Final Review algebra 1

Semester 1 Final Review

by Ms. Nguyen

Poll

Problem 1: Ms. Nguyen is buying tacos for the family. People in her family are allowed to choose between 2 types of tacos. The Lengua tacos cost $3.99 each and the Ensenada Shrimp tacos cost $4.99 each.

a. Write an expression that could represent the cost of all Lengua tacos.  If you use a variable, specify what it represents.

• 3.99

• 3.99 x

• 4.99

• 4.99 x

​Writing Expression

​Make sure to have NO equal sign

​

​There should be a coefficient (a number) and a variable ( a letter).

​

Fill in the Blanks

Problem 1: Ms. Nguyen is buying tacos for the family. People in her family are allowed to choose between 2 types of tacos. The Lengua tacos cost $3.99 each and the Ensenada Shrimp tacos cost $4.99 each.

b. Write an expression that could represent the cost of all Ensenada Shrimp tacos.  If you use a variable, specify what it represents.

​Writing Equation

​Make sure to always have an EQUAL SIGN (=)

​

​Check if, your variables and values are correct!

Fill in the Blanks

Problem 1: Ms. Nguyen is buying tacos for the family. People in her family are allowed to choose between 2 types of tacos. The Lengua tacos cost $3.99 each and the Ensenada Shrimp tacos cost $4.99 each.

c. Write an equation that could represent the total cost of all the tacos. If you use a variable, specify what it represents.

Multiple Choice

Problem 2: What is the slope and the y-intercept?

y = x + 2

• slope = 0

  y-int = 2

• slope = 1

  y-int = 2

• slope = x

  y-int = 2

• slope = 2

  y-int = x

Fill in the Blanks

Problem 3: Solve the equation. ( Hint: Isolate y)

2 x + 0.50 y = 120

Fill in the Blanks

Problem 4: Solve the equation. ( Hint: Isolate y)

y + 2x = 1

Then, GRAPH the equation.

Poll

Problem 5: A bowl weighs 340 grams when empty. It is then filled with sugar. One tablespoon of sugar weighs 12.5 grams.

Write an equation to represent the relationship between the total weight of the bowl in grams, W , and the tablespoons of sugar, S .

• I'm comfortable and know how to do this

• I'm confused

• I need more suppo

Multiple Choice

Problem 5: A bowl weighs 340 grams when empty. It is then filled with sugar. One tablespoon of sugar weighs 12.5 grams.

Write an equation to represent the relationship between the total weight of the bowl in grams, W , and the tablespoons of sugar, S .

• S = 340 + 12.5 W

• W = 340 + 12.5 S

• 340 + 12.5 W

• 340 + 12.5 S

Open Ended

Problem 6: Solve the system of equations without graphing. Show your reasoning. 

(Hint: Use Scratch paper if needed)

5x + y = 7

20x - y = - 2

Draw

Problem 7: C = 12 + a (m), FIND a if we know m and C

Fill in the Blanks

 Write these mixed fractions into their equivalent fraction.

$Fraction\ 1:\ \ \ \ \ \ \ 2\ \frac{1}{2}$   $Fraction\ 2:\ \ \ \ \ \ \ \ 4\ \frac{1}{2}$   $Fraction\ 3:\ \ \ \ \ \ \ \ \ \ 3\ \frac{1}{6}$  

Fill in the Blanks

Problem 8: A coach for a little league baseball team is ordering trophies for the team. Players on the team are allowed to choose between 2 types of trophies. The gold baseball trophies cost $3.99 each and the uniform baseball trophies cost $5.49 each. The team orders g gold trophies and u uniform trophies. 

               Write an expression that could represent the total cost of all the trophies.

Fill in the Blanks

Problem 9: A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $8. Each additional inch costs $2.50, and each additional topping costs $0.60.

Write an equation that represents the cost of a pizza. Be sure to specify what the variables represent.

Fill in the Blanks

Problem 10 : Here is the graph of a linear equation. Select ALL the true statement: 

a. If no adult chaperones were needed, 30 students could go to the zoo. 

b. If five students go to the zoo, then 17 adults can go. 

c. If four more adults go to the zoo, that means there will be room for six fewer students. 

d. If two more students go to the zoo, that means there will be room for three fewer adults. 

e. If 8 adults go to the zoo, then 18 students can go.

Open Ended

Problem 11: Solve the system of equations without graphing. Show your reasoning. 

2y = x - 6

4x + 2y = 4

Multiple Choice

 PrConsider the inequality $$\frac{x\ +\ 2}{5}\ >\ \frac{x}{4}\ +\ 1$$  . Which value of x is a solution to the inequality? 

• 10

• 13

• -13

• -10

Open Ended

Problem 13: An empty shipping box weighs 250 grams. The box is then filled with, T, T-shirts. Each T-shirt weighs 132.5 grams. 

A. Write an equation that represents the weight, W, in grams, of the filled box. 

B. Consider the equation 2,900 = 250 + 132.50T. In this situation, what does the solution to this equation tell us? 

Open Ended

Problem 14: A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work 20 hours per week. His goal is to make $300 per week. 

Create a system of equations that models the situation for one week. Define the variables you use.

Draw

Problem 14: A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work 20 hours per week. His goal is to make $300 per week.

The graph shows one of the relevant equations in this situation. Draw the graph of the other relevant equation. 

Open Ended

Problem 15: To raise money for soccer team at CAHS, a group of coaches is holding a weekend tacos at the quad. They charge $7 per person for entry into the event. The group would like to earn at least $600, after paying for the cost of renting the taco truck, which is $30 an hour. 

Let x represents the number of entry tickets sold and y the hours of space rental,

WRITE an inequality represents the constraints in the situation.