Precalculus Honors - AP Calculus A Information and Summer Assignment

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1 Precalculus Honors - AP Calculus A Information and Summer Assignment General Information: Competenc in Algebra and Trigonometr is absolutel essential. The calculator will not alwas be available for ou to use. We will review Trigonometr, so this will be part of the first semester course.. You must be able to eplain our answers, b mathematics or written language. Just getting the correct number or epression is not sufficient for demonstrating understanding. You must have our own graphing calculator and be familiar with how to use it. During the school ear, ou must dedicate approimatel to 4 hours to homework and studing each week. Need Help? If ou need help, tr these websites. The have tutorials, videos, practice problems as well as practice tests. Our Pre Calculus tetbook will also have instructional videos. Summer Assignment: Complete each problem following the directions below. Head each of our pages with our printed first and last name in the upper right hand corner. Work each problem on a full sheet of lined or grid paper. Work must be shown for ever problem. For the short answer problems that ma not require work, write an eplanation stating wh ou think our 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 the are mess; so don t second guess obscure epressions OR stress too much if it onl appears to be incorrect. Do not skip problems, if ou don t know how to do it, at least attempt it. Don t worr whether ou get them all correct. You will have an opportunit to ask questions when school begins. This assignment will be graded for completion. Ever problem must be attempted. Contact Information: If ou have questions or concerns, feel free to me at brad.matson@dvusd.org The intent of this assignment is for ou to be comfortable with these concepts and skills.

2 . *Factor as indicated: = ( ) + 6 = ( ) + 4 c. = ( ) d. + = ( ) + + e. ( ) 5 ( ) = ( + ) ( ) f. + 5 = ( )( ) g. e + + e = ( )( ). *Factor completel: (You ma have to use snthetic division.) c. 8. *Let = +. Find when = 0 4. *If f ( ) =, find f ( 0), f ( ), f ( a), and f ( a + 5) + 5. Is = a zero of the function g ( ) =? Wh or wh 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 wh cannot equal. 7. The height and the diameter of a clinder are equal. Epress the volume of the clinder as a function of the radius. 8. *Graph f ( ) = ( )( +). Then tell if the graph of = f ( ) is above or below the -ais for each of the given set of - values: < ; < < 0 ; 0 < < ; >. 9. Graph f ( ) = 4 + 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 = 64 0 = 000 c. = 5 4. Let g be a linear function such that g( ) = 5 and g ( 6) =. Find the equation for g ( ) Find the equation of a line perpendicular to g ( ) that passes through the point (, 6)

3 5. Find the average rate of change for the following functions on the indicated interval. f ( ) = ; [ 0,4] f ( ) = ; [ 4, 5] 6. Write the equation of a line in point slope form that is perpendicular to 4 = 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 984, the Caring Cola Compan sold million gallons of sod B 00, the compan was selling 7 million gallons of sod What is the average rate of change in the number of gallons of soda per ear? = 9. Graph the circle + ( ) 5 0. Find the domain and range: f = 9 ( ) g ( ) =. Solve for the variable: = ( ) a b. Simplif 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. () = f ( ) () = f ( ) () = f ( ) + (4) = f ( ) (5) = f ( ) (6) = f ( ) 4. Find all real solutions + + = 0 f = e 5. *Give the function ( ) Sketch the graph of the function and its inverse, f ( ) State the equation of the inverse. 6. Let = and 5 7. Solve each equation. Give our answers to the nearest thousandth. log = 0. 7 passing through the point ( ) on the same set of aes. =. Between what two integers is a solution of the equation 4 = c. ln = Epress in terms of. (Solve for.) log = + log = 4log( + ) 9. Wh is ln e equal to? 0. What is the value of e? Where does it come from?. *Simplif completel: =. *Solve for : ( )( )( ) 0. Let f ( ) = +. Find f ( ) and f ( f ( ) ) 4. Simplif the epression: 5. Simplif: 4 ( 6m ) ( + h) + ( + ) h to the nearest thousandth. = 5 located?

4 5 c. d. 7 98k m 8 8a b 0 6. Let =, = 8, = 9 and. Evaluate m 6 4 = 4 i = = i 4 7. Identif the parent Function, describe the transformations that occur to graph each of the functions. Identif an and intercepts. = 6 = c. = + d. = 5 + e. = ( ) + f. = + 8. Find the Domain of the function and Range of each function. = + = + c. = 5 d. = Use Long Division to divide

5 40. Find the Domain of the function, Decide if the function is continuous, and identif an horizontal or vertical asmptotes. Also identif an and intercepts. 0 = 5 = c. = 4 See Vocabular List on net page!

6 Vocabular: In a Word document, write a mathematical definition for each of the following in our own words. Avoid using mathematical notation. This will be submitted via Canvas at the beginning of the school ear. Asmptote Average Rate of Change Closed Interval Coefficient Constant Continuous Dependent Variable Difference Domain Equivalent Estimate (v.) Evaluate Epand Factor Finite Function Graph (n.) Identit Independent Variable Infinite Intercept Intersection Interval Inverse Open Interval Product Prove Quotient Radian Range Relation Simplif Slope Solution Solve Sum (n.) Smmetr Variable Verif Zero