AP Calculus AB Information and Summer Assignment

Transcription

1 AP Calculus AB Information and Summer Assignment General Information: Competency in Algebra and Trigonometry is absolutely essential. The calculator will not always be available for you to use. Knowing the unit circle is required throughout the entire course. Almost all problems are worked in radian measure, not degrees. You must be able to eplain your answers, by mathematics or written language. Just getting the correct number or epression is not sufficient for demonstrating understanding. You must have your own graphing calculator and be familiar with how to use it. During the school year, you must dedicate approimately to hours to homework and studying each week. Need Help? If you need help, try these websites. They have tutorials, videos, practice problems as well as practice tests. Summer Assignment: Complete each problem following the directions below. Head each of your pages with your printed first and last name in the upper right hand corner. Work each problem on a full sheet of lined or grid paper. Fold the paper lengthwise and work in columns as much as possible. (But always work down; NOT across.) You may use both sides of the paper. Work must be shown for every problem. For the short answer problems that may not require work, write an eplanation stating why you think your answer is correct. There is a difference between graphing a function and sketching the graph. A graph includes significant points on a graph (i.e. local etrema and intercepts); where a sketch would give the appearance of the graph. Here are eamples: Not all answers are neat. Often they are messy; so don t second guess obscure epressions OR stress too much if it only appears to be incorrect. Do not skip problems, if you don t know how to do it, at least attempt it. Don t worry whether you get them all correct. You will have an opportunity to ask questions when school begins. This assignment will be graded for completion. Every problem must be attempted. Contact Information: If you have questions or concerns, feel free to me at cindy.knoll@dvusd.org. The intent of this assignment is for you to be comfortable with these concepts and skills.

2 . *Factor as indicated: *Problems with stars net to them should be done without a calculator. a. + = ( ) + 6 = ( ) + sin + tan = sin c. = ( ) d. ( ) e. + = ( ) + + f. ( ) ( ) = ( + ) ( ) g. + = ( )( ) h. e + + e = ( )( ). *Factor completely: (You may have to use synthetic division.) a. 8 c. 8 d. cos sin + cos + sin. *Let y = +. Find when y = 0. *If f ( ) =, find f ( 0), f ( ), f ( a), and f ( a + ) +. Is = a zero of the function g ( ) =? Why or why not? 6. The sides of a rectangle are and - in length. Epress the rectangle s area as a function of. Epress the rectangle s perimeter as a function. Eplain why cannot equal. 7. The height and the diameter of a cylinder are equal. Epress the volume of the cylinder as a function of the radius. 8. *Graph f ( ) = ( )( +). Then tell if the graph of y = f ( ) is above or below the -ais for each of the given set of - values: < ; < < 0 ; 0 < < ; >. 9. Graph f ( ) = + and g ( ) = + on the same set of aes. Find the coordinates of each intersection point. 0. For what value(s) of is the function ( ) ( + )( ) g = undefined? + 7 ( )( ). Give the dimensions of three different rectangles with the area 6cm 6. Each leg of an isosceles triangle is twice as long as its base. Epress the perimeter of the triangle in terms of the length b of the base.. *Solve for a. = 6 0 = 000 c. =. Let g be a linear function such that g( ) = and g ( 6) =. a. Find the equation for g ( ) Find the equation of a line perpendicular to g ( ) that passes through the point (, 6)

3 *Problems with stars net to them should be done without a calculator.. Find the average rate of change for the following functions on the indicated interval. a. f ( ) = ; [ 0,] f ( ) = ; [, ] 6. Write the equation of a line in point slope form that is perpendicular to y = 8, 7. A car travels 60 miles in a period of 80 minutes. Find the average speed in miles per hour over this time period. 8. In 98, the Caring Cola Company sold million gallons of soda. By 00, the company was selling 7 million gallons of soda. What is the average rate of change in the number of gallons of soda per year? = 9. Graph the circle + ( y ) 0. Find the domain and range: f = 9 a. ( ) g ( ) =. Solve for the variable: y = y( y ) a b. Simplify the comple fraction: b a a b. Write a description of how the graph of f changes:. Find the circumference and the area of the circle. () y = f ( ) () y = f ( ) () y = f ( ) + () y = f ( ) () y = f ( ) (6) y = f ( ). Find all real solutions + + = 0 f = e. *Give the function ( ) a. Sketch the graph of the function and its inverse, f ( ) State the equation of the inverse. passing through the point ( ) on the same set of aes. 6. Let y = and = y. Between what two integers is a solution of the equation 7. Solve each equation. Give your answers to the nearest thousandth. a. log = 0. 7 = c. ln = Epress y in terms of. (Solve for y.) a. log y = + log y = log( + ) 9. Why is lne equal to? 0. What is the value of e? Where does it come from?. *Simplify completely: a. c. 6 ( sin + cos ) sin. *Solve for : ( )( + )( ) 0. Let f ( ) = +. Find f ( ) and f ( f ( ) ). Simplify the epression: = ( + h) + ( + ) h to the nearest thousandth. = located?

4 . Simplify: a. ( 6m ) c. y y 7 98k m 8 0 *Problems with stars net to them should be done without a calculator. d. 8a b 6. Why are there π radians in the circumference of a circle? 7. Draw a picture of a single radian. 8. Fill in a Unit Circle and learn it!!! A blank unit circle can be found at EmbeddedMath.com. 9. A 0 foot ladder rest against a building feet from the floor. How far does the ladder etend from the base of the wall? What angle does the ladder make with the ground? π 0. *If tan θ = and π < θ <, find: a. csc θ sec θ c. cot θ. *Graph y = tan for π π.. *Solve cos + cos + = 0 for π π.. *Complete the following trig identities a. sin + cos = = sin c. tan + =. Graph y = cos and y = on the same set of aes. How many solutions does the equation cos = have?. Let =, = 8, = 9 and. Evaluate m 6 = See Vocabulary List on net page! i = = i

5 *Problems with stars net to them should be done without a calculator. Vocabulary: In a Word document, write a mathematical definition for each of the following in your own words. Avoid using mathematical notation. This will be submitted via Canvas at the beginning of the school year. Asymptote Average Rate of Change Closed Interval Coefficient Constant Continuous Dependent Variable Difference Domain Equivalent Estimate (v.) Evaluate Epand Factor Finite Function Graph (n.) Identity Independent Variable Infinite Intercept Intersection Interval Inverse Open Interval Product Prove Quotient Radian Range Relation Simplify Slope Solution Solve Sum (n.) Symmetry Variable Verify Zero