HMS Pre-Algebra 2023

Dependent/Independent Variables

100

Wyatt is going backpacking in a couple of days and is buying trail mix for the trip. The amount of trail mix he will bring depends on how long he plans to backpack.

a = the amount of trail mix Wyatt will bring.

l = the length of the backpacking trip.

Which of these variables is independent and which is dependent?

l is the independent variable and a is the dependent variable.

200

Scott is building a trophy case for his son. The number of trophies will determine how many shelves the case will have. 

t = the number of trophies

s = the number of shelves

Which of the variables is independent and which is dependent?

s is the independent variable and t is the dependent variable.

300

The senior class at Arlington High School is graduating. The number of students receiving diplomas dictates the duration of the graduation ceremony. 

s = the number of students receiving diplomas

d = the duration of the graduation ceremony

Which of these variables is independent and which is dependent?

d is the independent variable and s is the dependent variable.

400

A solar farm in California produces much of its output during the summer, when the sun is the most intense. The more sunlight a solar cell receives, the more power it will produce. 

s = the amount of sunlight received 

p = the amount of power produced 

Which variable is the dependent variable?

p is the dependent variable.

500

Every day at lunch, Sarah swims laps in the pool for one hour. The number of laps she is able to swim in the hour depends on the speed at which she swims. 

l = the number of laps Sarah is able to swim in one hour

s = the speed at which Sarah swims

Which variable is the independent variable?

s is the independent variable.

Scientific Notation

100

Multiply. Write your answer in scientific notation.

3 x (1 x 10⁵)

 3 x 10⁵

200

Multiply. 

(1 x 10²)(3 x 10³) 

3 x 10⁵

300

Multiply.

50 x (2 x 10⁰) 

1 x 10²

400

Multiply. Write your answer in scientific notation.

(1 x 10^-3)(9 x 10^-6) 

9 x 10^-9

500

Multiply. Write your answer in scientific notation.

(9.5 x 10^-15)(4.6 x 10³)

4.37 x 10^-11

Rational and Irrational numbers

100

Is 10.482 an irrational number?

no

200

Is 5.741 a rational number?

yes

300

Is 1/7 an irrational number?

no

400

Is 11/70 a rational number?

yes

500

Which of the following are rational numbers?

839, 407/617, 467.539, 292/137

839, 407/617, 467.539, 292/137

All of them.

Multiply and Divide Integers

100

Multiply:

7 x -3 =

-21

200

Multiply: 

-5 x -7 = 

35

300

Divide:

48/8

6

400

Divide: 

-108 ÷ -12 =

9

500

Divide:

8,832 ÷ -96 =

-92

Solve one-step equations

100

Solve for f.

f - 2 = 3

f =

5

200

Solve for z.

6 = 2z

z =

3

300

Solve for u.

5 = u - 1

u =

6

400

Solve for j.

j/2 = -1

j = 

-2

500

Solve for s. 

-4s = -16

u = 

4