Algebra 1 Midterm
Where is the origin?
(0,0) The center point of the graph
How do you remove the denominator in an equation?
*Multiply it* and be fair so do the same to the other side
When there appears to be no x value in an equation, what is the x value?
0
Every whole number has what number under it?
1
When there is no coefficient on a variable, what number pops up?
1
How to find the proportion of similar figures?
1. After doing what the image shows, cross multiply. Example: 3 times x = 3x & 6 times 1 = 6 2. 3x = 6 <---- NOW SOLVE
How to measure distance on a map?
1. Look at how many miles fit in an inch Example: 1 inch/200 miles 2. Create a fraction with the length of the map Example: 14 inches/x miles 3. Cross multiply Example: 1 inch * x miles = 1x & 200 miles * 14 inches = 2800 4. Answer: 2800
How to solve one step equations?
1. Subtract or add (be fair) 2. Divide (do the opposite operations to isolate x)
Negative X Positive
= negative
Negative x Negative
= positive
What is negative slope?
A line that is trending downwards from left to right. The line's rise/run value is negative
When the word "per" is in a word problem, what symbol does it represent?
A variable attached to a number Example: $2 per person = 2x
How to find the area of a triangle?
A=bh 1/2
How to add or subtract fractions with the same denominators?
Add the numerators
When variable cancel each other out in an equation but the statement is true, what do you call it?
All Real Numbers
What are the real numbers?
All the numbers on the number line (negative, rational, irrational, decimal, integer) EVERYTHING
What are the irrational numbers?
An Irrational Number is a real number that cannot be written as a simple fraction. Ex: pi and the square root of 3
How to solve compound inequalities
Break up the compound inequality to two parts Example: a < b < c a < b & b < c Solve the left side first Solve the right side second Bring the answers back together a < b b < c a < b < c
How can a whole number become a rational number?
By placing a 1 underneath it (4/1 = 4)
How to solve absolute value equations?
Check your answer Input the absolute value for both versions of x into the equation
What is distributive property?
Distribute the multiplying within the parentheses
How to solve absolute value inequalities?
Do the opposite operations to get rid of a number if necessary Example: 2 |3x -1| > 8 -------- -- 2 2 |3x-1| > 4 Then complete the photo steps!
What are the characteristics of x?
Domain Input X Independent Variable (DIXI)
example of independent and dependent variable
Example problem: To determine the *cost* of mailing a letter, you must first know how much the letter *weighs*. The cost *depends* on the weight. The cost is y. The weight is x.
How to add numbers together in the family?
Example: 4 - 3x + 7 - x *4* - 3x *+ 7* -x 11 * -3x* *-x* 11 -4x
How to write a function rule from a word problem?
Example: The museum has a $40 trip fee and $2 per student y = 40 + 2x y = 40 + 2 x | | | | total flat student per cost trip fee student fee
How to graph a function rule?
First you must first create a table of values. Input numbers for x so you can find a value for y Example: (input) x 0 1 (output) y -3 -1 Then you graph the pairs on a chart Example: (0,-3) (1,-1) .... Last but not least you graph the answers on a chart
How to solve two step equations?
Focus on addition or subtraction first Be fair Do the opposite operations
When solving an equation with variables on both sides, what should you do?
Get rid of the variable on one side
What is the vertical line test?
If the line intercepts the graph 2 or more times it is a relation If it only intersects once it's a function
How do you solve for an input value using f(x)?
Instead of creating a table of values, input any number for x. The answer of the equation will be the output (y)
What happens when the slope is 0? (0x)
It forms a horizontal line because it does not rise 0/1
What is f(x)?
It's a function. f(x) can replace y because they mean the same thing
If the equation doesn't start with y, what kind of line is it?
It's a vertical line because it does not intercept with the y axis. It is *NOT A FUNCTION* x = 5
What does it mean when answers on a number line converge?
It's any answer between the two points
How to calculate percent change *with* the second quantity?
New value - old value ------------------------- old value
When the statement is false in a equation, what do you call it?
No Solution
What does it mean when answers on a number line diverge?
No answer between the two points are correct
What is the zero property?
No matter what number you multiply by zero, you'll get zero
What is the order of operations?
PEMDAS (Parentheses/ Exponents Multiplication/Division/ Addition/Subtraction)
How to calculate percentage change *without* the second quantity?
Problem: $50 stock went up by 40%. What's the profit? Step One: Create a fraction with the percent (percent is out of 100) Example: 40% = 40/100 Step Two: Create a fraction with the quantity Example: P (profit)/50 Step Three: Cross multiply Example: 40 x 50=2,000 & 100 x P=100P Step Four: Put the answers in an equation Example: 2,000=100P Step Five: Isolate P by division Example: 2,000=100P ----- ----- 100 100 Step Six: Answer -> 20 = P
What are the characteristics of y?
Range Output Y Dependent (ROY D)
How to convert meters into feet?
