Ohio ALGEBRA 1: all questions

ALGEBRA 1 AIR PREP

all released questions from previous exams

Fill in the Blanks

Multiple Choice

• mean: increase

  range: increase

• mean: increase

  range: decrease

• mean: decrease

  range: increase

• mean: decrease

  range: decrase

Multiple Select

• q= -6

  r= 2

  z= -4

• q= 6

  r= -2

  z= 4

• q= -4

  r= 3

  z= -1

• q= 4

  r= -2

  z= 2

• q= -12

  r= 1

  z= -11

Multiple Choice

Multiple Choice

Multiple Choice

Multiple Choice

PART B. Select the phrase for each blank box to complete a true statement about the likelihoods of juniors and seniors driving to school.

• The juniors are "LESS LIKELY" to drive to school than the seniors because because they have a "SMALLER" relative frequency.

• The juniors are "EQUALLY LIKELY" to drive to school as the seniors because because they have an "EQUAL" relative frequency.

• The juniors are "MORE LIKELY" to drive to school than the seniors because because they have a "GREATER" relative frequency.

• The juniors are "LESS LIKELY" to drive to school than the seniors because because they have a "GREATER" relative frequency.

• The juniors are "MORE LIKELY" to drive to school than the seniors because because they have a "SMALLER" relative frequency.

Multiple Choice

Francine creates a bar graph showing the distance between her city and each capital city in the United States.

Which unit of measure would be an appropriate unit for Francine to use to label her graph?

• centimeters

• inches

• miles

• meters

Multiple Choice

Which situation describes a quantity that increases by constant percent rate?

• The size of one photo is 15% larger than the size of another photo.

• The number of plants in a pond is 85% of the number from the previous year.

• The population of one city is 85% greater than the population of another city.

• The number of magazine subscriptions each year is 15% greater than the previous year.

Open Ended

An equation is given.

$$5y-2x=5$$


Create an ordered pair that represents one point on the graph of the equation.

(  _____ , _____ )   

Open Ended

An incomplete table of values for an exponential function is shown. The exponential function is of the form  $$y=a\cdot b^x$$  , where  $$a$$  is a real number such that $$a\ne0$$ and $$b$$  is a positive real number that is not equal to 1.

Complete the table with possible values for the exponential function.

Multiple Choice

Michelle holds a small rock in her hand.
Density (D ) can be found using the formula   $$D=\frac{mass}{volume}$$  

Which would be the most appropriate for calculating density calculating density of the rock in Michelle's hand?

• $$\frac{lb}{mm^3}$$  

• $$\frac{g}{cm^3}$$  

• $$\frac{kg}{m^3}$$  

• $$\frac{ton}{m^3}$$  

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Multiple Choice

The histograms shown display the number of cans of food donated by students in the freshman class and the sophomore class at a school.

Which statement is true?

• The freshman class has a lesser mean number of cans donated than the sophomore class.

• The freshman class has the same median number of cans donated as the sophomore class.

• The freshman class has a greater mean number of cans donated than the sophomore class.

• The freshman class has a greater median number of cans donated than the sophomore class.

Multiple Choice

A sequence is shown. $$3,\ 6,\ 12,\ 24,\ 48,\ ...$$  

Which function, $$f\left(n\right)$$  , represents the $$n$$  th term of the sequence, where $$f\left(1\right)=3$$  ?

• $$f\left(n\right)=2\cdot3^{n-1}$$  

• $$f\left(n\right)=3\cdot2^{n-1}$$  

• $$f\left(n\right)=2\cdot3^n$$  

• $$f\left(n\right)=6^n$$  

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Multiple Choice

The manager of a company uses the function shown to model its daily profit based on the price of a product in dollars, $$x$$ .

$$f\left(x\right)=\left(x-22\right)\left(53-x\right)$$  

A.   What is the minimum price, in dollars, to avoid a loss? 

B.  What is the maximum price, in dollars, to avoid a loss?

C.   What is the price, in dollars, that results in the greatest profit?

• A. $22
  
  B. $53
  
  C. $37.50

• A. $22
  
  B. $53
  
  C. $240.25

• A. $53
  
  B. $22
  
  C. $240.25

• A. $53
  
  B. $22
  
  C. $37.50

Multiple Choice

A new car wash business records the number of cars it washes each day for the first 7 days the business is open. The data are shown in the table.The car wash owner uses the equation $$y=x+44$$ to model the data, where $$x$$  represents the number of days the business has been open and  $$y$$  represents the number of cars washed.

