: ______ am/pm End: ______ am/pm

HappyCal Diagnostic Quiz

• No calculator is permitted.
• Do not consult notes, books, the Internet, or other people.
• Choose the best answer in each case.
• Look at a clock before you begin and after you finish. Record the times below your name.
• Show your work for question 10. (Work is optional for the other questions.)

1.	=
	(A) | x | (B) (C) –x	(D) (E) x
2.	{x Î Â: (x + 7)^2 = x^2 + 49} =
	(A) (B) 0 (C) {0}	(D) Â (E) {Â}
3.	Df = , where f (x) = . Use absolute value and set notation to give an equivalent expression for the domain.
	(A) {t Î Â: | t | } (B) {u Î Â: | u | } (C) {v Î Â: | v | }	(D) {w Î Â: | w | } (E) {x Î Â: | x | }
4.	=
	(A) 169 (B) 13 (C)	(D) 17 (E)
5.	cos^2 2x – sin^2 2x =
	(A) (B) (C) cos x	(D) cos 4x (E) 1
6.	tan^–1 =
	(A) (B) (C)	(D) (E) undefined
7.
	(A) 0 (B) 3 (C)	(D) (E)
8.	csc^–1 0.5 =
	(A) (B) (C)	(D) (E) undefined
9.	cos^–1 (–0.5) =
	(A) (B) (C)	(D) (E) undefined
10.	SHOW YOUR WORK FOR THIS QUESTION. Show by means of a rough sketch that the quadratic function y = –2x^2 – 7x + 349 has two real roots, and compute the exact mean of the two roots. On your sketch, show ballpark values for the x- and y-intercepts. An accurate sketch is not desired. Sketch: Exact mean of roots 1 and 2 = ____________________
11.	Essay question. On the reverse side, or on a blank sheet of paper, explain in your own words why every function that passes the “horizontal line test” is invertible. Your explanation should make sense to a reasonably intelligent ninth-grader who has never studied precalculus. You will need to write a paragraph or two plus at least one sketch.