To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers

Transcription

1 To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers Going into AP Calculus, there are certain skills that you have been taught to you over the previous years that we assume you have. If you do not have these skills, you will find that you will consistently get problems incorrect net year, not because you don t understand the Calculus but because you have forgotten the Algebra involved. The topics covered in the packet are skills that are used continually in AP calculus. The packet is due the first day of school. Do not fake your way through these problems. All work is to be shown. Page of 5

2 . Are the following statements true? If not, eplain why. a. a a a h a h y y y y 5 y 5y d. 5 e. 5 5 a b a b c c. Simplify: a. y h h h 5. Solve for y : y ' y y'. Find the average rate of change on the indicated intervals: a. f ( ) ; [0,] f ( ) ; [, 5] Page of 5

3 5. A car travels 60 miles in a period of 80 minutes. Find the average velocity of the car in miles per hour over this time period. 6. In 98, the Fizzy Cola Co. sold million gallons of soda. By 00, the company was selling 7 million gallons of soda. What is the average rate of change in number of gallons of soda per year? 7. Solve for : a Write as a single fraction with the denominator in factored form: Graph the function and answer the questions: f a. Is the point (, ) on the graph? Is the point (, 6) on the graph? Is the function even, odd or neither? d. What is the y intercept? e. Find the intercepts Page of 5

4 0. Determine if the function is even, odd, or neither. a. f ( ) 7 f ( ) f ( ). Find the equation of the straight line that passes through the point (, ) and is a. Parallel to y 8=0 Perpendicular to - y - 8 = 0. Given f ( ) 5 find f() f(5). Given f ( ), find f( +) f(). Find the domain for each function: a. f( ) 8 g( ) 5 h ( ) 6 0 d. k( ) ln( ) Page of 5

5 5. Find f( + ) for f ( ) f ( ) f ( ) if f ( ) 8 6. Find 7. Given ( ) ( ) ( ), : f h f Find f h 8. Sketch the graph of each function: a., 0 f( ), 0 f ( ),,,,,, Page 5 of 5

6 9. Given f ( ) and g( ), find the following a. f(g()) g(f()) f(f()) ( ) ( ) Given f and g a. f(g(7)), find the following: g(f(v)) g(g()). Let f()=-, find f. Simplify using only positive eponents. Do not rationalize the denominator. a. 6 ( ) Page 6 of 5 y y

7 . If f ( ), describe in words what the following would do to the graph of f(). a. f() - f( - ) f( + ) d. 5f() + e. f(-) f. f(). Epand the logarithms a. ln y ln e yz ln y 5. Condense into one logarithm a. ln ln y ln z ln ln y ln z ln ln( ) ln y 6. Divide using long division: 5 5 Page 7 of 5

8 7. Finish the factoring a. 6?? 5? 8. A 7 foot ladder, leaning against a wall, touches the wall feet above the ground. Write an epression in terms of, for the distance from the foot of the ladder to the base of the wall. 9. Evaluate without a calculator: (all angles are in radians) a. cos0 sin 0 tan d. cos e. sin f. sin g. arccos h. arctan sec i. arctan arctan j. k. cos l. csc 6 Page 8 of 5

9 0. Find the solution of the equations for [ 0, π]. a. sin sin sin sin 0 tan sec 0. Graph y sin for. If 5 tan, and, a. csc Find sec cot. Solve for, 0 cos sin Page 9 of 5

10 . If and y showthat y cos sin, ( ) 5. Evaluate a. Let 6, 8, 9, and Evaluate m i i Evaluate i i m 6. a. Solve to the nearest thousandth:.. ln.09 Epress y in terms of :. log y. ln y ln. ln yln Page 0 of 5

11 7. Find the limits: a. lim 0 8 lim lim 0 Page of 5

12 Answers to AP Calculus AB Review. a. No, is not a factor of the denominator No, right side equals y y true d. No, answer is 5 y e. No, answer is 5a 5b c. a. y h h. y y '. a mi/hr million gal. per yr. 7. a. -/, 6 8. i 5, a. no yes odd d. (0, 0) e. (-, 0), (0, 0),(, 0) 0. a. Even odd Neither. a. y. 0. y f = Page of 5

13 . a. All Real numbers not equal to -/ or 6 or 7 < - 5 or > 6 d. > h 8. a. 9. a a. 9 5 v 0v f ( ). a. ( y). a. moves down moves right moves left and reflects over the - ais d. steeper and up e. reflects over the y-ais f. area between - and, reflected over the -ais. a. ln ln( y ) ln ln y ln z ln ln ln ln y 5. a. ln y y ln z Page of 5

14 6 y ln z a a. 0 DNE d. e. f. 0 g. h. 6 i. 5 j. or k. - l. 0. a. 5,, 0,,,, ,,,.. a ,,,. Page of 5 cos sin 5. a. 9 cos sin

15 6. a. ) 0.79 ).97 y ) ) ) 7. a. - y y e Page 5 of 5