Which explanation best describes whether the equations is a good fit for the data?

• The equation is a good fit because the residual points are approximately linear.

• The equation is a good fit because the residual points have a positive association.

• The equation in not a good fit because a residual plot with the pattern from the data set indicates a bad fit.

• The equation in not a good fit because there should be an equal number of points below and above the x-axis in the residual plot.

Multiple Choice

This item has three parts.  Eleanor incorrectly solves the equation $$\frac{1}{2}\left(x+18\right)=4\left(2x-6\right)-9x$$ . Part A.  Select the first equation in which Eleanor makes an error. 

• step 1.   $$x+18=8\left(2x-6\right)-9x$$  

• step 2. $$x+18=16x-48-9x$$  

• step 3. $$x+18=7x-48$$  

• step 4. $$66=6x$$  

• step 5. $$x=11$$  

Open Ended

This item has three parts.  Eleanor incorrectly solves the equation $$\frac{1}{2}\left(x+18\right)=4\left(2x-6\right)-9x$$  

Part B.  Create an equation to correct Eleanor's error identified in Part A.

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Multiple Choice

A landscaper records the heights, in feet, of 15 newly planted trees in a community garden, as shown.

3.2, 4.3, 3.5, 5.4, 3.7,

5.5, 6.2, 3.1, 6.8, 7.1,

4.8, 6.5, 4.9, 5.3, 5.9

Complete the histogram by selecting frequencies for the heights of the newly planted trees in the community garden.

Multiple Choice

The graph of a function is shown.

What is the domain of the functions?

• $$x\ge-4$$

• $$x\ge-2$$

• $$x\ge0$$

• $$x\ge1$$

Multiple Choice

Samantha sells two types of wristbands, rope or beaded. She charges more for beaded wristbands than for rope wristbands. The amount of money, in dollars, that she collects from selling  $$x$$  wristbands of one type and  $$y$$  wristbands of the other type can be modeled by the expression $$5x+8y$$ .



What does the variable  $$y$$  represent in this situation? 

• the number of rope wristbands sold

• the number of beaded wristbands sold

• the selling price of one rope wristband

• the selling price of one beaded wristband

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Multiple Choice

The graph of a system of inequalities is shown.

Create the system that is represented by the graph.

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Open Ended

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.

Multiple Choice

Select the most appropriate unit for each situation.

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Multiple Choice

An equation is given.

$$A=4\ \pi\ r^2$$

Solve the equation for  $$r$$  . 

• $$r=\sqrt{\frac{4\ \pi}{A}}$$  

• $$r=\sqrt{\frac{A}{4\ \pi}}$$  

• $$r=\frac{4\ \pi\ A}{2}$$  

• $$r=\frac{A}{2\ \pi}$$  

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Multiple Choice

To start her collection of comic books, Joylin's uncle gives Joylin a box of comic books and several monthly subscriptions to comic books. The number of comic books in ther collection, y, after x months is modeled by the equation shown

y = 40 + 6x

What does the number 40 represent in this equation?

• the price of a comic book subscription

• the number of months of Joylin's subscriptions

• the number of comic books in the box she received

• the number of title subscriptions Joylin received each month

Multiple Choice

A system of linear euqations is shown.

-3x + y = K

2x + 3y = L

Which system has the same solution as the system shown?

• -9x + 3y = -3K

  2x + 3y = L

• 6x - 2y = -2K

  2x + 3y = L

• -3x + y = K

  2x + 4.5y = L

• -3x + y = K

  -8x - 12y = L

Multiple Choice

A function is shown.

f (x) = x² + 2x -1

Which graph represents the function?

Multiple Choice

Solve the equation

$$x^2+6x=-\frac{11}{4}$$  .

• $$x=-3$$  and $$x=2$$  

• $$x=-2$$  and $$x=3$$  

• $$x=\frac{1}{2}$$  and $$x=-\frac{11}{2}$$  

• $$x=-\frac{1}{2}$$  and $$x=-\frac{11}{2}$$  

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Multiple Choice

Henry places $$x$$ marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression shown. $$3x+8$$   What does the term 8 represent in this expression? 

• the weight of each marble

• the weight of the empty bucket

• the number of marbles in the bucket

• the total weight of the bucket and marbles

Multiple Choice

Ryan works for a delivery service. The function $$f\left(n\right)$$ is used to calculate his daily pay, in dollars, on a day when he makes $$n$$  deliveries.

$$f\left(n\right)=7n+96$$  

Use the function to complete the table shown. 

