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math

chapter1
by

Kremble Bailey

on 11 January 2013

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Transcript of math

MY MATH PROJECT
BY: KREMBLE BAILEY VOCABULARY WORDS: LESSON1-1
* QUANTITY~ anything that can be measured or counted. ex. a dozen is another way to describe a quantity of 12 eggs.
*VARIABLE~ a symbol, usually a letter, that represents one or more numbers. ex. k is the variable in the equation 14-k=5
*ALEBRAIC EXPRESSION~ a mathematical phrase that includes one or more variables. ex. 6+x is an algebraic expression.
*NUMERICAL EXPRESSION~ a mathematical phrase involving numbers and operaion symbols, but no variables. ex. 6+7 EXAMPLES WRITING EXPRESSIONS WITH ADDITION AND SUBTRACTION
WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.14 more than k{k+14} B. 14 less a number x {14-x}
WRITING EXPRESSIONS WITH MULTIPLICATION AND DIVISION
WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.43 times a number j{43j} B. the quotient of a number b and 22{b/22}
WRITING EXPRESSIONS WITH TWO OPERATIONS
WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A. 6 more than twice a number a{6+2a} B. 3 less than the quotient of 5 and a number c{5/c-3} C. the product of 7 and the sum of a number k and 6{7(k+6)}
USING WORDS FOR AN EXPRESSIONS
6k{three times a number k} CHAPTER 1 VOCABULARY WORDS :LESSON1-2
*POWER~ the base ad the exponent of an expression of the form 2^3. ex.6^7
*EXPONENT~a number that shows repeated multiplication. ex.5^6 :the exponent 6 indicates that 5 is used as a factor 6 times.
*BASE~a number that is multiplied repeatedly.ex.2^3 :the base 2 is used as a factor 3 times.
*SIMPLIFY~to replace an expression with its simplest name or form.ex.3+5=8,so 8 is the simplest form.
*EVALUATE~to substitute a given number for each variable, and then simplify.ex. to evaluate 3x+4 for x=2,substitute 2 for x and simplify 3(2)+4=6+4=10 EXAMPLES SIMPLIFYING POWERS
What is the simplified form of the expression?:A. 5^6{5^6=5×5×5×5×5×5=78,125
B.(0.2)^3{(0.2)^3=0.0016}
SIMPLIFYING NUMERICAL EXPRESSIONS
What is the simplified form of the expression?:
A.
(10-4)^3÷2 (10-4)^3÷2=6^3÷2=216÷2=108

