GCSE Maths revision booklet
... When you see a number, step the value of the number in the direction you are facing. After stepping, face the positive direction before continuing with the sum. Your position at the end will be the answer. ...
... When you see a number, step the value of the number in the direction you are facing. After stepping, face the positive direction before continuing with the sum. Your position at the end will be the answer. ...
Full text
... 1. T. I I'A. Bromwich, An Introduction to the Theory of Infinite Series, 2nd Ed., MacMiilan, London, 1931 . 2. I. 1 Good, "A Reciprocal Series of Fibonacci Numbers," The Fibonacci Quarterly, Vol. 12, No. 4 (Dec. 1974), p. 346. 3. I. J. Good and T. N. Grover, "The Generalized Serial Test and the Bina ...
... 1. T. I I'A. Bromwich, An Introduction to the Theory of Infinite Series, 2nd Ed., MacMiilan, London, 1931 . 2. I. 1 Good, "A Reciprocal Series of Fibonacci Numbers," The Fibonacci Quarterly, Vol. 12, No. 4 (Dec. 1974), p. 346. 3. I. J. Good and T. N. Grover, "The Generalized Serial Test and the Bina ...
1979 amc 12/ahsme - Art of Problem Solving
... Points A, B, C, and D are distinct and lie, in the given order, on a straight line. Line segments AB, AC, and AD have lengths x, y, and z , respectively. If line segments AB and CD may be rotated about points B and C, respectively, so that points A and D coincide, to form a triangle with positive ar ...
... Points A, B, C, and D are distinct and lie, in the given order, on a straight line. Line segments AB, AC, and AD have lengths x, y, and z , respectively. If line segments AB and CD may be rotated about points B and C, respectively, so that points A and D coincide, to form a triangle with positive ar ...
Numbers - The Basics
... the ratio of two integers, a/b. The numerator, "a", may be any whole number, and the denominator, "b", may be any positive whole number greater than zero. If the denominator happens to be unity, b = 1, the ratio is an integer. If "b" is other than 1, a/b is a fraction. Fractional Numbers - any numbe ...
... the ratio of two integers, a/b. The numerator, "a", may be any whole number, and the denominator, "b", may be any positive whole number greater than zero. If the denominator happens to be unity, b = 1, the ratio is an integer. If "b" is other than 1, a/b is a fraction. Fractional Numbers - any numbe ...
Solutions to RMO-2014 problems
... 3. Suppose for some positive integers r and s, the digits of 2r is obtained by permuting the digits of 2s in decimal expansion. Prove that r = s. Solution: Suppose s ≤ r. If s < r then 2s < 2r . Since the number of digits in 2s and 2r are the same, we have 2r < 10 × 2s < 2s+4 . Thus we have 2s < 2r ...
... 3. Suppose for some positive integers r and s, the digits of 2r is obtained by permuting the digits of 2s in decimal expansion. Prove that r = s. Solution: Suppose s ≤ r. If s < r then 2s < 2r . Since the number of digits in 2s and 2r are the same, we have 2r < 10 × 2s < 2s+4 . Thus we have 2s < 2r ...
Square Roots
... have finite (ends) number of digits. (ex 2/5= 0.40 ) • Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3=1.333333333) • Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole n ...
... have finite (ends) number of digits. (ex 2/5= 0.40 ) • Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3=1.333333333) • Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole n ...
Study Guide 7th gr decimals fractions 03/12/2010 Divide By
... right the same number of spaces as there are decimal places (so that it becomes a whole number). The decimal point must be moved the same number of places in the divisor and dividend. In this case, move the decimal point one place to the right in the divisor and on place to the right in the dividend ...
... right the same number of spaces as there are decimal places (so that it becomes a whole number). The decimal point must be moved the same number of places in the divisor and dividend. In this case, move the decimal point one place to the right in the divisor and on place to the right in the dividend ...
Name:
... To convert a decimal less than 1 into scientific notation, we move the decimal point to the ________ so that there is ___________ non-zero digit to the left of it. We then multiply by 10-n, where the number of n is __________ to the number of places we moved the decimal point. Convert the following ...
... To convert a decimal less than 1 into scientific notation, we move the decimal point to the ________ so that there is ___________ non-zero digit to the left of it. We then multiply by 10-n, where the number of n is __________ to the number of places we moved the decimal point. Convert the following ...
to your 11 Plus Maths assessment
... 73. A block of flats is 15 floors high, each floor has 6 flats on it and each flat has 10 windows. How many windows are there altogether in the block? ...
... 73. A block of flats is 15 floors high, each floor has 6 flats on it and each flat has 10 windows. How many windows are there altogether in the block? ...
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.