is less than, is smaller than, shade below, shade to the left
Back
graph of a linear function
Front
Back
How do the slopes of perdendicular lines compare?
Front
They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.
Back
How do the slopes of parallel lines compare?
Front
They are the same
Back
Absolute Value Parent Function
Front
Back
in y = mx + b, "m" stands for?
Front
slope
Back
domain
Front
set of all of the possible x-values. INPUTS
Back
other names for "x"
Front
domain, independent variable, input
Back
variable
Front
NOT A NUMBER. A letter or symbol that stands for a number.
Back
What is Direct Variation?
Front
y = mx, or y = ax, or y = kx. m, a, or k is just the coefficient in front of the x. They are also the SLOPE of the direct variation line. Direct variation lines have a y-intercept ot (0, 0)
Back
What is Inverse Variation?
Front
y = 1/x. As one quantity increases, the other decreases
Back
coordinate plane
Front
a plane formed by 2 perpendicular lines called axes (the x-axis goes sided to side, the y-axis goes up and down).
Back
graph of an inverse function: y=1/x
Front
Back
graph of exponential decay function
Front
Back
discreet function (scatter plot)
Front
data appears as individual points on a graph. Whatever is being graphed cannot be broken down in to smaller pieces.
Back
What is a system of equations or system of inequalities?
Front
2 or more equations or inequalities graphed on the same coordinate plane
Back
what is a linear inequality?
Front
It is an equation with a <, >, < or =, > or = in the place of the =.
Back
continuous function
Front
data appears as a smooth curve on a graph.
Back
Graph a parabola using a table
Front
Back
relation
Front
set of ordered pairs
Back
what slope does a VERTICAL line have?
Front
undefined slope
Back
Quadratic Parent Function
Front
Back
graph of exponential growth function
Front
Back
changing the "m" in the slope-intercept form of the equation of a line changes what?
Front
the steepness of the line
Back
what is the x-intercept?
Front
the point where the graph crosses the x-axis. It has the coordinates (x, 0)
Back
ordered pair
Front
the x and y coordinates of a point on the coordinate plane (x,y)
Back
Radical (square root) Parent Function
Front
Back
range
Front
set of all the possible y-values. OUTPUTS
Back
what is the y-intercept?
Front
the point where the graph crosses the y-axis. It has the coordinates (0, y)
Back
how is slope important for linear equations and lines?
Front
linear equations and lines have CONSTANT slopes. The slope is the SAME all the way up and down the line.
Back
dependent variable
Front
the OUTPUT or RESULT in a situation or problem. It's the variable YOU CANNOT control. It's the Y variable. In a equation, its the variable BY ITSELF on one side of the = sign.
Back
function
Front
special relation where each x-value is paired with ONLY ONE y-value. (x-values DO NOT repeat, it passes the vertical line test)
Back
Mapping
Front
Bubbles that represent the x-values and the y-values.
Back
Where are the solutions of a quadratic function?
Front
at the x-intercepts. They are also known as zeros and roots.
Back
what is the linear parent function?
Front
y = x
f(x) = x
Back
Table
Front
A way to represent ordered pairs.
Back
What is a quadratic equation or function?
Front
an equation of function that has "x-squared" as its highest order exponent.
Back
How many solutions can a system with 2 equations have?
Front
1) no solutions, if the lines are parallel and have the same slope. 2) one solution, if the lines intersect at one point. 3) infinite many solutions, if the two equations are the same and touch each other everywhere.
Back
define slope
Front
the steepness of a line, vertical change/horizontal change, (y-y)/(x-x), rise over run
Back
other names for "y"
Front
range, dependent variable, output
Back
words for ">"
Front
is more than, is greater than, is larger than, shade above, shade to the right
Back
graph of a quadratic function
Front
Back
vertical line test
Front
a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.
Back
changing the "b" in the slope-intercept form of the equation of a line changes what?
Front
moves the line up or down the y-axis.
Back
independent variable
Front
the INPUT or CAUSE in a situation or problem. It's the variable YOU CAN control. It's the X variable.
Back
What is a line of best fit?
Front
A line drawn through the points on a scatterplot to estimate the best line through the data.
Back
What is the SOLUTION of a system of equations?
Front
where the lines touch or cross
Back
Linear Function Parent Graph
Front
Back
what slope does a HORIZONTAL line have?
Front
slope = 0
Back
Section 2
(50 cards)
The solution to a system of linear inequalities
Front
The intersection of the two half-planes.
Back
ELIMINATION
Front
You have to get one of the variables to eliminate by getting them to be the same number just one positive and one negative, so they zero out.
Sometimes in order to do this you have to multiply one or both of the equations by a number. Then add straight down and continue to solve.
