ARE YOU READY FOR CALCULUS?

Transcription

1 ARE YOU READY FOR CALCULUS? Congratulations! You made it to Calculus AB! Instructions 1. Please complete the packet (see below), which will be due the day of registration. This packet will help you review for the test that you will have during the first week of school. If not turned in by the mentioned dates you will be dropped from the course.. Please make a copy of your summer work just in case something should happen. 3. Do your work on a separate sheet of paper clearly and neatly and write the answer the actual worksheet. 4. If you need help to review look up the topics on the Internet or in your book. 5. All of these topics should be review and are skills you will be epected to know the first day of class. (OF PARTICULAR IMPORTANCE IS THE UNIT CIRCLE which should be memorized.) Packet Learning Objectives There are 14 learning targets you need to be familiar with. If you get stuck on a problem please refer to the second part of the packet eamples which provides a mini lesson and eamples to help refresh your memory. If you need help you can me or check out the following sites \ tm You can also Google the topic terms and find your own resource to learn from. You will need at minimum a TI-84 calculator (any other TI is also good just make sure to know how to use it) which is required for the class. is a website where you can find tutorials on how to use the basic functions of the calculator and are also part of the learning packet. Answers to select problems will be posted throughout the summer. Good Luck! Mr. Dien

2 AP Calculus AB CCHS Summer Review Packet Name Topic 1: Functions

3 Topic : Domain and Range

4 Topic 3: Graphs of Common Functions

5 Topic 4: Even/Odd Functions and Symmetry

6 Topic 5: Function Transformations

7 Topic 6: Special Factorization

8 Topic 7: Linear Functions

9 Topic 8: Asymptotes

10 Topic 9: Negative and Fractional Eponents

11 Topic 10: Comple Fractions

12 Topic 11: Absolute Value Equations

13 Topic 1: Eponential Functions and Logarithms

14 Topic 13: Basic Right Angle Trigonometry

15 Topic 14: Special Angles

16

17 AP Calculus AB CCHS Summer Review Packet Name f = 4, find: 1.) If ( ) a.) f ( 4) f ( 4) b.) Topic 1: Functions 3 f c.) ( + ) ( ) f h f h.) If f ( ) and g( ) are given in the graph, find: a.) ( f g)( 3) b.) f g ( 3) ( ), < 0 f = 1, 0 <, find: +, 3.) If ( ) a.) f ( 0) f ( ) b.) 5 f ( 4) c.) f ( f ( 3) )

18 Topic : Domain and Range Find the domain of the following functions using interval notation: 1.) f ( ) = 3.) 3 y = + 3.) y = ) y = 16 f 5.) ( ) 1 = ) y= = 8.) y = 49 7.) y log( 10) 9.) y = 5 log Find the range of the following functions: 10.) y 4 = ) 100 y = 1.) y = Find the domain and range of the following functions using interval notation: 13.) 14.) 15.)

19 Topic 3: Graphs of Common Functions Sketch each of the following as accurately as possible. You will need to be VERY familiar with each of these graphs throughout the year. You may use a graphing calculator for some of them if you have access to one over the summer. Another option is to find a graphing app ( or generate a table of values. Again, these are VERY important graphs to know. Be very accurate with regards to open circles and closed circles. 1. y=. y = 3. y 3 = 4. y = 5. y= 6. y= 4

20 7. y= y= 3 9. y= sin 10. y = cos 1 1 π 3π/ π π/ π/ π 3π/ π π 3π/ π π/ π/ π 3π/ π y = e 16. y = ln y = 19. y =

21 Topic 4: Even/Odd Functions and Symmetry Show work to determine if the relation is even, odd, or neither. 3 f = 4 3.) f ( ) = 3 1.) f ( ) = 7.) ( ) 4.) f ( ) = ) f ( ) = 8 6.) f ( ) = 8

22 Topic 5: Function Transformations If f ( ) = 1, describe in words what the following would do to the graph of f ( ): 1.) f ( ) 4.) f ( 4) 3.) f ( + ) 4.) 5f ( ) ) f ( ) 6.) f ( ) Here is a graph of y f ( ) = : Sketch the following graphs: y f 7.) = ( ) 8.) y= f ( ) 9.) y= f ( 1) 10.) y= f ( ) + 11.) y f ( ) = 1.) y= f ( )

23 Topic 6: Special Factorization Factor completely. 3 1.) + 8.) ) 7 15y ) ) ac + cd ab bd 6.) y y 7.) y 8.) 3 3 y y y + 9.) ( 3) ( + 1) + ( 3) ( + 1) 3 3

24 Topic 7: Linear Functions 1.) Find the equation of the line in point-slope form, with the given slope, passing through the given point. a.) m = 7, ( 3, 7) b.) m = 1, (, 8 ).) Find the equation of the line in point-slope form, passing through the given points. 3, 6, 1, 7, 1, 3, 4 a.) ( ) ( ) b.) ( ) ( ) 3.) Find the equations of the lines through the given point that are a.) parallel and b.) normal to the given line. 6,, 5 y 7 3, 4, y = a.) ( ) + = b.) ( ) 4.) Find the equation of the line in general form, containing the point ( 4, ) the points ( 1, 4) and (, 3 ). and parallel to the line containing 5.) Find k if the lines 3 5y = 9and + ky= 11are a.) parallel and b.) perpendicular.

25 Topic 8: Asymptotes For each function, find the equations of both the vertical asymptote(s) and horizontal asymptote (if it eists) and the location of any holes ) y =.) y = 3.) y = ) y = ) y = 5 6.) y = ) y = 8.) y = ) y =

26 Simplify and write with positive eponents. 5 1.) 1 5.) ( 1 ) Topic 9: Negative and Fractional Eponents 1 3.) ( 4 ) 1 4.) ) 3 5 y ) ( ) ) ( ) ) ( ) ) ( 3 ) ) ( ) + y 1 11.) ( )

27 Topic 10: Comple Fractions Eliminate the comple fractions: 1.) ) ) + + y y 1 1

28 Topic 11: Absolute Value Equations Solve the following equations: 1.) = 0.) 1 7 = 13 3.) 8+ + = 40 4.) = 0

29 Topic 1: Eponential Functions and Logarithms Simplify the following: (remember ln of a number (not variable) is just a number!) ) log.) log ) ln 3 e log ) 5 5.) log + log 9 + log 8 ln1 e 6.) ) 3 4 log + log 8.) log 1 log ) log ( ) Solve the following: log ) ( ) 5 = 11.) log ( 9 3) 1 + = 1.) ( ) log 3 + log5 = 13.) log ( 1) + log ( + 3) = 5 14.) ( ) log + 3 log = 15.) 5 5 ln ln = ) 3 = ) 3 1 e + = ) 8 = 5 1

30 Topic 13: Basic Right Angle Trigonometry Solve the following: If point P is on the terminal side of θ, find all 6 trigonometric functions of θ. (Answers need not be rationalized.) 1.) (,4) P.) P( 5, ) Topic 14: Special Angles 1.) π 3π cos tan 3 4.) sin π tan π sin π tan π Determine whether each of the following statements is true or false. 5π 5π cos + 1 cos π π π π 3.) sin + sin = sin + 4.) 3 = π 5π tan sec Good job now go to and go through how to use basic functions of the graphing calculator. also has lessons to teach you how to use the more modern TI calculators.