CONCEPTS AND VOCABULARY ALGEBRA 1 - CH 1 Flashcards
What are the arithmetic operations?
addition, subtraction, multiplication, division
What is an expression? Describe with words
a collection of numbers and symbols (without an = sign)
Give three examples of expressions:
4x and 3x-8 and 4(3m-2)+ 9
What is meant by “evaluate?”
give a value to… figure out what it is worth
What is a variable? Describe with words
A symbol (letter, picture) that represents a number
Give three examples of variables
x, y and M
What does it mean to substitute?
Replace the variable with a number (or an expression)
EXPLAIN: SUM- DIFFERENCE-QUOTIENT- PRODUCT
SUM- addition DIFF- subtraction QUOT- division PRODUCT mult
Describe difference between TERMS and FACTORS
Terms are glued by addition (and subtraction) and Factors are glued by multiplication
Give examples of terms:
4a+ 3bc + 5xyz is an expression with THREE TERMS
Give three examples of factors:
4a+ 3bc + 5xyz The first TERM has two factors: 4 and a. The second TERM has three factors: 3, b and c. The third TERM has four factors: 5, x, y, and z.
What is a power?
It is an expression with a BASE and an EXPONENT
What does the exponent of a power tell us?
how many times you should MULTIPLY the base by itself
What does the base of a power tell us?
the base is the thing you are mulitplying by itself
2^3 write it out and evaluate
2x2x2= 8
x ^ m write it out to show what it means
XXXX….X (m times)
What is the order of operations?
P E M D A S or P E D M S A . Parentheses , Exponents, mult and div L to R, add and sub L to R
Why do we need an order of operations?
So we can all arrive at the same result, nice and organized. Clear communictation.
What do students often mess up when doing order of operations?
many do MULT before DIV, but you should do them together from left to right, whichever is first.
What can we pretend that paranthesis are?
BLINDERS, look into the inner most parentheses first.
How can you stay organized when doing order of operations?
everytime you simplify a part, re-write the entire expression on the next line. USE A LOT OF PAPER!
TRANSLATE: the sum of a number and nine
X + 9
TRANSLATE: six less than a number
X - 6 (NOT 6 - X)
TRANSLATE: the product of seven and the sum of a number and two
7 ( X + 2)
TRANSLATE: five less than the product of a number and three
3X - 5
TRANSLATE: the sum of the square of a number and twelve
X^2 + 12
What is an equation?
two expressions joined by an equal sign.
How are equations different than expressions?
equations are SOLVED and expressions are EVALUATED (or simplified)
You can evaluate _____ and you can solve ________
you evaluate expressions and simplify equations
Why can’t you “solve” an expression?
you can’t isolate the variable. there is nothing to solve. you can’t make it true
What does it mean to “solve an equation?”
MAKE IT TRUE! FIND VALUES THAT MAKE EQUATION TRUE… FIND THE TRUTH!
What are the “solutions” to an equation?
all values that, when substituted in for the variables, make the equation TRUE
How is “evaluate” different from “solve?”
evaluate is giving an overall value of symbols, you are given the values of the variables and asked to plug them into the EXPRESSION to find its value. When you solve, you need to FIND the value of the variables that make the EQUATION true!
Can equations have more than one solution?
YES
How can you transform an equation?
do stuff to both sides of the equation. It will look different but still be equal.
What is the GOLDEN RULE OF ALGEBRA?
DO ONTO ONE SIDE AS YOU DO TO THE OTHER
What does “isolate the variable” mean?
Get is ALL ALONE on one side of the equation
How does Mr. Nystrom look at equations that you have to solve?
He thinks of them as PUZZLES… a little game. Learn the rules, and use them to solve the puzzle. PEMDAS and the GOLDEN RULE are the key to solving the puzzle!
when you get it down to x=5, how can you think of this conceptually?
X IS FIVE ! in the beginning, you were asked to find out what x was. It was a puzzle. at the end you found it, so you can say “x is five!”
Does the variable have to be on the left side?
NO, if you get “10 = X” you can say “10 is X” which is the same as “X is 10”
What are inverse operations?
the UNDO eachother. Start with 5, multiply by 2, then divide by 2. What did you get?
How do you UNDO division? undo multiplication? undo addition? undo subtraction
division undoes multiplicaiton, addition undoes subtraction… etc..
What happens when you multiply a number by its reciprocal?
2/3 x 3/2 = 1 YOU ALWAYS GET ONE
If you have a fraction in front of x alone on one side of an equation, how can you quickly isolate the x ?
MULT BOTH SIDES BY THE REFLIPROCAL!
What is a perimeter?
distance around a 2D object
What is an area?
the number of squares inside a 2D object
Why would someone call area “squarea?”
because you are counting squares and measureing in squares: square feet, square inches, square meters, etc
When finding the perimeter you ____ up the side lengths, when you find the area you _____ the side lengths.
perimeter ADD up ALL of the sides. Area you MULTIPLY the sides
Perimeter is measured in ________ or _____ or ____….
feet or inches or miles or meters
Area is measured in ______ or _____ or ____….
square feet or square inches or square miles or square meters
What is the perimeter of a circle called?
CIRCUMFERENCE
FORMULAS: Area of triangle?
1/2 base * height
why is area of triangle 1/2 base * height
think: a triangle is like half the area of a rectangle :)
FORMULAS: Area of rectangle?
base * height
FORMULAS: Area of circle? (hint: measured in squares)
Area = pi * r squared
FORMULAS: perimeter of rectangle?
add up all the sides: length + width + length + width
FORMULAS: circumference of circle? (hint: not measured in squares)
distance around. Circumference = 2 pi r
Where does the formula for rectangle perimeter come from? A = 2L + 2W
Since you are adding all the sides, there are 2 lengths and 2 widths you will add. L + L + W + W is the same as 2L + 2W
