AP Calculus Calculator Boot Camp UCLA AP Readiness Oct 17 This Lesson is to prepare students to use the TI-84 calculator on the Calculus AB Exam 1. 2. 3. 4. Students should be familiar with the College Board AP Calculus AB Home Page Where can I get a graphing calculator? Official AP Policy on graphing calculators Other Resources A. desmos.com – Another great way to graph B. www.wolframalpha.com - Calculates everything (almost) C. www.calculusapplets.com - Great visualizer, calculator, lessons D. www.mathbits.com- Instructions on calculator use I. Graphing Functions and Analysis II. Derivatives “Math 8” NDeriv (f(x), x, c) Example: A particle moves along the x-axis according to the function s(t)= t 3 −10t 2 + 13t + 24 from t = 0 to 8.2 seconds.’ A. Change Window Settings ___ B. Examine a Table of Values ____ C. Find a Specific Value --- Find s(3.6) ___ D. Find Relative Minima and Maxima ___ E. Find an intersection -- Another particle travels according to the function s(t)=2t+1 When will they cross? ____ F. Find the Zeros ** How many times will the particle cross the y-axis? Where? G. Draw a tangent line to a point Draw the tangent to s(t) at t = 2 ___ Example: Use the same position function as above s(t)= t 3 −10t 2 + 13t + 24 Find the derivative at a certain point ** Find s’(3) Find Velocity -- Find v(2) Find Acceleration -- Find a(2) Find the equation of the tangent line to s(t) at t=3 Graph the Derivative Mean Value Theorem - What is the average velocity of the particle from t=0 to 8? When does the mean value theorem hold true for this velocity? E. Find a maximum/minimum Find the relative and absolute extrema on t=0 to 8.2 1. Second Derivative Test 2. Maximum rate of change What was the maximum acceleration? 3. Maximum velocity vs. maximum speed What was the maximum velocity? Speed? F. Related Rates A. 1. 2. B. C. D. III. Integrals “Math 9” Fnint(f(x), x, a, b) Examine f (x) = −x 2 + 4 x + 5 A. Calculate a Definite Integral (FTC I) Evaluate ∫ 4 0 f (x)dx B. Find the Area Under a Curve Find the area in Quadrant I bounded by f(x), and the x and y axis C. Find the Area Between Two Curves g(x)=2x-1 Find the area bounded by f(x) and g(x) AP Calculus Calculator Boot Camp UCLA AP Readiness Oct 17 D. Find Volume by Disks Find the Volume of the region bounded by f(x) and the x axis rotated about the x axis E. Find Volume by Washers Find the volume of the region bounded by f(x) and g(x) rotated about the line y=10 F. Find Volume With Cross Sections Find the volume of the region bounded by f(x) and the x axis whose cross sections are semicircles perpendicular to the x-axis G. Average Value Theorem Find the average value of f(x) in the interval x=0 to 5. At what value of c does f(x) obtain this value? H. Distance and Displacement IV. Special Reminders A. B. C. D. E. F. G. Radian mode for physics problems Do not use calculator language on the AP- write derivatives and integrals correctly Your calculator can lie to you- be careful Three Decimal Places!! You don’t need a calculator to get a 5 Use common sense and guessing strategies Don’t let the calculator slow you down!