Quiz about Spring 2023 Algebra I Benchmark Review

Question 1

Which graph best represents $$y=-x^2+60-1$$ ?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 2

A graph of $$f\left(x\right)=6x^2-11x+3$$ is shown on the grid.

What are the zeroes of f?

Accepted Answer

1/3 and 3/2

Answer

3

Answer

2 and 9

Answer

11/12

Question 3

The values in the table represent a linear relationship between x and y.

What is the rate of change of y with respect to x?

Accepted Answer

10

Answer

17

Answer

-10

Answer

-17

Question 4

The graph of a linear function is shown on the grid.

What is the rate of change of y with respect to x for this function?

Accepted Answer

-3/4

Answer

7/9

Answer

-7/9

Answer

3/4

Question 5

The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.

What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

Accepted Answer

7 ft/yr

Answer

14 ft/yr

Answer

3 ft/yr

Answer

10 ft/yr

Question 6

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

Accepted Answer

$$y=x+4$$

$$y=-2x-4$$

Answer

$$y=-x-4$$

$$y=2x-2$$

Answer

$$y=-x+4$$ $$y=2x-4$$

Answer

$$y=x-4$$

$$y=-2x-2$$

Question 7

The tables of ordered pairs represent some points on the graphs of lines q and v.

Which system of equations is represented by lines q and v?

Accepted Answer

$$3x-y=-27$$

$$x+2y=16$$

Answer

$$21x-y=9$$

$$5x+6y=40$$

Answer

$$21x-y=9$$

$$5x+6y=20$$

Answer

$$9x-y=27$$

$$x+2y=8$$

Question 8

Which table shows y as a function of x?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 9

Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

The first customer paid $12 for 14 postcards and 5 large envelopes.

The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

Accepted Answer

$1.42

Answer

$0.35

Answer

$1.15

Answer

$0.63

Question 10

What is the solution to this system of equations?

$$10x-7=53$$

$$y=\frac{-13x+92}{2}$$

Accepted Answer

(6, 7)

Answer

(2, 33)

Answer

(7, 6)

Answer

(33, 2)

Question 11

A graph of quadratic function f is shown on the grid.

Which of these best represents the domain of f?

Accepted Answer

All real numbers

Answer

$$-3\le x\le2$$

Answer

$$y\ge5.5$$

Answer

All real numbers less than 03 or greater than 2

Question 12

Which graph represents a function with a domain of all real numbers greater than or equal to -7 and less than 2?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 13

The value of y varies directly with x. If x=3, then y=21. What is the value of x when y=105?

Accepted Answer

15

Answer

3/5

Answer

1 2/3

Answer

7

Question 14

Which graph best represents the solution set of $$y<\frac{3}{4}x-4$$ ?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 15

The graph of $$2x-5y=10$$ is shown on the grid.

Which ordered pair is in the solution set of $$2x-5y=10$$ ?

Accepted Answer

(5, 0)

Answer

(0, 5)

Answer

(-2, 5)

Answer

(-5, 2)

Question 16

The table represents some points on the graph of an exponential function.

Which function represents this relationship?

Accepted Answer

$$f\left(x\right)=16\left(\frac{3}{2}\right)^x$$

Answer

$$f\left(x\right)=16\left(\frac{2}{3}\right)^x$$

Answer

$$f\left(x\right)=36\left(\frac{3}{2}\right)^x$$

Answer

$$f\left(x\right)=36\left(\frac{2}{3}\right)^x$$

Question 17

An exponential function is graphed on the grid.

Which function is best represented by the graph?

Accepted Answer

$$g\left(x\right)=6\left(\frac{1}{3}\right)^x$$

Answer

$$g\left(x\right)=6\left(3\right)^x$$

Answer

$$g\left(x\right)=6-\left(\frac{1}{3}\right)^x$$

Answer

$$g\left(x\right)=6-\left(3\right)^x$$

Question 18

Which expression is equivalent to $$\left(\frac{3}{2}p+1\right)\left(\frac{1}{2}p+3\right)$$ ?

Accepted Answer

$$\frac{3}{4}p^2+5p+3$$

Answer

$$2p^2+3$$

Answer

$$4p^2+3$$

Answer

$$\frac{3}{4}p^2+10p+3$$

Question 19

Which situation shows causation?

Accepted Answer

The amount of time a cell phone is used affects the charge of its battery.

Answer

The length of a rectangle affects the width of a rectangle.

Answer

The number of ice-cream bars sold affects the number of milkshakes sold.

Answer

The number of soccerballs a team owns affects the number of games the team wins during the soccer season.