Back
If y=f(x) and y=g(x), then.....
Front
f(x) = g(x) meaning you can set the two equations equal to each other in order to solve for the variable. Then to find y you plug the variable back into one of the original equations and solve.
Back
How do you Reduce FRACTIONS?
Front
Find one number that you can divide into both the numerator and denominator that is the same number. Then divide them both by that number.
Back
How to rearrange variables to solve for a specific variable.
Front
Solve A=P+PRT for T. You perform the opposite operation on each variable until you get the one you are solving for all by itself. Subtract P, then divide by P and R.
Back
How do you MULTIPLE exponents of like variables?
Front
ADD them
Back
Sales Tax
Front
Is added on to the cost of the item. To find the amount to add, multiply the cost of the item by the percent of tax.
Back
Range
Front
When talking about data sets, make sure the numbers are in order from smallest to largest, to find the RANGE you SUBTRACT the smallest from the largest.
Back
How do you Add and Subtract FRACTIONS?
Front
You have to have a common denominator.
Back
End Behavior
Front
Describes what is happening to the graph overall as the x-values change. As the x-values decrease, does the graph seem to go up or down? As the x-vales increase, does the graph seem to increase or decrease? This represents the end behavior as being positive or negative.
Back
How do you combine like terms?
Front
Add their coefficients.
Back
Integer
Front
A whole number, both positive and negative numbers, including zero.
... ,-3, -2, -1, 0, 1, 2, 3, ......
Back
How do you DIVIDE exponents of like variables?
Front
SUBTRACT them
Back
Quadratic Formula
Front
In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into the quadratic formula to find the x-intercepts, roots, zeros, or solutions.
Back
When do you flip an inequality symbol?
Front
Anytime you multiply or divide by a negative number.
Back
y= and f(x)=
Front
These are the same. They can be interchanged with one another. f(x) simply lets you know the equation is a function. Can also be written with other variables like g(x), p(x), etc.
Back
How do you multiply FRACTIONS?
Front
Cancel or reduce if possible, then multiply straight across. Some people like to multiply straight across and then reduce. Either way, if you can reduce, you MUST REDUCE.
Back
Median
Front
When the data is put in order from smallest to largest, it is the number in the middle. If there are two numbers in the middle, you add them together then divide by 2. (You take their average)
Back
Identify the effects of k on the graph y=f(x)
Front
y=f(x) + k moves the graph up k units or down k units.
y=f(x+k) moves the graph right if k is negative OR left if k is positive. Remember this is opposite of what's on the number line.
y=k f(x) vertical stretch if k is bigger than 1 and a vertical compression if k is less than 1.
Back
Natural numbers
Front
Counting numbers: 1, 2, 3, ......
Back
Percents
Front
15% can also be written as 0.15, or as 15/100 which then must be reduced to 3/20.
Back
Maximum or Minimum
Front
Maximum is at the highest point of a parabola.
Minimum is the lowest point.
Back
Calculate and interpret the average rate of change (symbolically or from a table)
Front
How fast is it changing? Sometimes you find out how much each one changes, then take their average.
Back
Whole numbers
Front
Start with 0, 1, 2, ......
Back
Use the structure of an expression to identify ways to rewrite it.
Front
Example: See x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as the difference of two squares that can be factored as (x^2-y^2)(x^2+y^2).
Back
How to solve when written in function notation.
Front
Ex: f(x) = 3x + 4, solve for f(-2). All you do is replace the x with a (-2) and solve. 3(-2) +4 = -2
Back
What is the "rate of change" on a graph?
Front
Slope
Back
Compound Interest Formula
Front
A=(P+r/n)^nt
Common n values are 12=monthly, 4=quarterly, 2=semiannually, 1=annually.
t is the time in years.
Back
How to tell when a function is increasing or decreasing?
Front
Always read a graph from left to right, just like the words on a page. If it goes up, it is increasing. If it goes down, it is decreasing.
Back
Explain each step in solving an equation.
Front
You may have to list the steps you performed explaining what you did, step by step. Know how to justify your solutions.
Back
Factoring with 3 terms
Front
ax^2 + bx + c = 0, where a=1
(x )(x )=0 Find the two numbers that multiply to get you c, AND they add/sub to get you b. If asked to SOLVE by factoring, then set each factor equal to zero and solve.
Back
Geometric Sequences
Front
There is a pattern in which you multiply or divide by a common number.
Back
Absolute value of a negative number. IxI = -3
Front
NO SOLUTION
Back
How do you Divide FRACTIONS?
Front
Keep, Change, Flip! Then multiply fractions!
Back
The Square Root Property to solve Quadratics
Front
To get rid of the exponent 2, you can take the square root of both sides. Remember the plus or minus symbol, which can give you two answers.
