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AP Review Questions Chapters 1 – 4
Complete the analogy. Clark Kent : Superman :: Bruce Wayne : 10 1.Hulk 2.Batman 3.Spiderman 4.Wolverine 1234
A calculator may not be used on these questions. Unless otherwise stated, the domain of a function is assumed to be all real numbers x for which f(x) is a real number.
If x 2 + xy = 10, then when x = 2, / /7 4.3/2 5.7/2 1234
If 1.ln 2 2.ln 8 3.ln nonexistent
What is the instantaneous rate of change at x = 2 of the function f given by /6 3.½ Answer Now 1234
A particle moves along the x- axis so that its position at time t is given by x(t)=t 2 -6t+5. For what value of t is the velocity of the particle zero?
If f(x)=sin(e -x ), then f(x) = cos(e -x ) 2.cos(e -x ) + e -x 3.cos(e -x ) - e -x 4.e -x cos(e -x ) 5.-e -x cos(e -x ) 1234
An equation of the line tangent to the graph of y = x + cos x at the point (0,1) is 1.y = 2x y = x y = x 4.y = x – 1 5.y = 0 :
If f(x) = x(x+1)(x-2) 2, then the graph of f has inflection points when x = 1.-1 only 2.2 only 3.-1 and 0 only 4.-1 and 2 only 5.-1, 0 and 2 only 10 Seconds Remaining 1234
If = ky and k is a nonzero constant, y could be 1.2e kty 2.2e kt 3.e kt kty ky2 +.5 Answer Now 1234
The function f is given by f(x)=x 4 +x On which of the following intervals is f increasing? 1.(-.707, ) 2.(-.707,.707) 3.(0, ) 4.(-,0) 5.(-,-.707)
If f(x) = tan(2x), then
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
The derivative of a function f(x), denoted f’(x) is the slope of a tangent line to a curve at any given point. Or the slope of a curve at any given.
AP Calculus AB Exam 3 Multiple Choice Section Name:_____________ 2. An equation of the line tangent to the graph of f( x ) = x ( 1 – 2x) 3 at the point.
Lesson 12.1 Inverse Variation pg. 642 Objectives: To graph inverse variation. To solve problems involving inverse variation.
TurningPoint is student response system that can conduct multiple assessments, track student learning, collect real-time responses and allow you to create.
E-learning extended learning for chapter 11 (graphs)
1. If f(x) =, then f (x) = 2. Advanced Placement Calculus Semester One ReviewName:___________________ Calculator Active Multiple Choice 3. If x 3 + 3xy.
Warm Up A particle moves vertically(in inches)along the x-axis according to the position equation x(t) = t 4 – 18t 2 + 7t – 4, where t represents seconds.
Chapter 11 Trigonometric Functions 11.3 Graphs of Sine, Cosine and Tangent Functions.
Sin x = 0.62 Solve for 0° ≤ x ≤ 720°. From the calculator: sin = 38.3°
Review Problems Integration 1. Find the instantaneous rate of change of the function at x = -2 _ 1.
Section 4.1 – Antiderivatives and Indefinite Integration.
Motion in One Dimension Average Versus Instantaneous.
Section 4.2 – Differentiating Exponential Functions THE MEMORIZATION LIST BEGINS.
X and Y Intercepts. The y intercept is the point at which the graph of an equation crosses the y axis. y (0,3)(0,3) x y = 2x + 3.
Exam Review Chapters Q. Find the exact value of sin 240° sin 240°
Warm Up 10/3/13 1) The graph of the derivative of f, f ’, is given. Which of the following statements is true about f? (A) f is decreasing for -1 < x <
Inverse Trigonometric Functions Recall some facts about inverse functions: 1.For a function to have an inverse it must be a one-to-one function. 2.The.
Higher Order Derivatives. Find if. Substitute back into the equation.
Chapter 6 – Trigonometric Functions: Right Triangle Approach Inverse Trigonometric Functions and Right Triangles.
Chapter 5 Inverse Trigonometric Functions; Trigonometric Equations and Inequalities 5.1 Inverse sine, cosine, and tangent 5.2 Inverse cotangent, secant,
Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.
76.8 – Average Rate of Change = = -9 = – Average Rate of Change = = -9 =
Section 4.2 – Differentiating Exponential Functions Section 4.3 – Product Rule/Quotient Rule THE MEMORIZATION LIST BEGINS.
4.7 INVERSE TRIGONOMETRIC FUNCTIONS. For an inverse to exist the function MUST be one- to - one A function is one-to- one if for every x there is exactly.
Warm-Up Explain how you made each match (Without a calculator!)
Warm Up No Calculator 2) A curve is described by the parametric equations x = t 2 + 2t, y = t 3 + t 2. An equation of the line tangent to the curve at.
1 Derivatives: A First Look Average rate of change Instantaneous rate of change Derivative limit of difference quotients Differentiable implies continuity.
Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1.
3.8 Derivatives of Inverse Trigonometric Functions.
Functions. Objectives: Find x and y intercepts Identify increasing, decreasing, constant intervals Determine end behaviors.
Derivatives. What is a derivative? Mathematically, it is the slope of the tangent line at a given pt. Scientifically, it is the instantaneous velocity.
EXAMPLE 5 Verify a trigonometric identity Verify the identity cos 3x = 4 cos 3 x – 3 cos x. Rewrite cos 3x as cos (2x + x). cos 3x = cos (2x + x) Use a.
Chapter 6 – Graphs and Inverses of the Trigonometric Functions.
Basic Differentiation Rules. Derivative Rules Theorem. [The Constant Rule] If k is a real number such that for all x in some open interval I, then for.
MATHPOWER TM 12, WESTERN EDITION Chapter 4 Trigonometric Functions 4.3.
Physics Chapter 5. Position-Time Graph Time is always on the x axis The slope is speed or velocity Time (s) Position (m) Slope = Δ y Δ x.
Physics Chapter 2 Notes. Chapter Mechanics Study of the motion of objects Kinematics Description of how objects move Dynamics Force and why.
Finding x- and y-intercepts algebraically. y-intercepts For every point along the y-axis, the value of x will be zero (x=0) We can use this fact to find.
Chapter 4 Trigonometric Functions Inverse Trigonometric Functions Objectives: Evaluate inverse sine functions. Evaluate other inverse trigonometric.
We now know how to differentiate sin x and x 2, but how do we differentiate a composite function, such as sin (x 2 -4)?
Let c (t) = (t 2 + 1, t 3 − 4t). Find: (a) An equation of the tangent line at t = 3 (b) The points where the tangent is horizontal. ` ` `
5-5 Solving Right Triangles. Find Sin Ѳ = 0 Find Cos Ѳ =.7.
3.8 Derivatives of Inverse Trigonometric Functions.
Change in position along x-axis = (final position on x-axis) – (initial position on x-axis)
Review Algebra 1 Chapter
1 To find the x-intercepts of y = f (x), set y = 0 and solve for x. INTERCEPTS AND ZEROS To find the y-intercepts of y = f (x), set x = 0; the y-intercept.
Review Derivatives When you see the words… This is what you know… f has a local (relative) minimum at x = a f(a) is less than or equal to every other.
Starter a 6 c A 53° 84° 1.Use Law of Sines to calculate side c of the triangle. 2.Use the Law of Cosines to calculate side a of the triangle. 3.Now find.
Differentiation Mean Value Theorem for Derivatives.
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