Question 20

The graph of $$f\left(x\right)=x^2$$ was transformed to create the graph of $$g\left(x\right)=f\left(x\right)-9$$ . Which statement about the graphs is true?

Accepted Answer

The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

Answer

The graph of g is a reflection of the graph of f across the x-axis.

Answer

The vertex of the graph of g is 9 units to the right of the vertex of the graph of f.

Answer

The graph of g is a reflection of the graph of f across the y-axis.

Question 21

The graph of $$f\left(x\right)=x^2$$ is reflected over the x-axis and stretched horizontally to create the graph of function g. Which graph could represent g?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 22

Which expression is a factored form of $$2x^2-25x+63$$

Accepted Answer

$$\left(x-9\right)\left(2x-7\right)$$

Answer

$$\left(x+9\right)\left(2x+7\right)$$

Answer

$$\left(x+7\right)\left(2x+9\right)$$

Answer

$$\left(x-7\right)\left(2x-9\right)$$

Question 23

Which expression is a factor of $$x^2-5x-6$$ ?

Accepted Answer

x-6

Answer

x-2

Answer

x-3

Answer

x-1

Question 24

Which expression is equivalent to $$m^2-13m-30$$ ?

Accepted Answer

$$\left(m-15\right)\left(m+2\right)$$

Answer

$$\left(m-10\right)\left(m-3\right)$$

Answer

$$\left(m+15\right)\left(m-2\right)$$

Answer

$$\left(m+10\right)\left(m+3\right)$$

Question 25

The graph of a linear function is shown on the grid.

Which function is best represented by this graph?

Accepted Answer

$$g\left(x\right)=-\frac{2}{3}x+4$$

Answer

$$g\left(x\right)=6x+4$$

Answer

$$g\left(x\right)=4x-\frac{2}{3}$$

Answer

$$g\left(x\right)=-\frac{3}{2}x+6$$

Question 26

The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.

Based on the table, which function models this situation?

Accepted Answer

$$f\left(n\right)=-3n+24$$

Answer

$$f\left(n\right)=-\frac{1}{3}n+16$$

Answer

$$f\left(n\right)=-3n+64$$

Answer

$$f\left(n\right)=-\frac{1}{3}n+8$$

Question 27

Which expression is equivalent to $$\frac{36x^4y^5}{\left(3xy\right)^2}$$ for all values of x and y where the expression is defined?

Accepted Answer

$$4x^2y^3$$

Answer

$$12x^3y^4$$

Answer

$$27x^2y^3$$

Answer

$$6x^3y^4$$

Question 28

Which expression is equivalent to $$\left(7x^3\right)^2\left(x^8\right)^{\frac{1}{2}}$$ ?

Accepted Answer

$$49x^{10}$$

Answer

$$14x^{10}$$

Answer

$$14x^7$$

Answer

$$49x^7$$

Question 29

Which value of x is a solution to this equation?

$$3x^2-30x-72=0$$

Accepted Answer

x= -2

Answer

x= -12

Answer

x= -4

Answer

x= -6

Question 30

The graph of linear function g is shown on the grid.

Which inequality best represtns the domain of the part shown?

Accepted Answer

$$-9<x\le2$$

Answer

$$-9\le x<2$$

Answer

$$-6<g\left(x\right)\le3$$

Answer

$$-6\le g\left(x\right)\le3$$

Question 31

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by $$f\left(x\right)=20x+4$$ .

What is the range of the function for this situation?

Accepted Answer

{4, 24, 44, 64, 84, 104, 124}

Answer

{0, 1, 2, 3, 4, 5, 6}

Answer

{0, 2, 4, 6}

Answer

{4, 44, 84, 124}

Question 32

The starting annual salary for an office worker at a company is $29,000. If the company awards an annual increase of 6.2%, which graph models this situation after the office worker receives x annual increases?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 33

A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function.

Which function best models the data?

Accepted Answer

$$n\left(t\right)=0.072t^2-0.15t+2.73$$

Answer

$$n\left(t\right)=-0.002t^2+0.55t+5.02$$

Answer

$$n\left(t\right)=-0.002t^2+5.02$$

Answer

$$n\left(t\right)=0.072t^2+2.73$$

Question 34

Which expression is equivalent to $$\left(10+7r-r^2\right)+\left(-6r^2-18+5r\right)$$ ?

Accepted Answer

$$-7r^2+12r-8$$

Answer

$$-7r^2+2r+8$$

Answer

$$7r^2+12r+8$$

Answer

$$7r^2+2r-8$$

Question 35

The solutions to $$f\left(x\right)=0$$ are $$x=-2.5$$ and $$x=2.5$$ . Which quadratic function could represnt f?

