AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

Mathematics

AHSME 1983

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematics
geometry
Mathematical analysis
pi
Division
Elementary arithmetic
Fraction
Numbers
Circle
religion

USA AIME 1983 1 Let x, y, and z all exceed 1 and let w be a positive number such that logxw = 24, logy w = 40, and logxyz w = 12. Find logz w. 2 Let f(x) = |x? p|+ |x? 15|+ |x? p? 15|, where 0 < p < 15. Determine the minimum value taken by f(x) for x in the interval p ? x ? 15. 3 What is the product of the real roots of the equation x2 + 18x+ 30 = 2 ? x2 + 18x+ 45? 4 A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is ? 50 cm, the length of AB is 6 cm, and that of BC is 2 cm. The angle ABC is a right angle. Find the square of the distance (in centimeters) from B to the center of the circle. A B C 5 Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of

AHSME 1984

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematics
Mathematics competitions
American Mathematics Competitions
Function
Area
Vehicle Identification Number
Number
Coil

USA AIME 1984 1 Find the value of a2 + a4 + a6 + ? ? ?+ a98 if a1, a2, a3, . . . is an arithmetic progression with common difference 1, and a1 + a2 + a3 + ? ? ?+ a98 = 137. 2 The integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0. Compute n15 . 3 A point P is chosen in the interior of 4ABC so that when lines are drawn through P parallel to the sides of 4ABC, the resulting smaller triangles, t1, t2, and t3 in the figure, have areas 4, 9, and 49, respectively. Find the area of 4ABC. A B C t3 t2t1 4 Let S be a list of positive integers - not necessarily distinct - in which the number 68 appears. The average (arithmetic mean) of the numbers in S is 56. However, if 68 is removed, the

AP Calc Study Guide

Subject: 
Calculus
Rating: 
0
No votes yet
Tags: 
Calculus
Mathematical analysis
Mathematics
Differentiation rules
Integral calculus
Integration by parts
Integration by substitution
Product rule
Natural logarithm
Quotient Rule
derivative
Differential equation
education

Copyright 1996,1997 Elaine Cheong All Rights Reserved Study Guide for the Advanced Placement Calculus AB Examination By Elaine Cheong 1 Table of Contents INTRODUCTION 2 TOPICS TO STUDY 3 ? Elementary Functions 3 ? Limits 5 ? Differential Calculus 7 ? Integral Calculus 12 SOME USEFUL FORMULAS 16 CALCULATOR TIPS AND PROGRAMS 17 BOOK REVIEW OF AVAILABLE STUDY GUIDES 19 ACKNOWLEDGEMENTS 19 2 Introduction Advanced Placement1 is a program of college-level courses and examinations that gives high school students the opportunity to receive advanced placement and/or credit in college. The Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus, covering a full-year college mathematics course.

great minds

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Topology
Geometric topology
Mathematics
space
Alexander polynomial
Knot theory
polynomials
Manifold
Alexander horned sphere
Knot
James Waddell Alexander II
about the great minds

Alexander, James Waddell, II born September 19, 1888, Sea Bright, New Jersey, U.S. ? died September 23, 1971, Princeton, New Jersey American mathematician and a founder of the branch of mathematics originally known as analysis situs, now called topology.

Precalculus Functions Anecdotes

Subject: 
Calculus
Rating: 
0
No votes yet
Tags: 
Mathematics
Mathematical analysis
geometry
trigonometry
Analytic geometry
Analytic functions
Functions and mappings
Conic sections
Hyperbola
Trigonometric functions
Sine
Logarithm
Precalculus Functions Anecdotes

1. Identity Function-This is the only function thats acts on every real number by leaving it alone 2. Square Root Function-Put any positive number into your calculator. Take the square root. Then take the square root again, and so on. Eventually you will always get 1. 3. Squaring Function-The graph of this function, called a parabola, had a reflection property that is useful in making flashlights and satellite dishes. 4. Cubing Function-The origin is called a ?point of inflection? for this curve because the graph changes the curvature at the point. 5. Reciprocal Function-This curve, called a hyperbola, also has a reflection property that is useful in satellite dishes. 6. Natural Log Function-This function increases very slowly. If the x-axis and y-axis

Pre-Calculus Functions Chart

Subject: 
Calculus
Rating: 
0
No votes yet
Tags: 
Mathematics
Mathematical analysis
trigonometry
Analytic functions
Trigonometric functions
Continuous function
Floor and ceiling functions
Sine
law
Other
Pre-Calculus Functions Chart

