Algebra 1 Midterm Review
Review the following topics:
- interpreting time-distance graphs and time-speed graphs
- identifying real number properties (commutative, associative, distributive,
additive inverse, multiplicative inverse)
- Basic algebra skills:
* simplifying monomial/polynomial expressions using GEMDAS(exponent rules)
* solving linear equations
* determining if a given number makes an equation true or false
- solving literal equations for a specified variable
- solving compound linear inequalities
- System of linear equations:
* solving algebraically by substitution & elimination
* solving graphically by sketching the lines
* determining if a given point is the solution to a system of equations
- solving a system of linear inequalities graphically
- Statistics:
* reading info from a dot-plot & box-and-whisker plot
* calculating mean, median & mode
* determining if mean or median is the more appropriate representation
of a “typical value” in a skewed or symmetric data set
* interpreting standard deviation for a set of univariate data
* determining if a scatterplot exhibits linear, exponential, or
quadratic growth
* representing data on scatterplots to determine what type of linear
correlation exists (positive/negative or weak/strong)
* performing a regression to calculate the line of best fit
* using the line of best fit on a scatterplot to make predictions
* calculating the residual for a given input
-Sequences:
* evaluating a given explicit or recursive sequence rule
* determining if a sequence is arithmetic or geometric
* determining an explicit or recursive rule for arithmetic/geometric
sequences
- Functions:
* evaluating a function (algebraically, from a graph, table, list or
mapping)
* determining if a relation represents a function
* stating the domain and range of a function
When you see the words. . .
This is what you should think of doing
Find the solution set
Solve for the variable in the equation or inequality. Use
inverse operations to isolate the variable.
Write a polynomial in standard form
Write the terms such that the exponents are in descending
order.
Simplify an expression
Follow GEMDAS. An expression is fully simplified when:
- all coefficients of polynomials have been distributed
- all terms have been raised to their exponent
- like terms have been combined
There’s an assumption here that you know HOW to work
with exponents!!
Solve a literal equation for a specified
variable
A literal equation contains multiple variables. Your job is to
isolate the specified variable using inverse operations.
Evaluate an expression
Plug in a specific number for the variable in an expression
then simplify.
Represent a scenario as a time-distance
graph
Sketch as piecewise function. Whenever the scenario
changes speed, the slope of the lines change.
Solve a system of linear equations using
the substitution method
Isolate one of the variables in one of the equations.
Substitute the isolated variable’s equivalent into the second
equation.
Solve for the remaining variable.
Solve for the other remaining variable.
Solve a system of linear equations using
the elimination method
Write the two equations up so that like terms line up.
Choose which variable you want to cancel out (eliminate).
Multiply an equation (if needed) by a nonzero constant so
that the variable you chose will cancel out.
Add the two equations down so they create one equation.
Solve for the remaining variable.
Solve for the other remaining variable.
Solve a system of linear equations
graphically
Graph and label each linear equation.
Mark where the two equations intersect.
State the point of intersection (which is the solution!)
Solve a linear inequality
Isolate the variable. Remember to flip the direction of the
inequality symbol when dividing/multiplying by a negative #
Solve a compound inequality
Separate the compound inequality into two single
inequalities using the word AND or OR (depends on the
problem). Solve each inequality separately.
Determine if a given value is in a solution
set
Substitute the possible solution into the equation/inequality
to check if the # makes the equation/inequality true
Determine if a sequence is arithmetic or
geometric
If the sequence changes by a constant difference (ie, the
same # was added over and over) then the sequence is
arithmetic.
If the sequence changes by a constant ratio (ie, the same #
was multiplied over and over) then the sequence is
geometric.
Determine a recursive rule for a sequence
Express an in terms of an – 1
Determine an explicit rule for a sequence
Express an in terms of n
Determine the strength/direction of a
scatterplot’s correlation
Examine the scatterplot. The closeness of the points
indicates the strength of the linear relationship. The slope of
the points indicates the direction.
Calculate the equation for the line of best
fit
Perform a regression on the graphing calculator.
(Input data into lists, then go to STAT–CALC–LINREG ax+b
Calculate the residual for a given input
Actual y-value
Determine which measure of central
tendency best represents a “typical” value
in a data set
If the data is skewed, then outliers are present. Outliers
distort the mean, so the median is a better measure to use.
-
predicted y-value (from the line of best fit)
If the data is symmetric, then the mean has not been
distorted by outliers. The mean or the median would be fine
to use as the “typical” value but the mean is more common.
Estimate standard deviation
If univariate data is quite spread out (varied) then the
standard deviation is high.
If the univariate data is not spread out, then the standard
deviation is low.
Determine if a relation is a function
Examine the inputs (x-values). If an input has more than
one output, then the relation is NOT a function. In other
words, each input must not repeat.
State the domain of a function
List out all of the inputs.
State the range of a function
List out all of the outputs.
Evaluate a function
A function rule will be given (an equation, a mapping, a
graph, etc). You will be given an input and have to state the
output associated with it.
Solve algebraically
Create an equation to model the situation. Identify what the
variable represents. Solve for said variable. Make sure it
seems logical in the constraints of the problem.
Justify
Show/explain how you arrived at your answer. Not limited to
algebraic solution.