問題一覧
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Consists of a set of elements called real numbers.
Real Number System
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May be positive, negative or zero, and can be classified as either rational or irrational number.
Real Numbers
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Any number that can be expressed in ratio of two integer i.e a number of the form a/b where a and b are integers and b≠0.
Rational Number
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In rational numbers, decimals classified as fractions may either be __ or __.
Terminating Decimals, Non-terminating Repeating Decimals
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Are real numbers that are not rational.
Irrational Numbers
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Irrational numbers are also called __.
Non-terminating Non-repeating Decimals
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Properties of Real Number
Closure Property, Commutative Property, Associative Property, Identity Property, Inverse Property, Distributive Property
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The set of real numbers is said to be closed under a given operation if upon performing any two elements in R, the result also belongs to R.
Closure Property
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a + b £ R for any a, b £ R
Closure Property
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ab £ R for any a, b £ R
Closure Property
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9 + 5 = 14
Closure Property
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4(5) = 20
Closure Property
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The sum product of two numbers is the same in whatever order they are added/multiplied.
Commutative Property
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a + b = b + a
Commutative Property
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ab = ba
Commutative Property
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4 + 5 = 5 + 4
Commutative Property
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4(5) = 5(4)
Commutative Property
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The product of three or more numbers is the same in whatever way the numbers are grouped.
Associative Property
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a + (b + c) = (a + b) + c
Associative Property
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2 + (5 + 7) = (2 + 5) + 7
Associative Property
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For addition, the identity element is __ (additive identity)
Zero
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For multiplication, the identity element is __ (multiplicative identity)
One
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For addition, the inverse element is __ (additive inverse)
-a
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For multiplication, the inverse element is __ (multiplicative inverse)
1/a
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a + (-a) = 0
Inverse Property
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a. 1/a = 1
Inverse Property
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The product of a number and the sum of other number is the same as the sum of the products obtained by multiplying each of the other numbers by the first number.
Distributive Property
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a (b + c) = ab + ac
Distributive Property
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(b + c) a = ba + ca
Distributive Property
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The basic language of algebra is __.
Symbolic
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Is an object or symbol that changes its value in a particular problem or discussion.
Variable
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Last few letters in the alphabet (x, y, z)
Variable
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Is an object or symbol that does not change its value in a particular problem or discussion.
Constant
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First few letters in the alphabet (a, b, c)
Constant
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Is a constant, a variable or a combination of constants and variables together with the operations of addition, subtraction, multiplication, division, raising to powers or extraction of roots.
Algebraic Expression
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Consist of a variable and constant separated by + or - sign.
Terms
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Is an expression which is composed of terms separated by the fundamental operations in Algebra.
Polynomial
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Exponents should be positive.
Polynomial
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If exponents are/have negative.
Algebraic Expression
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Is an algebraic expression consisting of only one term.
Monomial
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Is an algebraic expression which consists of two unlike terms.
Binomial
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Is an algebraic expression which consists of three unlike terms.
Trinomial
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Is an algebraic expression which consists of four or more unlike terms.
Multinomial
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Is the symbol or letter in a particular expression.
Literal Coefficient
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Is a numeral/number in a particular expression.
Numerical Coefficient
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Is the sum of the exponents of its variables.
Degree of Term
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Is the highest exponent found in any non-zero term of the polynomial.
Degree of a Polynomial
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Same variable and exponent.
Similar or Like Terms
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Same variable but different exponent.
Unlike Terms
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set of rational numbers
Q
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set of irrational numbers
Q¹
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set of real numbers
R
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2 ways of adding polynomials
Horizontal Form, Vertical Form