AP CALCULUS AB - SUMMER ASSIGNMENT 2018

Transcription

1 Name AP CALCULUS AB - SUMMER ASSIGNMENT 08 This packet is designed to help you review and build upon some of the important mathematical concepts and skills that you have learned in your previous mathematics class that you will be using in AP Calculus AB. All answers are epected to be accompanied by corresponding work. YOU MAY NEED TO LOOK UP INSTRUCTIONAL VIDEOS ONLINE FOR HELP! If needed, please reach out to me via (dhimmler@cvsd.net) if you have questions or concerns during the summer. Due Date: Wednesday (First Day of School) Points: 0 - THERE WILL BE A GRADED IN-CLASS ASSIGNMENT DURING THE FIRST DAY OF SCHOOL COVERING THIS MATERIAL - Section A Linear Equations For problems 7, based on the information given, write the linear equations in point-slope form y y m and slope intercept form y m b. NO CALCULATOR.. The line with a slope of passing through the point (, -).. The line that passes through the points (, ) and (, -).. The line that contains the point (-, ) and is parallel to y 7.. The line perpendicular to y 8containing the point (, -).. The line with a slope of -/ and an -intercept of. 6. A horizontal line that passes through the point (-, 6). Hint: what is the general equation for a horizontal line? 7. The line normal (perpendicular) to y = that passes through the point (, ). Hint: what is the general equation for a vertical line?

2 Section B Factoring, Simplifying, and Solving Equations using Factoring For problems -8, factor completely. NO CALCULATOR.. 8. t t t t For problems 9-0, simplify each epression using factoring. NO CALCULATOR For problems -, solve the following equations by factoring. NO CALCULATOR

3 Part C Eponents, Radicals, and Simplifying For problems -, simplify by writing without fractional or negative eponents. (fractional eponents should be epressed in radical form) NO CALCULATOR. f.. y. y 7. y For problems -8, write without fractional or negative eponents. Then evaluate the function at the given value. NO CALCULATOR.. f 6. g f g h 6 8. v t h6 v t 6 t

4 Part D Manipulating Equations and Solving Systems of Equations In problems -6, solve for y in terms of the other variable. You may need to use eponential/logarithmic properties some of them. NO CALCULATOR.. y. y 6 7y. ln y 6. e y 6. 7 y 6. lny 7 For problems 7-0, solve the system of equations using substitution or elimination. NO CALCULATOR. 7. y y 7 8. b a b a 9. y 9 y 6 0. a b 9 a b

5 Section E Intercepts and Functions For problems -, find the and y intercept(s), if they eist. NO CALCULATOR.. y 6. y For problems -, use the given functions to answer the following questions. NO CALCULATOR.. Given the function: f a. What are the zeros of the function? This means the intercepts. b. Find f.. Given f and g, find each of the following: a. f g0 b. g g c. g f d. f g. If f and g, find the following: a. g f b. gln c. f cos d. f gln

6 Section F Trigonometry For problems -6, determine the eact value of each epression. Try to envision the Unit Circle. NO CALCULATOR. cos. sin. csc. 0. cos 7. cos 6 6. cos 7 7. tan 8. tan 6 sin 0. sin 9.. cot. cos 7. cos. sin. tan 6. sin 6 6 For problems 7-0, find all solutions to each equation for factor before you can solve it. NO CALCULATOR. 0. For some of these problems, you may need to 7. sin sin 0 8. sin cos 0 9. cos 0 0. tan 0

7 Section G Eponentials and Logarithms For problems -, evaluate each epression. NO CALCULATOR. log 6. log. log. log 89 6 For problems -8, use properties of logarithms to epand each logarithmic epression. When possible, simplify if you can evaluate the logarithm. NO CALCULATOR. log 6. log y 7. ln 8. log 00 y. 000 For problems 9-, use properties of logarithms to condense each logarithmic epression. Write the epression as a single logarithm whose coefficient is. When possible, simplify if you can evaluate the logarithm. NO CALCULATOR. 9. ln ln 0. log log. ln 7ln y ln z. log log y For problems -6, solve the eponential or logarithmic equation. ONLY USE A CALCULATOR TO FIND THE DECIMAL APPROXIMATION TO THREE DECIMAL PLACES log ln ln ln