IF you participate fully in this boot camp, you will get full credit for the summer packet.

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1 18_19 AP Calculus BC Summer Packet NOTE - Please mark July on your calendars. We will have a boot camp in my room from 8am 11am on this day. We will work together on the summer packet. Time permitting, we will tackle additional FRQs from past AB exams. IF you participate fully in this boot camp, you will get full credit for the summer packet. If you have the time and if there is sufficient room in the afternoon AB session, you may wish to participate in that session as well. Welcome to AP Calculus BC at Boca Ciega High School. I m Mr Lynch - all of you know me already. You should feel free to reach me at lynchr@pcsb.org. I will check my most days. Whether or not you passed the AP Calculus AB exam in May, you can be successful in AP Calculus BC. We will spend a fair amount of time reviewing the math we learned this last year in AB. The following pages include a review of most of the key concepts we learned. You should spend 1- hours on each of these 5 pages. For the FRQs on the last two pages, you can obviously find the answers posted online. However, you should seriously attempt these problems PRIOR to checking your answers.

2 18_19 AP Calculus BC Summer Packet Focus 1: Log and Exponential Functions Brief Notes: If y = b x then x = log b y 1) Rewrite y = ln(x) as an exponential equation ) Rewrite P = e t as a logarithmic equation ) Rewrite Q = m as a logarithmic equation 4) Without a calculator, solve for the unknown: x + 4 = 8 5) Use a calculator to solve for the unknown: 5 r = 7 6) Without a calculator, solve for the unknown: 5 + log ( x ) = 1 7) Use a calculator to solve for the unknown: + ln(4x) = 16 8) Rewrite using properties of logarithms: ln (x y) rewrite as logs to solve exp equations rewrite as exp to solve log equations 9) Rewrite using properties of logarithms: log ( x5 sin (x) ) 1) Rewrite using properties of logarithms: ln ( x5 tan (x) x +1 ) 11) Rewrite using properties of logarithms: ln (5e x /x ) 1) Rewrite using properties of logarithms: ln ( e x /5x 7 ) 1) Condense using properties of logarithms: ln(x ) ln ( x + 1) 14) Condense using properties of logarithms: ln(x) ln(y) ln (z) 15) Condense using properties of logarithms: ln(x) ln(y) + ln (z) 16) Condense using properties of logarithms: ln(x).5ln (x + 1) 17) Find the derivative f (x): f(x) = ln ( x cos (x) ) 18) Find the derivative f (x): f(x) = ln ( tan (x) x ) 19) Find the derivative f (x): f(x) = log (5x + x)

3 Focus : Derivatives Some rules: constant, power, product, quotient 1) Find dy given y = x + x cos (x) ) Find y given y = e (x +x) ) Find dh given h = x x x trig fns, e x, ln(x), implicit 4) Given functions u and v, with u() = 4, u () = 1, v() =, and v () = 5, find at x = : a. d (uv) c. d ( v ) u b. d (u v ) d. d (u uv) 5) Given h = xe x, find h (x) 6) Given xy y cosx = y, find dy 7) Find the slope of the Witch of Agnesi, given by y = 8 at the point (,1) 8) Given y = sin (x ), find y (x) 4+x 9) Given ln(xy ) + x 4 y + y =, find the slope at point (1,1) 1) Given functions u and v and values shown in the table, determine the following quantities : t u v u v a. Average RoC of u on (,8) c. Instantaneous RoC of v at t = 5 b. d dt (u(v())) d. d (u() u(v())) dt 11) Find any horizontal tangents to the curve y = x 9x 1x + 5 1) Determine the point at which the function y = x is perpendicular to the line y + 8x = 11 1) Find dm ex given m = x +1 14) Given f(x) = tan (x), find f (x)

4 Focus : Integrals Brief Notes: Do you need u-substitution? (probably) 1) Find ( sin(x) + 4x) PATTERN RECOGNITION ) Without a calculator, determine e t dt ) Find 4x+6 x +x π/4 4) Without a calculator, determine tan(t) sec (t) dt 5) Without a calculator, determine ( x4 x+1 ) 5 x 9 6) Given f(x) = 7 9 and f(x) = 5, determine f(x) 5 x 7) Given f(x) = (e t t) dt, find f (x) 8) Without a calculator, determine xe (x +1) x 9) Given g(x) = ( x), find g (x) 1) Determine the average value of y = x ) Without a calculator, determine x ) Without a calculator, determine (e x ) on the interval (6,5) 1) Determine cos(1 x ) x 14) Each labeled region (A, B, and C) in the graph of f(x) (shown to the right) has an area of square units. Determine (f(x) + ). 15) Use a calculator to determine 9 e x x +1 6 accurate to decimal places. π/4 16) Use a calculator to determine 5sin ( x4 + π/6 ) x+1 accurate to decimal places. 17) The graph of g (x) is shown to the right. If g() = 6, determine g().

5 t=b Focus 4: Net Accumulation (rate in rate out)dt = Final Amt Initial Amt t=a 1) 9 B - Calculator Required ) 8 A Calculator Required ) 4 A Calculator Required

6 x=b Focus 5: Volume Vol = x=a (PerpendicularCrossSectionalArea) 1) 8 B Calculator Required ) 8 A Calculator Required ) 7 B Calculator Required