Section 1
Preview this deck
ordered pair
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 1, 2020
Cards (106)
Section 1
(50 cards)
ordered pair
the x and y coordinates of a point on the coordinate plane (x,y)
graph of exponential decay function
other names for "y"
range, dependent variable, output
variable
NOT A NUMBER. A letter or symbol that stands for a number.
in y = mx + b, "m" stands for?
slope
range
set of all the possible y-values. OUTPUTS
independent variable
the INPUT or CAUSE in a situation or problem. It's the variable YOU CAN control. It's the X variable.
how is slope important for linear equations and lines?
linear equations and lines have CONSTANT slopes. The slope is the SAME all the way up and down the line.
words for ">"
is more than, is greater than, is larger than, shade above, shade to the right
what is the x-intercept?
the point where the graph crosses the x-axis. It has the coordinates (x, 0)
What is the SOLUTION of a system of equations?
where the lines touch or cross
Where are the solutions of a quadratic function?
at the x-intercepts. They are also known as zeros and roots.
continuous function
data appears as a smooth curve on a graph.
discreet function (scatter plot)
data appears as individual points on a graph. Whatever is being graphed cannot be broken down in to smaller pieces.
graph of a quadratic function
Absolute Value Parent Function
How do the slopes of perdendicular lines compare?
They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.
How do you combine like terms?
Add their coefficients.
What is a line of best fit?
A line drawn through the points on a scatterplot to estimate the best line through the data.
Table
A way to represent ordered pairs.
relation
set of ordered pairs
what slope does a HORIZONTAL line have?
slope = 0
Mapping
Bubbles that represent the x-values and the y-values.
Quadratic Parent Function
in y = mx + b, "b" stands for?
the y-intercept
changing the "b" in the slope-intercept form of the equation of a line changes what?
moves the line up or down the y-axis.
what is the linear parent function?
y = x f(x) = x
Graph a parabola using a table
What are "like terms"?
mathmatical terms that have the SAME variables raised to the SAME exponents.
vertical line test
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.
what is the y-intercept?
the point where the graph crosses the y-axis. It has the coordinates (0, y)
What is the "rate of change" on a graph?
Slope
graph of a linear function
How do you MULTIPLY exponents of like variables?
ADD them
changing the "m" in the slope-intercept form of the equation of a line changes what?
the steepness of the line
How many solutions can a system with 2 equations have?
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.
words for "<"
is less than, is smaller than, shade below, shade to the left
What is a quadratic equation or function?
an equation of function that has "x-squared" as its highest order exponent.
what is a linear inequality?
It is an equation with a <, >, < or =, > or = in the place of the =.
How do the slopes of parallel lines compare?
They are the same
what slope does a VERTICAL line have?
undefined slope
coordinate plane
a plane formed by 2 perpendicular lines called axes (the x-axis goes sided to side, the y-axis goes up and down).
domain
set of all of the possible x-values. INPUTS
What is a system of equations or system of inequalities?
2 or more equations or inequalities graphed on the same coordinate plane
How do you DIVIDE exponents of like variables?
SUBTRACT them
function
special relation where each x-value is paired with ONLY ONE y-value. (x-values DO NOT repeat, it passes the vertical line test)
other names for "x"
domain, independent variable, input
dependent variable
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.
graph of exponential growth function
define slope
the steepness of a line, vertical change/horizontal change, (y-y)/(x-x), rise over run
Section 2
(50 cards)
How to rearrange variables to solve for a specific variable.
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.
Seven "less than" a number
n - 7 You subtract 7 from the number.
Geometric Sequence
A pattern in which you multiply or divide each term by the same number.
What percent of 200 is 40?
x/100 * 200 = 40. To solve you would divide by two hundred, then multiply by 100.
Factoring with 4 terms
Solve by grouping. Group two sets and then factor those two groups.
When do you flip an inequality symbol?
Anytime you multiply or divide by a negative number.
36% of 500 is what?
36/100 * 500 = x To solve you multiply 500 times 36/100.
Distinguish between situations that can be modeled with linear functions and with exponential functions.
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.
The Square Root Property to solve Quadratics
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.
Fractions to Decimals
Divide the numerator by the denominator. 1/4 = 1 divided by 4 = 0.25
Simple Interest Formula
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
Outliers
A data point that does not fit in with the rest of the data.
3 "more than" a number
n + 3 Add 3 to the number
25% of what is 150?
0.25 * x = 150. To solve you divide by 0.25.
Range
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.
Median
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)
Solid or Dotted Line? Open or Closed Circle?
If it has the line under it (or equal to) it will be a closed circle or solid line.
y= and f(x)=
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.
How to tell when a function is increasing or decreasing?
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.
Compound Interest Formula
A=(P+r/n)^nt Common n values are 12=monthly, 4=quarterly, 2=semiannually, 1=annually. t is the time in years.
How do you solve Proportions?
When two fractions are set EQUAL to one another. This is the only time you Cross multiply!
Exponential functions y=2^x Where the variable is the exponent.
Over equal intervals, the y-values increase by multiplying or dividing by the same number each time.
SUBSTITUTION
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.
Mean (Average)
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
Absolute value of a negative number. IxI = -3
NO SOLUTION
Normal Bell Curve
Let's you know where you should find most of your data.
How to solve when written in function notation.
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
Rate of Change
Is another name for slope usually used in word problems.
Two-way Frequency tables and Relative Frequency Tables
Comparing more than one thing in a table. Use the information in a table to answer questions.
Decimals to Fractions
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.
Whole numbers
Start with 0, 1, 2, ......
Mode
The number that shows up the MOST
Histogram
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.
Integer
A whole number, both positive and negative numbers, including zero. ... ,-3, -2, -1, 0, 1, 2, 3, ......
Quadratic Formula
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.
Seven "is less than" a number
7<n
3 "is more than" a number
3>n
Sales Tax
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.
Completing The Square
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.
Skewed Bell Curve
When the data is not evenly distributed.
Box Plots
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.
Axis of Symmetry
The equations x=0 is the axis of symmetry for a parabola in standard form.
Natural numbers
Counting numbers: 1, 2, 3, ......
Percents
15% can also be written as 0.15, or as 15/100 which then must be reduced to 3/20.
Maximum or Minimum
Maximum is at the highest point of a parabola. Minimum is the lowest point.
Arithmetic Sequence
A pattern in which you add a number each time.
Estimate the Rate of Change from a graph
Find the change in y-values, then divide by the change in x-values.
Calculate and interpret the average rate of change (symbolically or from a table)
How fast is it changing? Sometimes you find out how much each one changes, then take their average.
Exponent Rules
There are a bunch!
ELIMINATION
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.
Section 3
(6 cards)