Free Printable Algebra 1 AIR Review

1.

An Expression is shown:

(2x-3) + [4x(3x+2)]

a)

$9x-1$

b)

$14x+5$

c)

$12x^2+2x-1$

d)

$12x^2+10x-3$

2.

An expression is given:

(2x+8)(5x-7)

Which answer is equivalent to the given expression?

a)

36x-56

b)

$10x^2-56$

c)

$10x^2+26x-56$

d)

$10x^2+56x+56$

3.

Which expression is equivalent to $\left(2x^2+3\right)\left(x+4\right)$

a)

$2x^3+12$

b)

$2x^2+11x+12$

c)

$2x^3+6x^2+4x+12$

d)

$2x^3+8x^2+3x+12$

4.

An expression is shown:

$\left(3x^2+2x-5\right)-\left(5x^2-4x+1\right)$

Which expression is equivalent to the given expression?

a)

$-2x^2+6x-6$

b)

$-2x^2-2x-4$

c)

$8x^2+6x-6$

d)

$8x^2-2x-4$

5.

Trent plants a sunflower that is 6 inches tall. The sunflower is expected to grow at an average rate of 1.5 inches per day during the next month.

Create an equation that Trent can use to find the number of days, x, it will take to grow to a height of 45 inches.

(a)

6.

A factory has two assembly lines, M and N, that make the same toy. On Monday only assembly line M was functioning, and it made 900 toys.

On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and Line N made 480 toys per hour. Line N made as many toys on Tuesday as Line M did over both days.

Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

(a)

7.

The population of rabbits on a large island doubles each year. On January 1, the population is 150 rabbits.

Which equation can be used to find the number of years, x, it will take for the population to reach 4800?

a)

$4800\ =\ 2x\ +150$

b)

$4800=2\cdot150^x$

c)

$4800\ =\ 2^x+150$

d)

$4800=150\cdot2^x$

8.

Stephanie adds pennies, nickels, and quarters to a scale until the mass of the combined coins is 75 grams. Each penny has a mass of 2.5 grams, each nickel is 5 grams, and the quarters are 5.7 grams.

Create an equation to model this situation where x is the number of pennies, y is the number of nickels, and z is the number of quarters Stephanie can put on the scale so the mass of the combined coins is 75 grams.

(a)

9.

A scientist is studying wildlife. She estimates the population of bats in her state to be 270,000. She predicts the population to grow at an average of 2.9 percent.

Using the scientist's prediction, create an equation that models the population of bats, y, after x years.

(a)

10.

Chad buys pineapples , watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples cost $2.15 each, watermelons cost $3.75 each. The bag of grapes costs $4.48.

Create an equation to model the situation, where p represents the number of pineapples, and w represents the number of watermelons Chad can purchase.

(a)

11.

Kenji has at most $30 to spend on lily bulbs and tulip bulbs at his local flower store. Lily bulbs cost $4 each, and tulip bulbs cost $2 each. Tax is included in the prices of the bulbs.

Create a constraint that can be used to represent all possible numbers of lily bulbs, x, and tulip bulbs, y, Kenji can buy.

(a)

12.

The equation is used to find the force of gravity, F, between two objects, where

G is the gravitational constant

$m_{1\ }and\ m_2$ are the masses of the two objects

r is the distance between the two objects

$F\ =\ \frac{Gm_1m_2}{r^2}$

Which equation correctly shows the distance between the two objects?

a)

$r\ =\ \frac{\sqrt[]{F}}{Gm_1m_2}$

b)

$r\ =\ \frac{\sqrt[]{Gm_1m_2}}{F}$

c)

$r\ =\ \sqrt[]{\frac{F}{Gm_1m_2}}$

d)

$r\ =\ \sqrt[]{\frac{Gm_1m_2}{F}}$

13.

An equation is given:

y = 3x +c

Create an equivalent equation by solving for x in terms of y.

x = (a)

14.

An engineer is designing a conical container. It needs to hold a specific volume and have a specific height. She needs to know the radius of the container, r, in terms of its volume, V, and height, h.

Select the equation the engineer can use to determine the radius.

Volume of a cone - $V\ =\ \frac{\pi r^2h}{3}$

a)

$r=\sqrt[]{\frac{3V}{\pi h}}$

b)

$r\ =\ \sqrt[]{\frac{\pi h}{3V}}$

c)

$r\ =\ \frac{3V}{\pi h}$

d)

$r\ =\ \frac{\pi h}{3V}$

15.

Eleanor incorrectly solves the problem below. which step was the mistake?

a)

1

b)

2

c)

3

d)

4

e)

5

16.

A linear model is used to display the scores of baseball team's games using the batting averages of its top players. The correlation coefficient for the linear model is 0.37.

Which statement about the linear model is true?

a)

the correlation coefficient represents a strong, positive linear relationship

b)

the correlation coefficient represents a strong negative linear relationship

c)

the correlation coefficient represents a weak, positive linear relationship

d)

the correlation coefficient represents a weak, negative linear relationship

17.

Select all of the correlation coefficients that represent a linear model with weak correlation.

a)

-0.982

b)

-0.618

c)

-0.103

d)

0.204

e)

0.907

18.

Bryson collects data on the depth of a river at various points and the velocity of the river at those points. His data have a correlation coefficient of -0.9382

a)

b)

c)

d)

19.

The population of a town has grown by an average of 2000 people per year over the last 10 years.

Which equation could represent an appropriate linear model of the population?

a)

$y=25,000x+2,000$

b)

$y=2,000x+25,000$

c)

$y=-25,000x+2000$

d)

$y=-2,000x+25,000$

20.

Juan wants to rent a house. He gathers data on many similar houses. The distance from the center of the city, x, and the monthly rent for each house, y, are shown in the scatter plot. Juan models the data with a linear equation.

Based on the scatter pl0t, what could the number 1275 represent in his equation?

a)

the estimated rent for a house in the center of the city

b)

the estimated minimum rent for a house far from the center of the city

c)

the estimated change in rent for each additional mile from the center of the city

d)

the estimated change in distance from the center of the city for each dollar change in rent

Algebra 1 AIR Review

Total questions: 20

Worksheet time: 40mins

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