Back
Axis of Symmetry
Front
The equations x=0 is the axis of symmetry for a parabola in standard form.
Back
How to use the Discriminant when solving the Quadratic Formula?
Front
If the discriminant is positive, you will have 2 solutions or x-intercepts. If the discriminant is zero, you will have 1 solution or x-intercept. If the discriminant is negative, you will have No Solution (or really a complex solution (imaginary) in the form (a + bi)
Back
Solid or Dotted Line? Open or Closed Circle?
Front
If it has the line under it (or equal to) it will be a closed circle or solid line.
Back
Simple Interest Formula
Front
You can solve for any of the variables when given the other 3. The rate is the percentage rate usually written as a decimal. EX. 13%= 0.13
Back
SUBSTITUTION
Front
If you know what one variable equals, like y=35-10x, then you can plug that value in for y in the second equation,
4x - 7y = -23 becomes
4x -7(35-10x)=-23. Distribute and solve for x. Then you can plug back in to one of the original equations to solve for y.
Back
How to solve absolute value inequalities?
Front
Once the absolute value bars are on one side of the equal sign, by itself, you work two separate problems (1) Looks exactly the same as the original equation without the absolute value symbols. (2) Is the same on one side, but flip the inequality symbol and make the number negative.
Back
Factoring with 4 terms
Front
Solve by grouping. Group two sets and then factor those two groups.
Back
Mode
Front
The number that shows up the MOST
Back
Completing The Square
Front
Isolate x^2 + bx on one side, move the number to the other side of the equal sign. Take b, divide by 2, then square the result. Add that number to both side. It will then factor into a perfect square.
Back
Absolute Value when solving order of operations problems.
Front
Work any math that you need to within the absolute value bars. Then always give the positive of that number as the answer.
Back
Interpret parts of an expression
Front
Examples such as: C= 250 + 35m, Where C is the cost for renting a car. They pay $250 plus $35 for every extra mile they drive. You have to interpret what the numbers and variables mean in the form of a word problem.
Back
Mean (Average)
Front
Add up all the data points, then divide by however many data points there were. Ex. 3,6,9
3+6+9= 18 /3 = 6
Back
What are "like terms"?
Front
mathmatical terms that have the SAME variables raised to the SAME exponents.
Back
Discounts
Front
Are subtracted from the cost of the item. To find the amount to subtract, multiply the cost by the item times the percent being discounted.
Back
Factoring with 2 terms
Front
Factor out the number or variable that all the terms have in common.
Back
Section 3
(50 cards)
Standard Deviation
Front
When using a bell curve to represent data, the standard deviation tells you how far away a number is from the center of the data.
Back
Difference
Front
Subtract
Back
Product
Front
Multiply
Back
Arithmetic Sequence
Front
A pattern in which you add a number each time.
Back
Fractions to Decimals
Front
Divide the numerator by the denominator. 1/4 = 1 divided by 4 = 0.25
Back
The sum of two rational numbers is rational.
The product of two rational numbers is rational
A rational number is any number that can be written as a fraction. Whole numbers are rational numbers because the number 2 can be written as 2/1.
Front
EX: 1/5 + 2/5 = 3/5
EX. 2/3 * 1/3 = 2/9
Back
Outliers
Front
A data point that does not fit in with the rest of the data.
Back
Distributive Property
Front
Multiply a number or variable to everyone inside parenthesis.
Back
Simplifying Radicals
Front
Radical is the square root symbol.
sqrt(20) = sqrt(4*5) = 2 sqrt (5)
Back
Geometric Sequence
Front
A pattern in which you multiply or divide each term by the same number.
Back
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal description.
Front
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Back
Rate of Change
Front
Is another name for slope usually used in word problems.
Back
Box Plots
Front
Make sure the numbers are in order from least to greatest. Find the median, the Q1 and Q3 by finding the median again of the upper and lower sections.
Back
Histogram
Front
A bar graph that has a range of values on the x-axis. In the example, each bar represents an age range of 5 years.
Back
Seven "less than" a number
Front
n - 7 You subtract 7 from the number.
Back
Improper Fractions to Mixed Numbers
Front
How many times will the denominator go into the numerator without going over. Then how many little pieces are left over.
Back
Linear functions
Front
Over equal intervals, the y-values increase by adding or subtracting the same number each time. *Note that the slope in the example would be 3/1= 3
Back
Piecewise-defined function Graph
Front
When the graph is doing two (or more) different functions depending on what the x-vales are. EX. If x<-1, then y=1. If x>(or equal to) -1, then y=x^2 -3
Back
3 "more than" a number
Front
n + 3 Add 3 to the number
Back
PEMDAS "Order of Operations"
Front
Parenthesis
Exponents
Multiply/Divide
Add/Sub
Back
Skewed Bell Curve
Front
When the data is not evenly distributed.
