Interesting problems from the AMATYC Student Math League Exams
... the product of exactly three different primes. Let N be the sum of these three primes. How many other positive integers are the products of exactly three different primes with this sum N? 3002 2 19 79 , so N 2 19 79 100 . p1 p2 p3 100 , since the sum of three distinct ...
... the product of exactly three different primes. Let N be the sum of these three primes. How many other positive integers are the products of exactly three different primes with this sum N? 3002 2 19 79 , so N 2 19 79 100 . p1 p2 p3 100 , since the sum of three distinct ...
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... cycles are composite since they may be found using (c). Parts (b) and (f) together imply that Fl(d) is in a cycle whenever /' > k. Before continuing, we illustrate the previous theorem and definitions. We begin with g = 5. By Theorem 2(b), d is in an F5-cycle if and only if d is odd. Since F(l) = | ...
... cycles are composite since they may be found using (c). Parts (b) and (f) together imply that Fl(d) is in a cycle whenever /' > k. Before continuing, we illustrate the previous theorem and definitions. We begin with g = 5. By Theorem 2(b), d is in an F5-cycle if and only if d is odd. Since F(l) = | ...
ACT PRACTICE MATHEMATICS TEST 60 Minutes – 60 Questions
... A hiking group will go from a certain town to a certain village by van on 1 of 4 roads, from the village to a waterfall by riding bicycles on 1 of 2 bicycle paths, and then from the waterfall to their campsite by hiking on 1 of 6 trails. How many routes are possible for the hiking group to go from t ...
... A hiking group will go from a certain town to a certain village by van on 1 of 4 roads, from the village to a waterfall by riding bicycles on 1 of 2 bicycle paths, and then from the waterfall to their campsite by hiking on 1 of 6 trails. How many routes are possible for the hiking group to go from t ...
2-Year Scheme of Work: Overview
... 5 year Higher Scheme of Work This 5-Year Higher Scheme of Work offers a flexible approach for Year 7 to Year 11. It is based on a minimum of seven one hour Maths lessons per fortnight (assuming a two week timetable of three lessons in one week and four in the second). This accounts for an average of ...
... 5 year Higher Scheme of Work This 5-Year Higher Scheme of Work offers a flexible approach for Year 7 to Year 11. It is based on a minimum of seven one hour Maths lessons per fortnight (assuming a two week timetable of three lessons in one week and four in the second). This accounts for an average of ...
Scientific notation
... If the corresponding power of 10 is greater than 0 (ie positive), the prefix is known as a decimal multiple. If the corresponding power of 10 is less than 0 (ie negative), the prefix is known as a decimal sub-multiple. A list of common multiples and sub-multiples is shown in Table 4. EEE042A: Append ...
... If the corresponding power of 10 is greater than 0 (ie positive), the prefix is known as a decimal multiple. If the corresponding power of 10 is less than 0 (ie negative), the prefix is known as a decimal sub-multiple. A list of common multiples and sub-multiples is shown in Table 4. EEE042A: Append ...
What is a fraction
... Equivalent Fractions Equivalent fractions are fractions, which have the same value as each other. A quick way to tell whether or not two fractions are equivalent is to change them both into decimals using a calculator. If the two decimals are identical, then the fractions have the same value. ...
... Equivalent Fractions Equivalent fractions are fractions, which have the same value as each other. A quick way to tell whether or not two fractions are equivalent is to change them both into decimals using a calculator. If the two decimals are identical, then the fractions have the same value. ...
Farey Sequences, Ford Circles and Pick`s Theorem
... 1875, and published his first mathematics paper the following year. He studied both math and physics, and graduated with an endorsement to teach the two subjects. An interesting side note is that Leo Konigsberger was his advisor during this period. Pick received his doctorate in 1780. Pick studied o ...
... 1875, and published his first mathematics paper the following year. He studied both math and physics, and graduated with an endorsement to teach the two subjects. An interesting side note is that Leo Konigsberger was his advisor during this period. Pick received his doctorate in 1780. Pick studied o ...
scholastic aptitude test - 1995
... 5. Let ABCD be a square. Let P,Q,R,S be respectively points on AB,BC,CD,DA such that PR and QS intersect at right angles. Show that PR=QS. 6. Let ABC be any triangle. Construct parallelograms ABDE and ACFG on the outside D ABC. Let P be any point where the lines DE and FG intersect. Construct a para ...
... 5. Let ABCD be a square. Let P,Q,R,S be respectively points on AB,BC,CD,DA such that PR and QS intersect at right angles. Show that PR=QS. 6. Let ABC be any triangle. Construct parallelograms ABDE and ACFG on the outside D ABC. Let P be any point where the lines DE and FG intersect. Construct a para ...
Full text
... We can use the above results to derive some elementary bounds for lengths of the subtractive Euclidean algorithm valid for almost all pairs (777, ri) with 1 < n < x, 1 < 77? < x, as x -> 00. For convenience, we denote the subtractive length for the pair (m, n) by L(m9 n) and the set of all x2 pairs ...
... We can use the above results to derive some elementary bounds for lengths of the subtractive Euclidean algorithm valid for almost all pairs (777, ri) with 1 < n < x, 1 < 77? < x, as x -> 00. For convenience, we denote the subtractive length for the pair (m, n) by L(m9 n) and the set of all x2 pairs ...
Three Meanings of Fractions
... Operations with Fractions • The key to helping children understand operations with fractions is to make sure they understand fractions, especially the idea of equivalent fractions. • They should be able to extend what they know about operations with whole numbers to operations with fractions. ...
... Operations with Fractions • The key to helping children understand operations with fractions is to make sure they understand fractions, especially the idea of equivalent fractions. • They should be able to extend what they know about operations with whole numbers to operations with fractions. ...
2.4 BCD 2.5 Signed numbers
... • Binary Coded Decimal is just what it says it is. Here the decimal digits 0 - 9 are coded into binary. For each digit we need 4 bits. 0000, 0001, . . . , 1001. The remaining 4-bit numbers are not used. 13710 = 0001 0011 0111 (BCD) • This is not the same as Binary! looks like binary but... • BCD pro ...
... • Binary Coded Decimal is just what it says it is. Here the decimal digits 0 - 9 are coded into binary. For each digit we need 4 bits. 0000, 0001, . . . , 1001. The remaining 4-bit numbers are not used. 13710 = 0001 0011 0111 (BCD) • This is not the same as Binary! looks like binary but... • BCD pro ...
Geometry 1
... triangles, types of quadrilaterals and general polygons. Many exercises in this chapter on geometry need you to prove something or give reasons for your answers. The solutions to geometry proofs only give one method, but other methods are also acceptable. ...
... triangles, types of quadrilaterals and general polygons. Many exercises in this chapter on geometry need you to prove something or give reasons for your answers. The solutions to geometry proofs only give one method, but other methods are also acceptable. ...
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.