GCSE Revision Notes Mathematics – Number`s and Algebra
... Cube numbers are numbers multiplied by themselves and then multiplied by themselves again ...
... Cube numbers are numbers multiplied by themselves and then multiplied by themselves again ...
Sequences of Real Numbers
... {an} converges provided that it converges to some number. Otherwise we say that it diverges. In the particular case when an gets larger and larger without bound as n→∞, we say that {an} diverges to ∞. (Likewise {an} can diverge to -∞.) ...
... {an} converges provided that it converges to some number. Otherwise we say that it diverges. In the particular case when an gets larger and larger without bound as n→∞, we say that {an} diverges to ∞. (Likewise {an} can diverge to -∞.) ...
Sequences of Real Numbers--
... {an} converges provided that it converges to some number. Otherwise we say that it diverges. In the particular case when an gets larger and larger without bound as n→∞, we say that {an} diverges to ∞. (Likewise {an} can diverge to -∞.) ...
... {an} converges provided that it converges to some number. Otherwise we say that it diverges. In the particular case when an gets larger and larger without bound as n→∞, we say that {an} diverges to ∞. (Likewise {an} can diverge to -∞.) ...
2-5: Complex Numbers
... 1)2 = x2 + 2x + 1 2)2 = x2 + 4x + 4 3)2 = x2 + 6x + 9 4)2 = x2 + 8x + 16 5)2 = x2 + 10x + 25 6)2 = x2 + 12x + 36 7)2 = x2 + 14x + 49 8)2 = x2 + 16x + 64 9)2 = x2 + 18x + 81 10)2 = x2 + 20x + 100 ...
... 1)2 = x2 + 2x + 1 2)2 = x2 + 4x + 4 3)2 = x2 + 6x + 9 4)2 = x2 + 8x + 16 5)2 = x2 + 10x + 25 6)2 = x2 + 12x + 36 7)2 = x2 + 14x + 49 8)2 = x2 + 16x + 64 9)2 = x2 + 18x + 81 10)2 = x2 + 20x + 100 ...
M3.1 Introducing complex numbers
... ideas of arithmetic and algebra. In particular, you should be able to give clear definitions and be able to use the following terms: polynomial of degree n, quadratic equation, quotient, roots of an equation, set, solution of simultaneous equations, square root and zeros of a polynomial. You should ...
... ideas of arithmetic and algebra. In particular, you should be able to give clear definitions and be able to use the following terms: polynomial of degree n, quadratic equation, quotient, roots of an equation, set, solution of simultaneous equations, square root and zeros of a polynomial. You should ...
7.RP.1, 7.RP.2, 7.RP.3
... K. The unit rate in a proportional relationship L. A ratio comparing a number to 100 (Per 100) ...
... K. The unit rate in a proportional relationship L. A ratio comparing a number to 100 (Per 100) ...
Module 1 Homework
... Show that 15 is a deficient number – also in detail. Give an example – different from everybody else’s – of another deficient number. ...
... Show that 15 is a deficient number – also in detail. Give an example – different from everybody else’s – of another deficient number. ...
Section 3.1
... So far, we have studied historical cryptographic methods that are typically hand-based Modern cryptographic methods are computer based methods. To have an appreciation for these methods, we need to understand how computers communicate. In this section, we study the types of numbers that computers ty ...
... So far, we have studied historical cryptographic methods that are typically hand-based Modern cryptographic methods are computer based methods. To have an appreciation for these methods, we need to understand how computers communicate. In this section, we study the types of numbers that computers ty ...
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.