Station #1: Solving Equations
Solve the following equations for the missing variable:
1) −3𝑥 + 5𝑥 − 5 = 13
2) 8(𝑥 − 1) = 6𝑥 + 4 + 2𝑥
3) You paid $600 for a new guitar. Your guitar cost $40 more than
twice the cost of your friend’s guitar. How much did your friend’s
guitar cost?
4) A new pizza shop is going to create new menus. Each menu
costs $.50 to produce. The owners have a total of $2500 to spend
on the new menus. How many menus can they produce at that
price?
5) Membership for the Alpine Rock-Climbing Gym costs $25 per
month plus a $125 sign-up fee. Membership for Rocco’s RockClimbing Gym costs $30 per month and a $50 sign-up fee. After
how many months will the memberships cost the same?
Station #2: Graphing Points and
Lines
1) Identify the slope and y-intercept of the following equation:
−3𝑥 + 6𝑦 = 12
2) What are the four different types of slope?
3) What is the equation of the line in the following graph?:
4) A server at a local restaurant is paid a minimum of wage of
$2.13/hr, plus all the tips they receive. If the variable t can be
used to represent the amount of tips in a given night, and h can
be used to represent the hours worked in a given night, write an
expression that can be used to find the server’s pay.
5) Graph the following equation: 4𝑥 − 2𝑦 = 8
Station #3: Writing Linear Equations
Slope Formula: 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏
Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
1) Find the slope given the following points: (−4, 3); (−1, −3)
2) Identify the slope and the point that were used to create the
following point-slope equation: 𝑦 + 8 = −3(𝑥 − 4)
3) Write a linear equation given the following information:
1
𝑚 = − ; (4, 7)
2
4) Write the equation of the line given the following information:
(2, 4) and (−3, −6)
4
5) Write the equation of the line given that 𝑚 = and 𝑏 = −3
5
Station #4: Solving Inequalities
Solve the following inequalities and graph the solution.
1) 3(𝑥 + 1) − 4𝑥 ≥ −5
2) 6𝑣 − 1 > 3𝑣 + 8
3) 3 < 2𝑥 − 3 ≤ 12
4) The perimeter of a rectangle is at least 32cm. The length of the
rectangle is 9cm. What are the possible widths of the rectangle?
5) Graph the following inequality: 3𝑦 + 2𝑥 > 6
Station #5: Systems of Equations
(Graphing Method)
Solve the following system of equations using the graphing
method:
{
4𝑥 + 𝑦 = 2
𝑥−𝑦 =3
𝑦 = −3𝑥 + 4
1) {
𝑦 = 3𝑥 − 2
2𝑥 − 𝑦 = −5
3) {
−2𝑥 − 𝑦 = −1
2𝑦 − 𝑥 = 2
2) {
1
𝑦= 𝑥+1
2
Station #6: Systems of Equations
(Substitution Method)
Solve the following systems of equations using the substitution
method:
{
4𝑥 − 𝑦 = 20
−2𝑥 − 2𝑦 = 10
𝑦 = 5𝑥 − 7
1) {
−3𝑥 − 2𝑦 = −12
−3𝑥 − 8𝑦 = 20
2) {
−5𝑥 + 𝑦 = 19
3) Adult tickets to a play cost $22. Tickets for children cost $15.
Tickets for a group of 11 people cost a total of $228. Write and
solve a system of equations to find out how many adult and
children tickets were purchased by the group.
Station #7: Systems of Equations
(Elimination Method)
Solve the following system of equations using the elimination
method:
{
−𝑥 − 7𝑦 = 14
−4𝑥 − 14𝑦 = 28
3𝑥 − 2𝑦 = 2
1) {
5𝑥 − 5𝑦 = 10
4𝑥 + 8𝑦 = 20
2) {
−4𝑥 + 2𝑦 = −30
3) A photo studio offers portraits in 8 x 10 and wallet size formats.
One customer bought two 8 x 10 portraits and four wallets size
portraits and paid $52. Another customer bought three 8 x 10
portraits and two wallet size portraits and paid $50. What is the
cost for each 8 x 10 and wallet size portrait?
Station #8: Systems of Inequalities
Solve the following systems of inequalities:
4𝑥 + 3𝑦 > −6
{
𝑥 − 3𝑦 ≤ −9
3𝑥 + 𝑦 ≥ −3
1) {
𝑥 + 2𝑦 ≤ 4
𝑥+𝑦 ≥2
2) {
4𝑥 + 𝑦 > −1
3) Suppose you have a job mowing lawns that pays $12 per hour.
You also have a job at a clothing store that pays $10 per hour.
You need to earn at least $350 per week, but you can work no
more than 35 hours per week. You must work a minimum of 10
hours per week at the clothing store. What is a graph showing
how many hours per week you can work at each job?
Station #9: Functions
1) How does the vertical line test work and what does it help us to determine?
2) Given that 𝑓(𝑥 ) = −4𝑥 + 5; find 𝑓(−7)
3) Create a mapping diagram for the following coordinates and determine if it is a
function or not:
(−1, 5); (6, −2); (0, 5); (2, 2); (−2,0); (2, −1)
4) What is the domain and range of the relation from question 3?
5) A car salesman sells John a car for a down payment of $2500 and a monthly cost
of $205. How much money will John spend after 3 years?
6) What is the Domain and Range of the following graph?
Station #10: Arithmetic and
Geometric Sequences
Arithmetic Sequence: 𝑎𝑛 = 𝑑 (𝑛 − 1) + 𝑎1
Geometric Sequence: 𝑎𝑛 = 𝑎1 ((𝑟)𝑛−1 )
For the following problems, determine whether the sequence is
arithmetic or geometric then find the indicated term.
1) -7, -3, 1, 5…; find the 13th term.
2) 3, 6, 12, 24…; find the 10th term
3) A manager at a clothing store documented the original price
and the marked down price of a new pair of jeans. Using this
information, what will the price of the jeans be after the 7th
markdown?
$60 (original price), $52, $44…
4) You have a gift card to Sheetz worth $50. After you buy lunch
on Monday, the value left on the card is $46.75. After buying
lunch on Tuesday, the value on the card is $43.50. How much
money will be left on the card after 15 lunches?
Station #11: Properties of
Exponents
Exponent Rules:
( 𝑎 𝑚 )𝑛 = 𝑎 𝑚 ∙ 𝑛
𝑎0 = 1
𝑎
−𝑛
=
(𝑎𝑏)𝑚 = 𝑎𝑚 𝑏 𝑚
1
𝑎𝑛
𝑎𝑚
𝑎𝑛
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
= 𝑎𝑚−𝑛
𝑎 𝑚 𝑎𝑚
( ) = 𝑚
𝑏
𝑏
Simplify the following using the properties of exponents:
4
1) 2𝑥 ∙ 4𝑥
4)
2𝑥 2 𝑦 4 ∙4𝑥 2 𝑦 4 ∙3𝑥
3𝑥 −3 𝑦 2
4 −3 )−1
2) (2𝑥 𝑦
5)(
3𝑥 6 𝑦 9 𝑧 4 ∙2𝑦 5
7𝑧 −1
3)
)
0
2𝑥 4 𝑦 −4 𝑧 −3
3𝑥 2 𝑦 −3 𝑧 4
3
6)
(2𝑥 3 𝑧 2 )
𝑥 3 𝑦 4 𝑧 2 ∙𝑥 −4 𝑧 3