Step 1: Turn the meter into a fraction Example: 96m = 96m/1 Step 2: Multiply the meter by 3.3ft/1m (because 3.3 ft = 1m) Example: 96m/1 x 3.3ft/1m Step 3: Cancel out the meter sign and cancel the 1 under the meter Example: 96 x 3.3ft/1 Step 4: Multiply the meter by the feet Example: 96 x 3.3 = 316.8 Step 5: Add the feet sign back Example: 316.8 ft.
How to convert pounds into dollars?
Step 1: Turn the pounds into a fraction Example: £10 = £10/1 Step 2: Multiply £10/1 by $1.60/£1 (because $1.60 = £1) Example: £10/1 x $1.60/£1 Step 3: Cancel the pound sign (£) Example: 10/1 x $1.60/1 Step 4: Multiply the numerators Example: 10 x $1.60 = $16 Step 5: Multiply the denominators Example: 1 x 1 = 1 Step 6: $16/1 = $16 the answer!
What is arithmetic sequence?
The amount a sequence of numbers goes up or down 1, 6, 11, 16, 21 (it goes up by 5)
What is absolute value?
The distance a number is from zero on a number line. Represented by vertical bars.
What is output?
The result of an equation Example: (y output: 3) y = 1 + 2 (3) = 1 + 2
How to solve a multi step inequality?
The same way you'd solve an equation
What is slope?
The steepness of a line. Y change/X change *Rise over run*
If the answer is 'less than' when graphing an inequality on a number line, what direction does the arrow go in?
To the left
If the answer is 'greater than' when graphing an inequality on a number line, what direction does the arrow go in?
To the right
What does it mean to have ratio proportions?
Two equivalent ratios Example: 1/2 = 3/6
How to graph an inequality on a number line?
Use an arrow that matches the amount
What is input?
What goes into an equation Example: (x input: 1) y = x + 2 y = (1) + 2
What is the identities property?
When you add 0 or multiply 1,. you'll get the number again. Example: 4+0=4 / 5x1=5
If you choose any two pairs on the graph, will you get the same slope?
Yes
What do you do to shift a number up the y axis?
You add to the y-intercept
What happens when you multiply a number by a negative?
You get the opposite. Example: -1 x 3= -3 or -1 x -3= 3
What happens when you divide or multiply and inequality by a negative number?
You have to flip the inequality sign
What do you do to shift a number down the y axis?
You subtract from the y-intercept
Any equation that begins with a 'y' is a what?
a function
What is a non linear function?
a function that do not have a pattern and is curved x and y do not have to have a continuous pattern on a data table
What is a linear function?
a function that is a continuous straight line x and y both have to have a continuous pattern on a data table
What are the integers?
all positive and negative numbers including zero. Examples - 0, 1,2,3, -1,-2,-3
What does all real numbers mean?
any number can be inserted in and it will always be correct
What is a function?
data where is every x value is unique
What is an inequality?
difference in size, quantity, etc
What is the associate property?
either order you add or multiple you'll still get the same sum
What does a closed dot mean when graphing inequalities on a number line?
equal to (•)
What is the equation to find the ?rd term in a sequence?
first term (+ or -) how much it goes up or down in the sequence (term - 1) Example: find the 81st term sequence: 55, 49, 43, 37, 31,.. 55-6 (81-1)
The smaller the slope, the _____er the line
flat
What does "is" mean in: 15% *is* what percent of 100?
is = equals
What is a relation?
is allowed to have the x value repeat
What is the constant of variation?
k How x and y change
What direction do you have to multiply/divide and add/subtract in order of operations?
left to right
how to analyze graph patterns?
look at the input & output table Example: Input: 1 2 3 4 5 6 7 8 9 Output: 3 4 5 6 7 8 9 10 11 Graph the number pairs Example of a number pair: (1,3) (2,4) (3,5) etc. You'll see that with this problem, input is two steps ahead of output!
How to find square feet?
multiply length by width
How to add or subtract fractions with different denominators?
multiply the denominators so they match and then add the numerators
what does no solution mean?
no matter what number is inserted in, it will never be correct
What does an open dot mean when graphing inequalities on a number line?
not equal to ( °)
What is a coefficient?
number in front of a variable
What are natural numbers?
numbers 1 and on
What are the rational numbers?
numbers that can be written as a fraction
What does "of" mean in: 15% is what percent *of* 100?
of = multiply
What is the momentum formula?
p=mv p-momentum m-mass v-velocity
What is a whole number?
positive numbers that are zero or greater
What is an expression?
something that contains a variable
What is a variable?
something that we don't know. A letter goes in its place
Adding a negative = the same as what?
subtracting Example: 2+-3 = 2-3
What do parentheses do in algebra?
tells you to multiply
What is 'm' in slope intercept form?
the slope
What is cognitive dissonance?
the state of having inconsistent thoughts. Example: Things not making sense when you say it out loud
What is direct variation?
two unknown quantities change directly with one another Equation: y=kx
Which variable changes directly with x, *k* or *y*?
y
What is slope intercept form?
y = mx + b
What is 'b' in slope Intercept form?
y-intercept
What is the commutative property?
you can add or multiply numbers flipped and it'll still equal the same thing Example: 2+4 or 4+2 / 3x7 or 7x3
