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Analytic geometry

bccalcclassact6avectors

Subject: 
Calculus
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Vectors
Vector Calculus
Linear algebra
Abstract algebra
Euclidean vector
Vector
Analytic geometry
Vector notation
Geometric algebra

Name:________________________ Date:________________________ AP Calculus BC Class Activity 6a: Vectors Given the following vectors: and : Find the vector: Find the vector: Find the direction (in radians) and magnitude of the following vectors: Given the following direction and magnitude, find a vector that represents it: , 12 2 rad, 6 Find a unit vector in the direction of . Find the angle between the vectors and . Find the magnitude of the vector between the vectors and .
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bccalcclassact5bparametric

Subject: 
Calculus
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Analytic geometry
Differential geometry
Curves
Multivariable calculus
equations
Parametric equation
Tangent
Parametric
derivative
Generalizations of the derivative
Implicit curve
Envelope

Name:________________________ Date:________________________ AP Calculus BC Class Activity 5b: Parametric Equations and Calculus Find the derivative for the following parametric equations: x = t2 + 1 and y = 2t3 ? t2 x = 3 sin t and y = 4cos t ? 1 Find the second derivative for the following parametric equations: x = t2and y = t2 + 6t + 5 x = ln t and y = t2 + t A curve C is defined by the parametric equations x = t2 + t ? 1 and y = . Find in terms of t. Find an equation of the tangent line to C through the point where t = 2. A curve C is defined by parametric equations x = t2 ? t + 1 and y = t3 ? 3t. Find all points where the tangent line is horizontal. Find all points of vertical tangency.

bccalcclassact5aparametric

Subject: 
Calculus
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Curves
Functions and mappings
Analytic geometry
equations
Multivariable calculus
Parametric equation
Function
Calculus
Parametric
Parameter
Fish curve
Implicit curve

Name:________________________ Date:________________________ AP Calculus BC Class Activity 5a: Parametric Equations Complete the value of table below and graph the curve for and y = t x y -2 -1 0 1 2 3 Complete the table below and graph the curve for and . t x y 0 ? 2? For the following problems eliminate the parameter and find y as a function of x. and and Given the function below and an equation for x, find one parametric curve that could represent it: and and Use

Precalc conic review station activity

Subject: 
Trigonometry
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Conic sections
Analytic geometry
Curves
Orbits
Hyperbola
Semi-minor axis
Ellipse
focus
Parabola
eccentricity
Semi-major axis
Asymptote

Station 1: Write the equation for a circle with a diameter that has endpoints of (1, 5) and (12, -2). Station 2: Find an equation for the hyperbola with center at (1, -2) and vertices at (4, -2) and (-2, -2), with a conjugate axis of length 10. Station 3: Determine an equation for the parabola with focus (3, 6) and directrix y = -2. Station 4: Find the vertex, focus, directrix and focal width of the parabola with equation , then graph it. Station 5: Determine an equation for the parabola with vertex (2, 4) and focus (0, 4). Station 6: Determine the major and minor vertices, center, and foci of the ellipse , then graph it. Station 7: Determine what type of conic is, then identify all key information and graph it. Station 8:

AP calc pre req practice test

Subject: 
Calculus
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Functions and mappings
Analytic geometry
Asymptote
Mathematical analysis
Limit of a function

AP Calculus AB Name:________________________________________ AP Problem Set: Prerequisites and Limits Signature (indicating you worked alone):___________________________________________ No calculator allowed. ALL WORK MUST BE COMPLETED ON A SEPARATE SHEET OF PAPER IN NUMERICAL ORDER WITH THIS SHEET STAPLED BEHIND IT. If I can?t read it, you will earn a 0 on this assignment. If your work does not support your answer choice, you will earn a 0 on this assignment! 1. If , then the inverse function, , is given by (A) (B) (C) (D) (E) 2. Which of the following function are continuous for all real numbers x? I. II. III. (A) None (B) I only (C) II only (D) I and II (E) I and III

