Group 1 - Sara, Heather, and Bill Week 11 – Day 1 Title: Prime
... NYS Standards: Key Idea 3 – Operations 3A: Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions. Anticipatory Set: (5 minutes) Write this set of numbers on the board: 3, 7, 8, 11, 9, 12, and 24. Ask students to categorize the numbers i ...
... NYS Standards: Key Idea 3 – Operations 3A: Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions. Anticipatory Set: (5 minutes) Write this set of numbers on the board: 3, 7, 8, 11, 9, 12, and 24. Ask students to categorize the numbers i ...
Group 1 - Sara, Heather, and Bill Week 11 – Day 1 Title: Prime
... NYS Standards: Key Idea 3 – Operations 3A: Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions. Anticipatory Set: (5 minutes) Write this set of numbers on the board: 3, 7, 8, 11, 9, 12, and 24. Ask students to categorize the numbers i ...
... NYS Standards: Key Idea 3 – Operations 3A: Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions. Anticipatory Set: (5 minutes) Write this set of numbers on the board: 3, 7, 8, 11, 9, 12, and 24. Ask students to categorize the numbers i ...
IMO Shortlist 2004
... an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer n ≥ 4, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on n vertices (where ea ...
... an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer n ≥ 4, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on n vertices (where ea ...
Pascal`s triangle and the binomial theorem
... 4. The binomial theorem If we wanted to expand a binomial expression with a large power, e.g. (1 + x)32 , use of Pascal’s triangle would not be recommended because of the need to generate a large number of rows of the triangle. An alternative method is to use the binomial theorem. The theorem enabl ...
... 4. The binomial theorem If we wanted to expand a binomial expression with a large power, e.g. (1 + x)32 , use of Pascal’s triangle would not be recommended because of the need to generate a large number of rows of the triangle. An alternative method is to use the binomial theorem. The theorem enabl ...
Study Guide and Review
... for all positive integers n. Use Pascal’s triangle to expand each binomial. ...
... for all positive integers n. Use Pascal’s triangle to expand each binomial. ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.