Algebra 1 Practice questions

The density of an object is related to its mass and volume. The equation below shows the relationship between density (d), mass (m), and volume (V).

d= m/V

Which equation represents the volume of an object in relation to its density and mass?

• V= d - m

• V= dm

• V= d/m

• V= m/d

Kaylee is building a rectangular enclosure with an area of 90 square yards. She wants the length of the enclosed area to be 6 yards longer than the width, x. To represent this, she writes the equation x ^2 + 6x = 90. She then completes the square to help solve her equation for x. Which equation is equivalent to Kaylee’s equation after she completes the square?

• $\left(x+3\right)^2=\ 93$

• $\left(x+3\right)^2=\ 99$

• $\left(x+6\right)^2=\ 96$

• $\left(x+6\right)^2=\ 126$

Amil is given the equation shown. x^2 + 14x + 37 = 0 He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

•  $\left(x+7\right)^2-12=0$  

•  $\left(x-7\right)^2-12=0$  

•  $\left(x+7\right)^2+12=0$  

•  $\left(x-7\right)^2+12=0$  

A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03)^x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

• The number of users increases by 3 each day

• The number of users increases by 103 each day

• Each day after the first, the number of users is 3% greater than it was the day before.

• Each day after the first, the number of users is 103% greater than it was the day before.

Reggie carves and sells wooden sculptures online. He uses the function f(x) = 15x + 60 to determine the selling price, f(x), for a sculpture that took him x hours to make. Which statement explains the meaning of the value of f(75)?

• The selling price of a sculpture that took Reggie 1 hour to make is $75.

• The selling price of a sculpture that took Reggie 5 hours to make is $75.

• The selling price of a sculpture that took Reggie 5 hours to make is $135.

• The selling price of a sculpture that took Reggie 75 hours to make is $1,185

Which situation can be modeled by an exponential function?

• Photos cost $0.08 each.

• The population of a town increases by 3% each year

• The pay for an employee is $12.25 an hour plus 5% sales commission.

• The number of gallons of water in a tank decreases by 52 gallons each day

Central High School has 1,023 students. Approximately 75% of the school’s students attended the last home football game. Which attendance number is the most appropriat

• 760

• 767

• 767.3

• 767.25

Which of the following situations is best represented by a linear function?

• The amount Jeremy tips at a restaurant is a function of the total bill. He tips 15% of the total bill.

• The area of a square is a function of the length of the side of the square

• The distance a ball travels after being dropped is a function of acceleration and time. The distance is one-half of the acceleration multiplied by the square of the time

• The length of the side of a rectangle with an area of 48 is a function of the width of the rectangle.

Which equation represents the line passing through the points (-2, 4) and ( 2, 8)

• y= -x +2

• y= -x+6

• y = x+4

• y = x+6

Population A is 800. It grows by 5% each month. Population B is 500. It grows by 20 each month. Which set of statements correctly describes the growth of both populations?

• Population A is linear. Population B is exponential.

• Population A is exponential. Population B is linear.

• Population A is exponential. Population B is exponential.

• Population A is linear. Population B is linear.