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GT/AP Calculus

Test #9 (through Lesson 36)

  1. Antiderivative (Lesson 36 #4, #5, #6)
  2. Graphing Functions (Lesson 36 #12)
  3. Indefinite Integral (Lesson 35 #3, #4, #5, #6)
  4. Critical Numbers (Lesson 36 #2, #3)
  5. Limit of a Function (Lesson 36 #20)
  6. Critical Numbers (Lesson 37 #8)
  7. Implicit Differentiation (Lesson 36 #7, Lesson 35 #7, Lesson 34 #2)
  8. Slope of Tangent Line (Lesson 36 #10)
  9. Conic (Lesson 35 #23, Lesson 32 #15)
  10. Change of Base (Lesson 33 # 16)
  11. Graph of Rational Function (Lesson 36 #15)
  12. Use words to explain the behavior of a graph (Lesson 36 #13)
  13. Graph of Rational Functions (Lesson 34 #16)
  14. Product Rule (Lesson 34 #11 & #12)
  15. Implicit Differentiation (Lesson 37 #12)
  16. Integrate (Lesson 37 #9 & #10)

Test #8 (through Lesson 32)

  1. Equation of Tangent Line (Lesson 31 #12)
  2. Composition of Function
  3. Zeros of Functions (Lesson 31 #11)
  4. Antiderivative (Lesson 32 #3 & #4)
  5. Differentials with Product Rule (find dy) (Lesson 32 #9 & #10)
  6. Volume of a box in terms of x (Lesson 31 #1)
  7. Find sin(A – B)
  8. Find ’’(x) with Product Rule (Lesson 33 #9 but take second derivative)
  9. Identify & Graph Conic—ellipse (Lesson 31 #18)
  10. Trig Equation (Lesson 29 #12)
  11. State Zeros & Asymptotes of Rational Function (Lesson 32 #13)
  12. Sketch graph of cot(x) (page 165)
  13. Differentials (find dy)
  14. Differentials (find dy)
  15. Definition of Derivative (Show your work!!)
  16. Integrate

 

Test #7 (through Lesson 28)

  1. Derivative with GC (Lesson 28 #7)
  2. Definition of the Derivative (Lesson 28 #9)
  3. Third Derivative of Function (Lesson 27 #6, #7 #8)
  4. Derivative of Polynomials (Lesson 27 #2, #3, #4)
  5. Limit of a Function—from L or R     lim x→ -5+  (x2 + 4x – 5)/(x4 + 5x3) (Lesson 28 #15)
  6. A(t) = A0ekt Exponential Growth or Decay (Lesson 28 #1)
  7. Sketch a Graph of Function 
  8. Double Angle Identify 
  9. Sketch Graph of Rational Function (Lesson 28 #2 #3)
  10. Log Equation (Lesson 28 #14)
  11. Remainder Theorem (Lesson 28 #13)
  12. Definition of the Derivative—SHOW WORK
  13. Derivative of Functions (Lesson 25 #8)
  14. Derivative of Functions
  15. Derivative of Functions
  16. Derivative of Functions
  17. Derivative of Functions

 

Test #6 (through Lesson 24)

  1. Binomial Expansion (Lesson 24, #10)
  2. Translating a Graph based on Equation
  3. Translation of Graph (Lesson 24, #13)
  4. Limit → ∞ (Lesson 24, #18 & Lesson 23, #14 & 16)
  5. Approximate Zeros of a Polynomial
  6. Solve Trig Equation (Lesson 24, #8)
  7. Distance between a Point & Curve (Lesson 25, #1)
  8. Show that (Need to know sin2x + cos2x = 1)
  9. Find Derivative of Function (Lesson 24, #2-#6)
  10. Identify and graph BY HAND a Conic (Hyperbola) https://www.youtube.com/watch?v=E9jVNc4Phhg
  11. Domain
  12. Definition of the Derivative 
  13. Definition of the Derivative
  14. Definition of the Derivative
  15. Definition of the Derivative

 

