Unit 2 Mid-Module Review

Unit 2 Mid-Module Review

Multiple Select

Select all equations that are equivalent to  $$\frac{\left(5x+6\right)}{2}=3-\left(4x+12\right)$$  

• $$5x+6=3-\left(4x+12\right)$$  

• $$\frac{\left(5x+6\right)}{2}=-4x-9$$  

• $$\frac{5}{2}x+3=3-\left(4x+12\right)$$  

• $$\frac{\left(5x+6\right)}{2}=-4x+15$$  

• $$5x+6=-8x-18$$  

​A. Multiplied only the left side of the equation by 2.

​B. Simplified the right side of the equation by distribution and combining like terms.

​C. Simplified the left side of the equation by expanding quotient.

​D. Incorrectly distributed (used 12 instead of -12) and then combined terms.

​E. Multiplied both sides of the equation by 2

​Correct Answers: B, C, E

Multiple Choice

A phone company charges a base fee of $12 per month plus an additional charge per minute. The monthly phone cost C can be represented by this equation: $$C=12+a\cdot m$$  , where a is the additional charge per minute, and m is the number of minutes used.

                Which equation can be used to find the number of minutes a customer used if we know a and C?

• $$m=\frac{\left(C-12\right)}{a}$$  

• $$m=\left(C-12\right)-a$$  

• $$m=C-12a$$  

• $$m=\frac{C}{a}-12$$  

​Students selecting B have subtracted a rather than divided by a to isolate m. Students selecting C have not attended to which value is the coefficient of a. Students selecting D have divided before subtracting.

​Correct Answer: A

Multiple Select

Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is $$240=12x+8y$$  . Here is a graph of this equation.  Select all the true statements.

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

• If ten students go to the zoo, then 15 adults can go.

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

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

• If 16 adults go to the zoo, then 6 students can go.

​Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is . Here is a graph of this equation.

Select all the true statements.

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

b.          If ten students go to the zoo, then 15 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 16 adults go to the zoo, then 6 students can go.

​Correct Answers: A, C, E

Open Ended

A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $8. Each additional inch costs $1.50, and each additional topping costs $0.75.

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

A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $8. Each additional inch costs $1.50, and each additional topping costs $0.75.

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

​Sample response: C = cost of pizza, s = additional inches above 10 for the pizza diameter, t = number of toppings. C = 8 + 1.50s + 0.75t

Open Ended

Consider this system of equations: 

$$y=-\frac{1}{2}x\ +\ 4\frac{1}{2}$$  

$$3x-4y=12$$  

Solve the system by graphing: https://www.desmos.com/practice

Label each graph and the solution. Type the solution below. Explain how you used the graph to get the solution.

Solution: (6, 1.5)​

​

The solution to the system of equations is the coordinate pair of the point where the two lines intersect. ​

Fill in the Blank

Solve the system of equations without graphing.

2y = x-4

4x + 3y = 5

Type your answer as (x,y) - include parentheses and do not put spaces