Math A Guide

Subject: 
Algebra
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Differential calculus
Data analysis
rates
Analytic geometry
equations
Normal distribution
Variance
Expected value
derivative
Linear equation
Trigonometric functions
Cumulative distribution function

A-Level Maths Revision notes 2015 1 Contents Coordinate Geometry ........................................................................................................................... 3 Trigonometry ......................................................................................................................................... 5 Basic Algebra ......................................................................................................................................... 8 Advanced Algebra ............................................................................................................................... 10

Calculus AB #1

Subject: 
Calculus
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Mathematics
Analytic geometry
Elementary mathematics
geometry
Elementary algebra
equations
Linear equation
Slope
Y-intercept
Multivariable calculus
Second partial derivative test
law

?4 ?2 2 4 ?2 2 ?4 ?2 2 4 ?2 2 ?4 ?2 2 4 ?2 2 ?6 ?4 ?2 2 4 6 ?6 ?4 ?2 2 4 6 Ws zero ? review intercepts, linear equations Calculus AB SHOW WORK IN YOUR NOTEBOOK. Name the equation of the line from the graph below. 1. Find the slope. 2. ( ) ( )2,3 , 2, 5? ? 3. 7 3 5 1, , , 8 4 4 4 ? ? ? ??? ? ? ?? ? ? ? 4. ( ) ( )4,3 , 4, 1? ? ? Name three points on the line indicated. 5. 2 3y x= ? 6. 2 3 8x y? = Find the equation of the line that 7. passes thru the points (2,-3) and (-4, -6) in standard form. 8. passes thru the points (-1,3) and (5, 7) in standard form. 9. parallel to 2 3 8x y? = and thru (-2,-2) in point slope form. 10. perpendicular to 3 5 8x y? = and thru (-1,- 4) in standard form.

AP Calc AB 2004 Scoring Guidelines (Form B)

Subject: 
Calculus
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Mathematical analysis
Mathematics
Functions and mappings
Integral calculus
Analytic geometry
Differential geometry
Elementary geometry
Tangent
integral
Calculus
Mean value theorem
Antiderivative
education

AP? Calculus AB 2004 Scoring Guidelines Form B The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT?, the PSAT/NMSQT?, and the Advanced Placement Program? (AP?). The College Board is committed to the principles of

6.2 Notes

Subject: 
Algebra
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geometry
Elementary geometry
Quadrilaterals
Analytic geometry
Orientation
Perpendicular
Slope
line
Trapezoid
Parallelogram
Rectangle
Parallel

Unit 6 ? Linear Functions ? Slopes of Parallel & Perpendicular Lines Example 1 Plot points A(-4, 0) and B(-2, 4) and connect them. Plot points C(0, -2) and D(3, 4) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Example 2 Plot points A(1, 4) and B(-2, 3) and connect them. Plot points C(-2, 5) and D(0, -1) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Parallel lines have ________________ slope. Perpendicular lines have slopes that are the ______________________ of each other. When you multiply the slopes of perpendicular lines together, the product will be ______.

Relations and Functions Final Review

Subject: 
Algebra
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Mathematics
Analytic geometry
Elementary mathematics
Elementary algebra
equations
Functions and mappings
Linear equation
Slope
line
Continuous function
Function
Bresenham's line algorithm

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 t (Min) 1 2 3 4 5 6 d (km) 1 2 3 4 5?1?2?3?4?5 x 1 2 3 4 5 ?1 ?2 ?3 ?4 ?5 y Relations and Functions Practice Questions 1. The following distance-time graph represents the distance (in kilometres) a person bicycled during a 50-min period. Describe a possible scenario. 2. The table of values shows the cost of movie tickets at a local theatre. Number of Tickets Cost ($) 1 12 2 24 3 36 4 48 (a) Is this a linear or non-linear relationship? Explain how you know. (b) Assign a variable to represent each quantity in the relation. Which variable is the dependent variable and which is the independent variable?

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