Show:
Functions and Solutions
Solving Equations
Inequalities
Systems of Equations
Simplifying Expressions
100

What is a solution to the function f(x) = 3x - 4 when x= 0?

The solution (f(x)) = -4

100
Solve the following equation:


3x + 4 = 16

x = 4

100

Solve the following inequality:

3x + 5 < 23

x < 6

x is less than 6

100

Does the system of equations below have 1 solution, no solutions or infinite solutions?

2x + 3y = 1

4x + 6y = 2

Infinite Solutions

100

Simplify the following expression:

3x + (x+2)2

x2 + 7x + 4

200
The function, f(x) represents the amount of money spent on coffee over the course of days (x).

f(x) = 1.5x

How much have you spent on coffee after 6 days?

$9

200

Solve the following equation:

3(x - 1) + 10 = 19

x = 4

200

Solve the following inequality:

2(x - 4) + 10 > 12

x > 5

x is greater than 5

200

Solve the following system of equations:

3x - y = 10

2x + y = 15

x = 5

y = 5

200
If (x - 5)2 - 6x is equal to x2 + bx + 25, what is the value of b?

B is -16

300

What are the zeros of the following quadratic function?f(x) = x2 - 5x - 50

x = 10 and -5

300

Ellis runs around a track at a constant speed.

  • The distance around the track is 1/4 mile.
  • It takes Ellis 3.2 minutes to run around the track once.

What is the total amount of time, in minutes, it takes Ellis to run one mile? Show or explain how you got your answer.

12.8 minutes per mile

3.2 minutes

1/4 miles


If you divide, you get 12.8 minutes for every mile.

300

If you graph the solution of y > 4x + 5, is the solution above the line or below the line?

Above the line

300

Solve the following system of equations:

-6x + 2y = 22

3x + 10y =11

x = -3

y = 2

300

Expand the following expression:

(x + 3)(x - 10)

x2 - 7x - 30

400

What kind of function has the highest rate of growth: linear, quadratic or exponential?  Why?

Exponential has the highest rate of growth because the exponent is represented by the x.  As x grows, y increases at the highest rate.

400

All the students in Mr. Greene’s class are either 17 years old or 18 years old.

  • There are a total of 20 students in Mr. Greene’s class.
  • The sum of the ages of the 20 students is 345 years.

What is the total number of 17-year-old students in Mr. Greene’s class?

There are 15 17-year olds in her class.
400

Mikaila is saving money to purchase a laptop computer. She already has saved $150 in her savings account. Next week Mikaila will begin a tutoring job that pays $10 per hour. All the money she earns tutoring will be added to her savings account. 

The least expensive laptop that Mikaila is considering purchasing costs $550, including tax.

Write and solve an inequality to determine the minimum number of hours Mikaila needs to tutor to have enough money in her savings account to purchase a laptop that costs $550 or more. Show or explain how you got your answer.

y > 10x + 150

Inequality: 550 > 10x + 150

Solving: 550 > 10x + 150

             400 > 10x

              40 > x

She needs to work at least 40 hours to afford the laptop.

400

Consider this system of equations.

h+c=2.25

h−c=1.75

What value of h makes the system of equations true?

h = 2

400

If a and b are rational numbers and c is an irrational number, what type of number is abc?

Irrational

500

Consider the linear function, f(x) = -3x + 5:

a) what is the y intercept of the function?

b) what is the slope of the function?

c) is (-1, 2) a solution of the function?

a) 5

b) -3 (bonus points if they identify the direction and/or the rise and run of the function)

c) no, if x = -1, y = 8

500

Ellis runs around a track at a constant speed.

  • The distance around the track is 1/4 mile.
  • It takes Ellis 3.2 minutes to run around the track once.

Ellis will run for 40 minutes every day for 5 days, with a goal of running a total of 15 miles. Will Ellis meet this goal? Explain your reasoning.

Yes, he will have run 15.625 miles in total over the 5 days.

You can build a proportion:

3.2 min = 200 min

1/4 mil       ?  mil

You cross multiply and get: 3.2 (?) = 200 * 1/4

3.2x = 50

x = 15.625

500

Mikaila is saving money to purchase a laptop computer. She already has saved $150 in her savings account. Next week Mikaila will begin a tutoring job that pays $10 per hour. All the money she earns tutoring will be added to her savings account.

The most expensive laptop that Mikaila is considering purchasing costs $1,150, including tax.

Write and solve a compound inequality to determine the number of hours Mikaila needs to tutor to have enough money in her savings account to purchase a laptop that costs at least $550 but not more than $1,150. Show or explain how you got your answer.

Enter your answer and your work or explanation in the space provided.

 

y > 10x + 150

Compound Inequality: 550 < 10x + 150 < 1150

Solving:   550 < 10x + 150 < 1150

               400 < 10x < 1000

               40 < x < 100

She needs to work between 40 and 100 hours to afford a laptop at least $550 but not more than $1150.

500

Which of the following has the same solution as this system of equations?

4x+9y=10

2x+3y=12

a) 4x+9y=10

    4x+3y=24

b) 4x+9y=10

    2x+9y=36

c) 4x+9y=10

    4x+6y=24

d) 4x+9y=10

    2x+9y=12


c) 4x+9y=10

    4x+6y=24

500

Identify the irrational numbers below:

a) square root of 3

b) 4/5

c) square root of 121

d) 6.123...

a (square root of 3) and d (6.123...)