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Number

Weather Station Models

Subject: 
Environmental Science
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Mathematics
Arithmetic
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Elementary arithmetic
Binary arithmetic
Complex analysis
pi
Decimal
Atmospheric pressure
Hexadecimal
Number
Year 10,000 problem
behavior
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87 87 87 How to convert between station model number and actual barometric pressure: If the first number is less than or equal to 5, place a 10 in front of the number and a decimal between the last two digits If the first number is greater than 5 place a nine in front of the number and a decimal between the last two digits. * * *
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AHSME 1992

Subject: 
Algebra
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Mathematics
Abstract algebra
Integer sequences
Number theory
Triangles
Triangle geometry
Combinatorics
Number
Prime number
Triangle
Coprime
Integer
sports

USA AIME 1992 1 Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. 2 A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascending positive integers are there? 3 A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly .500. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than .503. What?s the largest number of matches she could?ve won before the weekend began?

AHSME 1991

Subject: 
Algebra
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Mathematics
Abstract algebra
Group theory
Number
quadratic equation
Summation

USA AIME 1991 1 Find x2 + y2 if x and y are positive integers such that xy + x+ y = 71x2y + xy2= 880. (0) Rectangle ABCD has sides AB of length 4 and CB of length 3. Divide AB into 168 congruent segments with points A = P0, P1, . . . , P168 = B, and divide CB into 168 congruent segments with points C = Q0, Q1, . . . , Q168 = B. For 1 ? k ? 167, draw the segments PkQk. Repeat this construction on the sides AD and CD, and then draw the diagonal AC. Find the sum of the lengths of the 335 parallel segments drawn. Expanding (1 + 0.2)1000 by the binomial theorem and doing no further manipulation gives ( 1000 0 ) (0.2)0 + ( 1000 1 ) (0.2)1 + ( 1000 2 ) (0.2)2 + ? ? ?+ ( 1000 1000 ) (0.2)1000 = A0 +A1 +A2 + ? ? ?+A1000, (0) where Ak = (1000 k )

AHSME 1984

Subject: 
Algebra
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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

Algebra 1

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Algebra
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Mathematics
Abstract algebra
Algebra
Elementary arithmetic
Binary operations
Elementary algebra
Negative number
Addition
multiplication
Number
Inequality
Distributive Property
education

Curriculum Map Staff Name: Mr. Kurth Course: Algebra 1 Month/Unit: Sept 6 ? Sep 17 UNIT 1 ? Tools of Algebra C O N T E N T Using Variables Exponents and Order of Operations Addition and Subtraction of Real Numbers Multiplication and Division of Real Numbers Distributive Property Various Properties of Real Numbers Graphing Data on a Coordinate Plane S K I L L S Add, Subtract, Multiply and Divide Variables Solve for variables Correct processing real numbers through the order of operations Use the distributive property Compare integers and real numbers

Rational Functions

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Algebra
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Mathematics
Abstract algebra
Algebra
Division
Polynomial
Fraction
Rational function
Number
Partial fraction
Algebraic number
education

Extending function arithmetic to division results in the family of "rational" functions (Quotients of polynomials) with the property that Let be the degree of the numerator and be the degree of the denominator A rational function is said to be: Strictly proper if Proper if Improper if Any rational function which is not strictly proper can be expressed as the sum of a polynomial and a strictly proper rational function Given with Let be the result of the quotient and be the remainder of the same quotient, then EXAMPLE: Any strictly proper rational function can be expressed as the sum of simpler rational functions whose denominators are quadratic or linear polynomials Display Mode:
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