Back
Sum
Front
Add
Back
Which quantity increases fastest?
Front
exponential functions > quadratic functions > linear functions
Back
Step-Function Graph
Front
A function that is not continuous. It has levels which represent the y-value for a set of x-values.
Back
How do you solve Proportions?
Front
When two fractions are set EQUAL to one another. This is the only times you Cross multiply!
Back
Joint and Marginal Frequencies
Front
Joint is the individual data in the middle. Marginal is the sum of the data for each row or column.
Back
Quotient
Front
Divide
Back
Exponential functions y=2^x Where the variable is the exponent.
Front
Over equal intervals, the y-values increase by multiplying or dividing by the same number each time.
Back
25% of what is 150?
Front
0.25 * x = 150. To solve you divide by 0.25.
Back
Seven "is less than" a number
Front
7<n
Back
Correlation Coefficient
Front
A number between -1 and 1 that tells you if you have a strong or weak correlation. It also lets you know if it is a positive or negative correlation.
Back
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Front
A linear function would be best for situation in which something is increasing at a constant rate. An exponential function is best for situations in which the rate increase over time. EX. The growth of bacteria cells in a petri dish would be exponential growth.
Back
Estimate the Rate of Change from a graph
Front
Find the change in y-values, then divide by the change in x-values.
Back
Associative Property
Front
The way numbers are grouped is different, but the result is the same.
Back
Normal Bell Curve
Front
Let's you know where you should find most of your data.
Back
Rounding Rules
Front
Round to the nearest TENTH means you keep ONE decimal place EX 0.5648 rounds to 0.6 The 6 behind the five tells the 5 to go up. Round to the nearest HUNDRETH means to keep TWO decimal places EX 0.56 The 4 tells the 6 to stay the same.
Back
Interquartile Range
Front
Q3 - Q1
Back
Dot plot
Front
Each x or dot represent one person that has that number of pets. EX: One person has 5 pets.
Back
Decimals to Fractions
Front
Know your decimal places. Tenths, hundredths, thousandths. 0.36 say "36 hundredths" So you write the fraction 36/100. Then reduce divide top and bottom by 4 to get 9/25.
Back
36% of 500 is what?
Front
36/100 * 500 = x To solve you multiply 500 times 36/100.
Back
Communitive Property
Front
With addition and multiplication, it does not matter what order the numbers are written, you still get the same result.
Back
Correlation vs. Causation
Front
CORRELATION is just a recognizable pattern: EX. In the summer ice cream sales increase and so do the number of shark attacks. CAUSATION is the reason something occurs: EX. The number of ice cream sales is NOT the cause for the increase of shark attacks.
Back
The product of a rational number(other than zero) and an irrational number is irrational
Positive Correlation, Negative Correlation, or No Correlation.
Back
Conditional Relative Frequencies
Front
Comparing the individual data to the whole, represented as a percentage.
Back
Two-way Frequency tables and Relative Frequency Tables
Front
Comparing more than one thing in a table. Use the information in a table to answer questions.
Back
What percent of 200 is 40?
Front
x/100 * 200 = 40. To solve you would divide by two hundred, then multiply by 100.
Back
3 "is more than" a number
Front
3>n
Back
The sum of a rational number and an irrational number is irrational.
An irrational number is one that has decimal places that keep going forever such as pi= 3.14......
Front
2 + 3.14.... = 5.14....
and is still an irrational number.
Back
Mixed Number to Improper Fractions
Front
Multiply, then add! Keep the same denominator.
Back
Section 4
(10 cards)
Slope-intercept form
Front
y=mx +b
Back
Standard Form of a line
Front
Ax + By = C NO fractions, NO decimals, A has to be positive!
Back
Point-Slope Form
Front
(y - y) = m (x - x) When given a point and the slope, plug in the m, x, and y into the equation. You can then convert it into slope-intercept form to find the graph of the line.
Back
Cube Root
Front
What number multiplies times itself 3 times to get the number under the house?
Back
Exponent Rules
Front
There are a bunch!
Back
Flow Charts
Front
Follow the lines by answering questions until you get to your answer!
Back
Inverse Variation
Front
y=k/x
Back
Direct Variation
Front
Set up a proportion and solve.
y1/x1 = y2/x2
Back
Perfect Squares
Front
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, etc. The resulting number when you multiply a number times itself. EX: 4 X 4 = 16
Back
Square Root
Front
sqrt(9) = 3
It means what number multiplies times itself to get the number under the house.