FRQ Review

Test Review Retakes by Wed

FRQs 7(AB) or 10(BC) types 6 questions per year 9 points each Questions 1 and 2 – calculator Questions 3-6 – non calculator Do NOT use pronouns Review 1 type each day Quiz on 3 types after 3 days

FRQs – 7 types 1) Rate/accumulation 2) Particle motion on line 3) Graph analysis 4) Area Volume 5) Table Questions 6) Implicit Differentiation / Related Rates 7) Differential Equations

3 more types 8) Parametric / Vectors 9) Polar 10) Series

Rate/Accumulation Section 5.5, 5.4 Net change = definite integral of rate How much (total amount) at t = ? – Add the initial amount to the integral Derivative concepts can appear in these questions – Increasing/decreasing – Max/min

Wed March 16 Do Now The velocity of a particle is v(t) = 4t + 5 for [0, 5]. If the particle is at x = 2 when t = 0, find the position of the particle at t = 5

Particle Motion on a Line Particle traveling on a line Finding the position = Def Integral of velocity Distance traveled = Integral of |velocity| Acceleration = 2 nd deriv of position Speed = |velocity| Particle moving right/left -> +/- velocity Note: remember which derivative applies to position/velocity/acceleration

Thurs March 17 Do Now

HW Review

Graph Analysis ( , ) Identify what the graph represents – F(x), F’(x), or F’’(x) Does the question match the graph? – Min/max, inc/dec, concavity, inflection pts… – 1 st derivative: min/max = 0 and change sign, inc/dec = +/- – 2 nd derivative: inflection pts = 0 and change sign, concavity = +/- Remember the area function!

FRQ4: Area / Volume (Ch 6) Definite Integrals Bounds: intersection points Area: Greater area – smaller area – Dx: higher - lower – Dy: right - left Volume: cross sections – Integral area – Perpendicular to the __ axis: d__ Volume: rotations – Revolve around horiz/dx or vert/dy – Disks vs washers

FRQ7: Implicit(3.10) / Related Rates(3.11) and misc. When differentiating other variables (not “x”), we must use chain rule – Leave a placeholder (dy/dx, da/dt, etc) – Solve for whichever derivative Related Rates: – Set up equation relating all variables we need rates for – Differentiate equation implicitly with respect to T – Solve for missing rate

FRQ5: Table Questions Given a table of values, things that can be asked: – Rectangular or Trapezoidal sum (5.1, 7.8) – Definite integrals (5.4, 5.5) – Approximating derivative / slope (2.1) – Confirmation of IVT, MVT, etc (2.8, 4.3) – Derivative formulas (product rule, chain rule, etc) (3.3, 3.7) – Do NOT use regression to find functions!

Differential Equations April 4 Do Now Take the antiderivative of each 1) x ) tan x

FRQ6: Differential Equations (Ch 9) Separable Differential Equations – Don’t forget all integral rules – + C Slope Fields – Drawing, matching, sketching curve Euler’s Method (BC) – Only a few iterations Logistic Equations (BC) – Don’t need to solve; know how to find limit

FRQ8: Parametric/Vectors Parametric: – Dy/dx formula; use this to find tangent lines, horizontal/vertical tangents, etc – Speed and arc length formulas Vectors: – Change each component individually – All calculus techniques apply here (limits, derivatives, integrals)

FRQ9: Polar Remember the conversion formulas between (r,θ) and (x,y) Know the difference between dr/dθ and dy/dx – Dy/dx requires product rules for dy and dx Area Integrals – Recognize which region – May have to subtract or add multiple regions

FRQ10: Series Power Series – Radius of convergence / Interval of convergence – Ratio test Taylor Polynomials – Know the basic ones (e^x, sinx, cosx, 1/1-x) – Differentiate/integrate – Legrange error bound VS approximation error