Sheet1 Formula Name Domain Range Increasing Interval Decreasing Interval Maximum Minimum x-Intercept y-Intercept End-Behavior VA HA Symmetry Continuity 1a(Parent) f(x)=x Identity Function (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Odd Continuous 1b f(x)=x-6 None (-?,?) (-?,?) (-?,?) None None None (6,0) (0,-6) y-->? None None Neither Continuous 1c f(x)=x+3 None (-?,?) (-?,?) (-?,?) None None None (-3,0) (0,3) y-->? None None Neither Continuous 1d f(x)=3x None (-?,?) (-?,?) (-?,?) None None None (0,0) (0,0) y-->? None None Neither Continuous 1e f(x)=-x None (-?,?) (-?,?) None (-?,?) None None (0,0) (0,0) y-->-? None None Neither Continuous 1f f(x)=-3x+6 None (-?,?) (-?,?) None (-?,?) None None (2,0) (0,6) y-->-? None None Neither Continuous 1g y=a(x-h) +k

Handbook

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematical analysis
Mathematics
Analytic functions
Integral calculus
Complex analysis
trigonometry
Exponentials
Hyperbolic function
Bessel function
Euler's formula
Integration by parts
Differential equation

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Bibliography; Physical Constants 1. Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Arithmetic and Geometric progressions; Convergence of series: the ratio test; Convergence of series: the comparison test; Binomial expansion; Taylor and Maclaurin Series; Power series with real variables; Integer series; Plane wave expansion

Formula

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
geometry
Mathematics
Triangles
equations
Triangle geometry
Exponentials
Elementary algebra
Area
Volume
Surface area
Circle
Right triangle
Algebra
Formula

| COMMON?MATH?FORMULAS? AREA(A) Square Rectangle Parallelogram Triangle Circle Trapezoid Sphere ? ? ??; ? ? ??; ? ? ??; ? ? 1/2??; ? ? ???; ?? ? ?1/2???1? ? ??2???; ? ? 4??? where s = any side of the square where l = length and w = width where b = base and h = height where b = base and h = height where ?= 3.14 and r = radius where s= Surface area SURFACE AREA (SA)of a: cube SA = 6?? where s = any side cylinder (lateral) ?? ? 2???; where ?=3.14, r = radius, and h = height PERIMETER (P) of a Square ? ? 4?; where s = any side Rectangle ? ? 2? ? 2?; where l = length and w = width Triangle ? ? ?1 ? ?2 ? ?3; where s = a side

Algebra Practice Exam

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Elementary algebra
Mathematics
equations
Linear
Algebra
Linear equation
education
algebra practice exam

GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ SCORE:?____/14 Part?1:?Identifying?slopes?and?y?intercepts Identify?the?slope?and?y?intercept?of?the?given?linear?equations 1.?? [y 2 ?4 2. y ? [? 4 ?2 3.? 0[ 0y 1 ?2 4.? y 3 2 [ ?1 5.? y [ 6.?? ?y 8 9 ?7 Part?2:?Graphing?Linear?Equations Graph?the?following?linear?equations 7.? ? [y 2 ?3 Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 8. [y 2 1 ?4 9.?? ?y [ Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 10.?? ? [y 2 3 ?1 Part?3:?True?or?False Circle?the?letter?T?is?the?statement?is?True?and?circle?the?letter?F?is?the?statement?is

Graphing Linear Equations

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematics
Elementary algebra
Elementary mathematics
Analytic geometry
Linear
Slope
Linear equation
education

GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ SCORE:?____/14 Part?1:?Identifying?slopes?and?y?intercepts Identify?the?slope?and?y?intercept?of?the?given?linear?equations 1.?? [y 2 ?4 2. y ? [? 4 ?2 3.? 0[ 0y 1 ?2 4.? y 3 2 [ ?1 5.? y [ 6.?? ?y 8 9 ?7 Part?2:?Graphing?Linear?Equations Graph?the?following?linear?equations 7.? ? [y 2 ?3 Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 8. [y 2 1 ?4 9.?? ?y [ Algebra?1?Honors GRAPHING?LINEAR?EQUATIONSName:____________________ Date:_________ 10.?? ? [y 2 3 ?1 Part?3:?True?or?False Circle?the?letter?T?is?the?statement?is?True?and?circle?the?letter?F?is?the?statement?is

Pages

Subscribe to RSS - Mathematics

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!