Accepted Answer

$$f\left(x\right)=x^2-6.25$$

Answer

$$f\left(x\right)=x^2+6.25$$

Answer

$$f\left(x\right)=x^2-5$$

Answer

$$f\left(x\right)=x^2+5$$

Question 36

What is the equation in slope-intercept form of hte line that passes through the points (-26, -11) and (39, 34)?

Accepted Answer

$$y=\frac{9}{13}x+7$$

Answer

$$y=-\frac{9}{13}x+7$$

Answer

$$y=-\frac{9}{13}x-7$$

Answer

$$y=\frac{9}{13}x-7$$

Question 37

A grill at a barbecue restaurant will be used to cook sausage links that are 2 lbs each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.

Which inequality represents all possible combinations of x, the number of sausage links that will be cooked on the grill, and y, the number of briskets that will also be cooked?

Accepted Answer

$$2x+6y\le120$$

Answer

$$6x+2y<120$$

Answer

$$6x+2y>120$$

Answer

$$2x+6y\ge120$$

Question 38

The scatterplot shows the monthly high temperatures for Austin, Texas in degrees Fahrenheit over a 12-month period.

Which function best models the data from Month 1 to Month 9?

Accepted Answer

$$y=2.5x+90$$

Answer

$$y=-1.6x+111$$

Answer

$$y=3.5x+85$$

Answer

$$y=-3.3x+130$$

Question 39

Given $$g\left(x\right)=x^2-6x-16$$ , which statement is true?

Accepted Answer

The zeroes are -2 and 8, because the factors of g are (x+2) and (x-8).

Answer

The zeroes are -8 and 2, because the factors of g are (x+8) and (x-2).

Answer

The zeros are -8 and -2, because the factors of g are (x+8) and (x+2).

Answer

The zeros are 2 and 8, because the factors of g are (x-2) and (x-8).

Question 40

Linear function t has an x-intercept of -1 and a y-intercept of 5. Which graph best represents t?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 41

Which graph represents $$-3x+5y=-15$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 42

What is the equation of the line that passes through the point (-2, 7) and has a slope of zero?

Accepted Answer

y = 7

Answer

x = 7

Answer

y = -2

Answer

x = -2

Question 43

A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by $$b\left(x\right)=850\left(1.025\right)^x$$ .

Which statement is the best interpretation of one of the values in this function?

Accepted Answer

The balance in the initial account increases at a rate of 2.5% each year.

Answer

The initial balance of the account decreases at a rate of 97.5% each year.

Answer

The initial balance of the account was $1,025.

Answer

The balance in the account at the end of one year was $850.

Question 44

Which graph best represents the solution set to this system of inequalities?

$$x+y<1$$

$$x-y\le2$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 45

Terms in a geometric sequence of numbers are shown.

...0, 6, 12, 18, 24...

Based on this information, which equation can be used to find the nth term in the sequence?

Accepted Answer

$$a_n=6n-18$$

Answer

$$a_n=-6n+18$$

Answer

$$a_n=-18n+6$$

Answer

$$a_n=18n-6$$

Question 46

What is the solution to this equation?

$$-4\left(2m-7\right)=3\left(52-4m\right)$$

Accepted Answer

32

Answer

46

Answer

-6.4

Answer

-40.75

Spring 2023 Algebra I Benchmark Review

50 questions

The values in the table represent a linear relationship between x and y.
What is the rate of change of y with respect to x?

The graph of a linear function is shown on the grid.
What is the rate of change of y with respect to x for this function?

The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.
What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

A system of equations is graphed on the grid.
Which system of equations does the graph represent?

The tables of ordered pairs represent some points on the graphs of lines q and v.
Which system of equations is represented by lines q and v?

Which table shows y as a function of x?

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Spring 2023 Algebra I Benchmark Review

50 questions

The values in the table represent a linear relationship between x and y.What is the rate of change of y with respect to x?

The graph of a linear function is shown on the grid.What is the rate of change of y with respect to x for this function?

The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

A system of equations is graphed on the grid.Which system of equations does the graph represent?

The tables of ordered pairs represent some points on the graphs of lines q and v.Which system of equations is represented by lines q and v?

Which table shows y as a function of x?

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

The values in the table represent a linear relationship between x and y.
What is the rate of change of y with respect to x?

The graph of a linear function is shown on the grid.
What is the rate of change of y with respect to x for this function?

A system of equations is graphed on the grid.
Which system of equations does the graph represent?

The tables of ordered pairs represent some points on the graphs of lines q and v.
Which system of equations is represented by lines q and v?