Multiple Choice

A store manager records the total visitors and sales, in dollars, for 10 days. The data are shown in the scatterplot.

What conclusion can the store manager draw based on the data?

• An increase in sales causes a decrease in visitors.

• An increase in visitors causes an increase in sales.

• An increase in sales is correlated with a decrease in visitors.

• An increase in visitors is correlated with an increase in sales.

Multiple Choice

The equation shown 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, and

$$r$$  is the distance between two objects. 

$$F=\frac{Gm_1m_2}{r^2}$$  

• $$r=\frac{\sqrt{F}}{Gm_1m_2}$$  

• $$r=\frac{\sqrt{Gm_1m_2}}{F}$$  

• $$r=\sqrt{\frac{F}{Gm_1m_2}}$$  

• $$r=\sqrt{\frac{Gm_1m_2}{F}}$$  

Multiple Choice

Which scatterplot represents the data that would be best modeled by a quadratic function?

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Multiple Choice

Some values for a functin are shown in the table.

Which statement best describes the function?

• It is linear because $$f\left(x\right)$$ increases by a constant amount compared to $$x$$ .

  
  

• It is linear becauseundefinedincreases by a constant percentage compared toundefined .

• It is not linear becauseundefineddoes not increase by a constant amount compared toundefined .

• It is not linear becauseundefineddoes not increase by a constant percentage compared toundefined .

Multiple Select

Select all of the expressions that are equivalent to $$16^{\frac{5}{2}}$$ . 

• $$4^5$$  

• $$8^5$$  

• $$\sqrt{16^5}$$  

• $$\left(16^2\right)\left(16^{\frac{1}{2}}\right)$$  

• $$\left(16^5\right)\left(16^{\frac{1}{2}}\right)$$  

Multiple Choice

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

.

Which scatterplot could represent Bryson's data?

Multiple Choice

What statistical measure changes when every number in a data set is increased by 10?

• range

• mean

• standard deviation

• interquartile range

Multiple Choice

Which correctly factored form of the function $$f\left(x\right)=36x^2+15x-6$$ can be used to identify the zeros? 

• $$f\left(x\right)=\left(4x-1\right)\left(3x+2\right)$$  

• $$f\left(x\right)=\left(12x-2\right)\left(3x+3\right)$$  

• $$f\left(x\right)=3\left(4x-1\right)\left(3x+2\right)$$  

• $$f\left(x\right)=3\left(12x-2\right)\left(3x+3\right)$$  

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Open Ended

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 has a mass of 5 grams and each quarter has a mass of 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 that Stephanie can put on the scale so that the mass of the combined coins is exactly 75 grams.

Multiple Choice

The population of snails in a tank at the aquarium is found to triple every year. Mark visits the aquarium and counts 80 snails in the tank.
Write a function

$$f\left(n\right)$$  to model the number of snails in the tank $$n$$  years after Mark's visit.
$$f\left(n\right)=$$  

• $$3\left(80\right)^n$$  

• $$80\left(3\right)^n$$  

• $$80+3n$$  

• $$3+80n$$  

Open Ended

Two freight trains are traveling to Columbus, Ohio. A graph is shown representing each train's remaining distance to Columbus over time.

A. Compare the distances relative to Columbus from which the trains begin their trip.

B. Tom claims both trains traveled at the same spedd over a certain interval. Sara claims that both trains traveled at different speeds the entire time. Justify which claim is correct.

Multiple Choice

Which graph represents a function whose domain is the set of non-negative numbers?

Multiple Select

The points $$\left(0,1\right)$$  and $$\left(1,4\right)$$ are contained in the graph of an equation with only two variables,  $$x$$ and  $$y$$  .

Select all of the true statements. 

• There is exactly one equation in the form  $$y=mx+b$$  that contains these points.

• There are two equations in the form undefined that contains these points.

• There are no equations in the form $$y=a\cdot b^x$$  that contains these points.

• There is exactly one equation in the formundefined that contains these points.

• There is more than one equation in the formundefined that contains these points.

Multiple Choice

An expression is shown. $$\left(2x-3\right)+\left[4x\left(3x+2\right)\right]$$

Which expression is equivalent to the given expression?

• $$9x-1$$  

• $$14x+5$$  

• $$12x^2+2x-1$$  

• $$12x^2+10x-3$$  

Open Ended

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.



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



B. How many days will it take the sunflower to gorw to a height of 45 inches?