Download 7A-8B Benchmark Study Guide

7A/8B 2nd 9 Weeks Benchmark Study Guide
Comprehensive Exam
Equations:
Solving Multi-Step Equations
1. Use the distributive property (if necessary)
2. Combine like terms on each side
3. Get the variables on the same side of the equation
4. Use inverse operations to isolate the term with the variable
5. Use inverse operations to isolate the variable
6. Check your answer.
Equation Example
Functions or Not:
Input = Independent Variable = x-value; Output = Dependent Variable = y-value
 Start with relations.
 Relations are sets of ordered pairs.
 A relation is a function if for every input (x-value) there is exactly one
output (y-value). No x’s are repeated.
 A function is a linear function of the input and output change at a constant
rate and when graphed they form a line.
Function or Not Example
Linear Functions
Slope is the ratio of change between the dependent variable to the independent
variable.
𝑦 −𝑦
𝑟𝑖𝑠𝑒
Formula: 𝑚 = 𝑥2−𝑥1 or 𝑟𝑢𝑛
2
1
Slope-Intercept Form: y = mx + b; where m = slope and b = y-intercept
Writing Equations in Slope Intercept Form:
1. Find the slope either using the graph of the function or the slope formula
2. Find the y-intercept by using one given ordered pair (x, y) and the slope you
just found, m. Plus it into y = mx + b and solve the equation for b.
3. Take your recently calculate m and b and plug it into y = mx + b for your final
answer.
Slope Intercept Form Example
Graphing Linear Equations:
1. Graph the y-intercept first (y = mx + b). This point will be (0, b).
2. Use the slope (y = mx + b) to rise then run to your next point. (Remember: if
your slope is a whole number it is the whole number over 1 and if it is a
negative slope only one of the numbers is negative)
3. Repeat Step 2 a minimum of 3 times.
4. Draw in your line across the entire coordinate plane.
Graphing Examples
Distance Time Graphs
 Time is always the independent variable
 Distance is always the dependent variable
 The graph shows how your distance changes from a certain point over time.
It does not show your movements.
Distance Time Example
Scatter Plots
Shows the relationship between two sets of numerical data
Can Be:
 Linear Association – can be fit (even if not perfectly) to a line
o Positive Relationship: as one variable increases, the other variable
increases.
o Negative Relationship: as one variable decreases, the other variable
decreases.
 Nonlinear Association – no obvious relationships, cannot be fit to a line in any
way
Equations of a Trend Line
 A trend line is a linear equation (in our case) that represents the data shown.
 A trend line does not have to pass through all or any of the points. It just
has to fit closely to most of the points.
 A good rule of thumb would be to have as many points above the line as there
are below the line, but this is not always true or necessary.
 You write an equation of a trend line just as your would a line in slope
intercept form.
o Start by picking two points on the line. These do not have to be data
points.
o Follow the steps from the Slope-Intercept Form Section
Two-Way Tables
Two-way tables display bivariate categorical data.
Relative frequency percentages are found using the table’s total and the individual
box values.
You can make predictions using either row or column totals, depending on what you
are given.
Two Way Table Example
Systems of Linear Equations
*The solution to a system of equations is the point(s) of intersection for the lines
within the system.
Graphing:
 Make sure both lines are in slope-intercept form (y = mx + b)
 Graph the lines like we would any linear equation
 Find the point of intersection
 If the lines have
o Same slope and different y-intercepts: Parallel lines with no solution
o Same slope and same y-intercepts: Same lines with infinitely many
solutions
Graphing Example