Test #4

  1. Evaluate Limit
  2. Domain
  3. Use Double-Angle Identities
  4. Postive/Negative Intervals
  5. Sketch sin-1, cos-1, AND tan-1 (Page 84)
  6. Word Problem
  7. Definition of the Derivative
  8. Solve Exponential Equation
  9. Expand Log/Ln
  10. Solve Absolute Value Equation & Graph Solution
  11. Solve Trig Equation (sin2x + cos2x = 1 will be needed)
  12. Graph absolute value function
  13. Limit from a graph
  14. Limit from a graph
  15. Limit from a graph
  16. Limit from a graph
  17. Limit from a graph
  18. Limit from a graph
  19. Limit from a graph
  20. Limit from a graph

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/e/two-sided-limits-from-graphs

 

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-3/a/approximating-limit-values-from-a-graph

 

https://calcworkshop.com/limits/finding-limits-graphically/

 

Test #3

  1. Domain
  2. Limit of a graph
  3. Possible Rational Roots
  4. Sketch an Absolute Value Function
  5. Graph a Piecewise Functions
  6. Find Dimensions of a Rectangle & Square
  7. Evaluate a function
  8. Log Equation
  9. Quadratic Equation with Given Roots
  10. Use a Tangent Identity
  11. Remainder Theorem
  12. Develop a Double-Angle Identity
  13. Evaluate a Trig Expression
  14. Solve an Equation
  15. Points of Intersection (GC)
  16. Zeros of a Function (GC)
  17. Simplify Exponents

Test #2

  1. Graphing Exponential
  2. Definition of a Function
  3. Coordinates of point P
  4. Evaluate Trig Expression
  5. Similar Triangles
  6. Area of the region in terms of x
  7. Linear Variation
  8. [f(x + h) – f(x)]/h
  9. Point of Intersection (GC)
  10. Domain & Range
  11. Graph Sinusoid
  12. Develop an Identity
  13. Factor to solve for x
  14. Multiply Expressions
  15. Find Zeros (GC)
  16. Simplify Trig Expression

 

Test #1

  1. Simplify Trig Expressions
  2. Sum & Difference of Cubes
  3. Equation of Line
  4. Evaluate Trig Expression
  5. Summation
  6. System of Equations
  7. Factorials
  8. Converse, Inverse, & Contrapositive
  9. Complex Fraction
  10. Perpendicular Lines
  11. Quadratic Formula
  12. Graphing Calculator Questions (Intersection of two curves)
  13. Distance Formula
  14. Rationalizing Fractions
  15. Simplifying Radicals
  16. Simplifying Exponents

 

https://www.google.com/imgres?imgurl=https%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fc%2Fc9%2FUnit_circle_angles.svg%2F720px-Unit_circle_angles.svg.png&imgrefurl=https%3A%2F%2Fen.wikibooks.org%2Fwiki%2FTrigonometry%2FTrigonometric_Unit_Circle_and_Graph_Reference&docid=QG4XqAmcN5dozM&tbnid=Oeo5GOQ0YHmFvM%3A&vet=10ahUKEwj-8qixh7rkAhUNP6wKHblWCrYQMwhzKAEwAQ..i&w=720&h=720&safe=active&bih=969&biw=1920&q=unit%20circle&ved=0ahUKEwj-8qixh7rkAhUNP6wKHblWCrYQMwhzKAEwAQ&iact=mrc&uact=8

 

https://www.google.com/imgres?imgurl=https%3A%2F%2Fi.pinimg.com%2Foriginals%2F4a%2F76%2F71%2F4a767121ecfd926be5af413ee207c6a5.jpg&imgrefurl=https%3A%2F%2Fwww.pinterest.com%2Fpin%2F458100593341941515%2F&docid=PikN-Rt8s-uaRM&tbnid=VKuw1loMSBj3aM%3A&vet=10ahUKEwj-8qixh7rkAhUNP6wKHblWCrYQMwiUASgVMBU..i&w=2564&h=3314&safe=active&bih=969&biw=1920&q=unit%20circle&ved=0ahUKEwj-8qixh7rkAhUNP6wKHblWCrYQMwiUASgVMBU&iact=mrc&uact=8

 

Helpful links:

https://www.zweigmedia.com/RealWorld/calctopic1/derivgraphex.html

https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-9/e/connecting-function-and-derivatives

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_first_second.html