RMO 2000 - Olympiads
... 4. All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000-th number in this list. Solution: The number of 7-digit numbers with 1 in the left most place and containing each of the digits 1, 2, ...
... 4. All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000-th number in this list. Solution: The number of 7-digit numbers with 1 in the left most place and containing each of the digits 1, 2, ...
General Formulas Polygons
... pair of corresponding sides. AA’-. Theorem: if 2 Ls of I A are to 2 /s of other A. then As are SSS Theorem: if measures of corresponding sides of 2 As are proportional then As are SAS- Theorem: if measures of 2 sides of A are proportional to measures o12 corresponding sides of then As are another A ...
... pair of corresponding sides. AA’-. Theorem: if 2 Ls of I A are to 2 /s of other A. then As are SSS Theorem: if measures of corresponding sides of 2 As are proportional then As are SAS- Theorem: if measures of 2 sides of A are proportional to measures o12 corresponding sides of then As are another A ...
infinite series
... which is less than 1/108 when N = 5: the error bound is .000000001008 . . . ≈ 10−8 . The partial sum of (10) for n ≤ 5 with its error bound puts π in (3.141592651 . . . , 3.141592653 . . . ), so π = 3.14159265 . . . . The partial sum of (9) over n ≤ 10 with its error bound verifiably gives π to 15 d ...
... which is less than 1/108 when N = 5: the error bound is .000000001008 . . . ≈ 10−8 . The partial sum of (10) for n ≤ 5 with its error bound puts π in (3.141592651 . . . , 3.141592653 . . . ), so π = 3.14159265 . . . . The partial sum of (9) over n ≤ 10 with its error bound verifiably gives π to 15 d ...
3. f(x)
... 30. Find the length of the arc on a circle with a radius of 10 inches intercepted by a central angle of 145°. ...
... 30. Find the length of the arc on a circle with a radius of 10 inches intercepted by a central angle of 145°. ...
review for Exam #1: 5.1-7.2
... flavor can be used more than once and the order of the scoops does not matter? ...
... flavor can be used more than once and the order of the scoops does not matter? ...
Math Vocabulary
... ** To write fractions as percents: Rewrite the fraction with a denominator of 100 (making an equivalent fraction). Rewrite the new number that is on top of 100 as a % without the denominator. You may also divide the bottom into the top (denominator into the numerator) creating a decimal. Then move t ...
... ** To write fractions as percents: Rewrite the fraction with a denominator of 100 (making an equivalent fraction). Rewrite the new number that is on top of 100 as a % without the denominator. You may also divide the bottom into the top (denominator into the numerator) creating a decimal. Then move t ...
1.2 Adding and Subtracting Whole Numbers The Commutative
... 1) Align the numbers on the right side, making sure to stack digits so that all the ones digits are in one column, all the tens digits are in the next column, etc. 2) Begin with the ones column (the farthest right column). 3) Subtract the digits (top digit – bottom digit). -If top digit is smaller t ...
... 1) Align the numbers on the right side, making sure to stack digits so that all the ones digits are in one column, all the tens digits are in the next column, etc. 2) Begin with the ones column (the farthest right column). 3) Subtract the digits (top digit – bottom digit). -If top digit is smaller t ...
David Essner Exam 28 2008-2009
... 3. John invests $10,000 at 6% compounded once per year and George invests $10,000 at 6% compounded twice per year. At the end of one year, George’s investment is worth how much more than John’s? (a) $9 (b) $12 (c) $15 (d) $18 (e) $36 4. Towns A,B,C,D all lie in a straight line. Towns A,B are between ...
... 3. John invests $10,000 at 6% compounded once per year and George invests $10,000 at 6% compounded twice per year. At the end of one year, George’s investment is worth how much more than John’s? (a) $9 (b) $12 (c) $15 (d) $18 (e) $36 4. Towns A,B,C,D all lie in a straight line. Towns A,B are between ...
MATH-0910 Review Concepts (Haugen) Dividing Whole Numbers
... Unit 3 Decimals Exam 3 – Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, and 3.7 Writing a Word Name for a Decimal Using the Place Value System Comparing Two or More Decimals Rounding Decimals Identify the round off place and then apply rounding rules Adding and Subtracting Decimals Helps to add or subtract ...
... Unit 3 Decimals Exam 3 – Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, and 3.7 Writing a Word Name for a Decimal Using the Place Value System Comparing Two or More Decimals Rounding Decimals Identify the round off place and then apply rounding rules Adding and Subtracting Decimals Helps to add or subtract ...
Other Number Systems & Base-R to Decimal
... Repeated Multiplication-by-2 Method To convert decimal fractions to binary, repeated multiplication by 2 is used, until the fractional product is 0 (or until the desired number of decimal places). The carried digits, or carries, produce the answer, with the first carry as the MSB, and the last as ...
... Repeated Multiplication-by-2 Method To convert decimal fractions to binary, repeated multiplication by 2 is used, until the fractional product is 0 (or until the desired number of decimal places). The carried digits, or carries, produce the answer, with the first carry as the MSB, and the last as ...
Approximations of π
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.