EVALUATING ALGEBRAIC EXPRESSIONS
What is the value of the expression for k=5 and s=2 A. K^2+K-14÷S^2{5^2+5-14÷2^2=25+5-14÷4=25+5-3=30-3=27} VOCABULARY WORDS:LESSON1-3
*SQUARE ROOT~ a number a is the square root of a number b if a"^"=b ex. 7^2= 49, so 7 is the square root.
*RADICAND~ the expression under the radical symbol. ex.the radicand of the radical expression √x+2 is x+2.
*RADICAL~together the radical symbol and radicand form a radical.ex.√a
*PERFECT SQUARE~the square of an integer. ex.the numbers 1,4,9,16,25,36... are perfect squares ecause they are the squares of integers.
*SET~a well-defined collection of objects.ex.{...,-3,-2,-1,0,1,1,2,3...}
*ELEMENT OF A SET~members of a set. ex.cats and dogs are elements of the set of mammals.
*SUBSET~ a subset of a set consists of elements from the given set.ex. if B={1,2,3,4,5,6,7} and A ={1,2,5}, then A is a subset of B.
*RATIONAL NUMBERS~a real number that can be written as a ratio of two integers. Rational numbers in decimal form are terminating or repeating. ex. 2/3,1.548,and 2.292929
*NATURAL NUMBERS~ the counting numbers.ex. 1,2,3...
*WHOLE NUMBERS~the nonnegative numbers.ex.0,1,2,3,.....
*INTEGERS~whole numbers and their opposites.ex. ...-3,-2,-1,0,1,2,3...
*IRRATIONAL NUMBERS~a number that cannot be written as a ratio of two integers. Irrational numbers in decimal form are nonterminating and nonrepeating.ex.
*REAL NUMBERS~a number that is either rational or irrational. ex.5,-3,0.666,0
*INEQUALITY~a mathematical sentence that compares the values of two expressions using an inequality symbol.ex.3<7 SIMPLIFYING SQUARE ROOT EXPRESSIONS
What is the simplified form of each expression.
A. 81/=9 {9^2=81, so 9 is the square root of 81.
B.9/16=3/4{(3/4)^2= 9/16, so 3/4 is the square root of 9/16.
CLASSIFYING REAL NUMBERS
To which subsets of the real numbers does each number belong?
A.15={ natural numbers, hole numbers, integers, rational numbers.
B. -1.4583{rational numbers
(since -1.4583 is a terminating decimal)}
C. √57={irrational numbers(since 57 is not a perfect square)} VOCABULARY WORDS:LESSON1-4
*EQUIVALENT EXPRESSIONS~algebraic expressions that have the same value for all values of the variable(s). ex.6a +7a and 13a are equivalent expressions.
*DEDUCTIVE REASONING~ a process of reasoning logically from given facts to a conclusion. ex.based on the fact that the sum of any two even numbers is even, you can deduce that the product of any whole number and any even number is even.
*COUNTEREXAMPLE~ an example showing that a statement is false.
example statement: all apples are red
counter ex. a Granny Smith apple is green. VOCABULARY WORDS: LESSON 1-5
*ABSOLUTE VALUE~the distance that a number is from zero on a number line. ex. -5 is 5 units from 0, so |-7| =7
*OPPOSITES~ a number that is the same distance from 0 on the number line as a given number, but lies in the opposite direction. ex. -4 and 4 are opposites.
*ADDITIVE INVERSES~ the opposite or additive inverse of any number a is -a. The sum of opposites is 0. ex. -6 and 6 are additive inverses because -6+6=0. IDENTIFYING PROPERTIES
What properties is illustrated by each statement?
A.14*0=0{Zero property of multiplication}
B.(y+6)+28=y+(6+28){Associative property of addition}
C.6x+0=6x{Identity property of addition}
WRITING EQUIVALENT EXPRESSIONS
Simplify each expression.
A.6(5n)=(6*5)n{associative property of multiplication}
30n{simplify}
B.(3+8b)+6=(8b+3)+6{commutative property of addition}
(8b+3)+6
8b+(3+6){associative property of addition}
8b+9{simplify}
C.4xy/y=4x*y/1*y{rewrite denominator using identity property of multiplication}
4x/1*y/y{use rule for multiplying fraction}
4x*1{x/1=x and y/y=1}
4x{identity property of multiplication} -3 -2 -1 0 1 2 3 4 5 -4 -5 6 7 USING NUMBER LINE MODELS
What is each sum? Use a number line. 3+2 start at 3 3+2=5 A. B. 3+(-2) 0 -1 -2 -3 -4 1 2 3 4 3+(-2)=1 C. -3+2 0 1 2 3 4 -1 -2 -3 -4 -3+2=-1 VOCABULARY WORDS:
LESSON 1-6
*MULTIPLICATIVE INVERSE~given a nonzero rational number a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero number and its multiplicative inverse is 1.ex. 4/3 is the multiplicative inverse of3/4 because 3/4*4/3=1
*RECIPROCAL~given a nonzero rational number a/b, the reciprocal, or multiplicative inverse, is b/a. the product of a nonzero number and its reciprocal is 1. ex. 2/5 and 5/2 are reciprocals because 2/5*5/2=1. MULTIPLYING REAL NUMBERS
What is each product?
A.5(-9)=-45 {the product of two numbers with different signs is negative.}
B.24(0.5)=12{the produt of two numbers with the same sign is positve.}
SIMPLIFYING SQUARE ROOT EXPRESSIONS
What is the simplified form of each expression? A.-√169=-13{(-13)^2=169, so -√169=-13}
B.√1/36=1/6{(1/6)^2=1/36, so 1/36=1/6}
DIVIDING FRACTIONS
What is the value of x/y when x=3/4 and y=2/3?
x/y=x÷y=-3/4÷(-2/3)=-3/4×(-3/2)=9/8 VOCABULARY WORDS:
LESSON1-7
*DISTRIBUTIVE PROPERTY~For all real number a, b , and c: a(b+c)=ab+ac
(b+c)a=ba+ca a(b-c)=ab-ac (b-c)a=ba-ca
ex.3(19+4)=3(19)+3(4)
(19+4)3=19(3)+4(3)
7(11-2)=7(11)-7(2)
(11-2)7=11(7)-2(7)
*TERM~a number, variable, or the product or quotient of a number and one or more variables. ex.the expression: 5x+y/2-8 has three terms: 5x,y/2, and-8.
*CONSTANT~a term that has no variable factor. ex.in the expression 4x+13y+17, 17 is the constant term.
*COEFFICIENT~the numerical factor when a term has a variable. ex. in the expression 2x+3y+16, 2 and 3 are coefficients.
*LIKE TERMS~terms with exactly the same variable factors in a variable expression. ex. 4y and 16y are like terms. SIMPLIFYING FRACTIONS
What is the simplified form of each expression?
A. 3(x+8){3(x+8)=3(x)+3(8) distributive property
=3+24 simplify}
B.(5b-4)(-7) {(5b-4)(-7)= 5b(-7)-4(-7)
=-35b+24
REWRITING FRACTION EXPRESSIONS
What sum or difference is equivalent to 7x+2/5?
7x+2/5=1/5(7x+2)
=1/5(7x)+1/5(2)
=7/5x+2/5
USING THE MULTIPLICATION PROPERTY OF -1
What is the simplified form of -(2y-3x)?
-(2y-3x)=-1(2y-3x)
=(-1)(2y)+(-1)(-3x)
=-2y+3x VOCABULARY WORDS:
LESSON1-8
*EQUATION~ a mathematical sentence that uses an equal sign(=). ex. x+5=3x-7
*OPEN SENTENCE~ an equation that contains one or more variables and may be true or false depending on the value of its variables. ex.5+x=12 is an open sentence.
*SOLUTION OF AN EQUATION~ any value or values that make an equation true. ex.3 is the solution of the equation 4x-1=11 CLASSIFYING EQUATIONS
Is the equation true, false, or open?
A.14+6=11+9{true, because both expressions equal 20.}
B.9×5=48{false, because 9×5=45 and 45≠48}
C.6x-12=18{open, because it has a variable}
IDENTIFYING SOLUTIONS OF AN EQUATION
Is x=9 a solution of the equation 52=5x+11?
52=5x+11
52=5(9)+11
52≠56
no, x=9 is not a solution of the equation 52=5x+11. VOCABULARY WORDS:
LESSON1-9
*SOLUTION OF AN EQUATION~a solution of a two-variable equation with the variables x and y is any ordered pair(x,y) that makes the equation true. ex.(4,1) is one solution of the equation x=4y
*INDUCTIVE REASONING~making conclusions based on observed patterns. IDENTIFYING SOLUTIONS OF A TWO-VARIABLE EQUATION
Is (5,9) a solution of the equation y=2x?
y=2x
9=2×5
9≠10 EXAMPLES EXAMPLES EXAMPLES EXAMPLES EXAMPLES
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