Monroe Township High School Mathematics Department

Transcription

1 To: AP Calculus AB Re: Summer Project 017 Date: June 017 Monroe Township High School Mathematics Department To help begin your study of Calculus, you will be required to complete a review project this summer. This project consists of problems that review important concepts from Algebra, Geometry and Precalculus. The purpose of this assignment is to keep your skills sharp so that you will be successful net year. Please follow these directions very carefully. All students must complete the problems in this packet independently and document their OWN work!! You may collaborate and share ideas with other students, but you alone are responsible for documenting your own work. 1. DUE DATE: SEPEMBER 6, 017 (THE FIRST DAY OF SCHOOL FOR THE SCHOOL YEAR). This review assignment will be weighted as a double homework grade. Late assignments will NOT be accepted for credit.. You are required to make a photocopy of the project before you hand it in so that you can correct your answers during class discussion. 4. There will be an assessment on all material covered in this packet on the third class meeting which is SEPTEMBER 8, 017. THIS WILL BE A NON-CALCULATOR ASSESSMENT. 5. You are encouraged to use your notes from previous classes as a guide. The problems in this packet review key concepts that are necessary for your study of Calculus. 6. It is recommended that you work on this assignment throughout the summer, periodically reviewing the material. Waiting until the end of summer to begin this packet is strongly discouraged. 7. You may use Khan Academy, Wolfram and other websites to assist you. 8. Please use pencil and show all work neatly and clearly to receive full credit. Put answers on the line, if provided or circle the final answer in RED. 9. You may use a graphing calculator on this project only as a reference source. The Teas Instrument TI-8 plus or TI-84 plus (the most recent version) is recommended. (It will be used throughout the year). Best wishes for a happy and safe summer. I m looking forward to seeing you in September.

2 CALCULUS SUMMER PROJECT 017 NAME DATE SHOW ALL WORK FOR FULL CREDIT! 1. Find the domain and range of f () = 1 4 Domain: Range:. Identify each function as even or odd. Justify your answer. a) y = b) y = 1 c) y = 4. Let f () = and g() = 6 +, find the following (Hint: Use the tet as a guide if needed): a) ( f( g( )) b) The domain of ( f( g( )) c) ( g( f( )) d) The domain of ( g( f( ))

3 4. Sketch the graph of g() = 5, > 1, = 1, < 1 5. Write the formula for the piecewise function. y Hint: The curve is quadratic. 6. Write the piecewise formula for the given function. f () = 1 5

4 7. Write the equation for the line with slope 4 and passing through ( 1, 4) in point-slope form. Draw a graph of the line using the given window. [ 10,10] by [ 10,10 ] 8. Find the equation of the line through (4,) and perpendicular to the line through (,4) and (6,). Write the answer in point-slope form. 9. Find the equation of the circle with center ( 5,) and radius One root of P ( ) = is = 1. Find the other roots algebraically.

5 11. Divide using LONG DIVISION Solve using factoring and sign analysis. 1. Solve and sketch your solution on a number line A fence for a rectangular garden with one side against an eisting wall is constructed by using 60 feet of fencing. What is the maimum area that can be enclosed?

6 15. Change from degrees to radians in terms of π : (Show the conversion factor) a) 150 o b) 4 o o c) Change from radians to degrees: (Show the conversion factor) π π a) b) c) Find eact values for the sine, cosine, tangent, cosecant and cotangent of each angle. a) π 6 b) 4 π sinθ : cosθ : tanθ : cscθ : secθ : cotθ : sinθ : cosθ : tanθ : cscθ : secθ : cotθ : 18. Evaluate 7π sin 1 as sin π π +. The original problem is in terms of radians Sketch the graph of y = cos on [ π, π ]. Label the graph carefully!!

7 0. Graph the specified function. Identify at least three points that lie on the curve. Include these in your graph. a. f( ) g ( ) = log ( ) 1 = b. (, ) (, ) (, ) (, ) (, ) (, ) 1. The figure below shows the graph of y = shifted to four new positions. Label each graph CLEARLY with its correct equation chosen from A-D below. A. y = ( 4) + 5 B. C. D. y= 4 y= ( 4) y= ( 4) 5 [ 5,10] by [ 5,10]

8 Problems -4 may require completing the square to write a conic section in standard form.. Rewrite the relation as a conic in standard form, then sketch the graph of the the relation. (show all work) = 8y y.. Write the equation = y + y + 4 in verte form then sketch the graph. 4. Rewrite the equation below in standard form and sketch it s graph. 4 + y 6y = 7

9 5. Find the -intercept(s) and y-intercepts(s) for the following equation. Confirm your answers algebraically. (This is factorable!) Sketch the curve using intercepts and end behaviors. y = intercept(s): y-intercept(s): 6. Let h ( ) = ( ). 1 a. Find the inverse function h 1 ( ) : b. Sketch the graphs of h and 1 h. Hint: It is helpful to identify ordered pairs on one curve to help sketch the second curve.

10 7. Solve cos + sin = 0 8. Simplify ( + ) 4 9. Simplify ( + 1)( ) ( 1)( ) ( + 1) 0. Write as a sum of integer powers of. (eample: + should be written as + ) a) b) 1 ( + )( + 1) c) Simplify using properties of logs tan a) ln( e ) 5 log (8 )

11 . Epand each epression using properties of logarithms 4 a) log 15y b) ln Evaluate the limit for #-7. Justify each answer.. lim lim lim lim Find lim f( ) where f () =, <, > Hint: Consider the piecewise function for

12 8. For the function f graphed at the right, find the following: a) lim f( ) = b) c) lim f( ) = + lim f( ) = d) f () = e) lim f( ) = + 0 f) lim f( ) = For the function g graphed at the right, find the following: a) lim g ( ) = b) c) 1 lim g ( ) = + 1 lim g ( ) = 1 d) g( 1) = e) lim g ( ) = Using the function f at the right, find the following: a) lim f( ) = b) c) lim f( ) = + lim f( ) = d) f ( ) = e) f (0) =