Free Printable Spring 2023 Algebra I Benchmark Review

1.

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

a)

b)

c)

d)

2.

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

What are the zeroes of f?

a)

3

b)

2 and 9

c)

11/12

d)

1/3 and 3/2

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?

a)

10

b)

17

c)

-10

d)

-17

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?

a)

7/9

b)

-7/9

c)

3/4

d)

-3/4

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?

a)

14 ft/yr

b)

3 ft/yr

c)

7 ft/yr

d)

10 ft/yr

6.

A system of equations is graphed on the grid.

Which system of equations does the graph represent?

a)

$y=-x-4$

$y=2x-2$

b)

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

c)

$y=x-4$

$y=-2x-2$

d)

$y=x+4$

$y=-2x-4$

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?

a)

$21x-y=9$

$5x+6y=40$

b)

$3x-y=-27$

$x+2y=16$

c)

$21x-y=9$

$5x+6y=20$

d)

$9x-y=27$

$x+2y=8$

8.

Which table shows y as a function of x?

a)

b)

c)

d)

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?

a)

$1.42

b)

$0.35

c)

$1.15

d)

$0.63

10.

What is the solution to this system of equations?

$10x-7=53$

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

a)

(6, 7)

b)

(2, 33)

c)

(7, 6)

d)

(33, 2)

11.

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

Which of these best represents the domain of f?

a)

$-3\le x\le2$

b)

All real numbers

c)

$y\ge5.5$

d)

All real numbers less than 03 or greater than 2

12.

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

a)

b)

c)

d)

13.

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

a)

3/5

b)

1 2/3

c)

7

d)

15

14.

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

a)

b)

c)

d)

15.

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

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

a)

(0, 5)

b)

(5, 0)

c)

(-2, 5)

d)

(-5, 2)

16.

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

Which function represents this relationship?

a)

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

b)

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

c)

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

d)

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

17.

An exponential function is graphed on the grid.

Which function is best represented by the graph?

a)

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

b)

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

c)

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

d)

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

18.

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

a)

$2p^2+3$

b)

$4p^2+3$

c)

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

d)

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

19.

Which situation shows causation?

a)

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

b)

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

c)

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

d)

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

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?

a)

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

b)

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

c)

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

d)

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

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?

a)

b)

c)

d)

22.

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

a)

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

b)

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

c)

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

d)

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

23.

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

a)

x-6

b)

x-2

c)

x-3

d)

x-1

24.

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

a)

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

b)

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

c)

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

d)

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

25.

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

Which function is best represented by this graph?

a)

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

b)

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

c)

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

d)

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

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?

a)

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

b)

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

c)

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

d)

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

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?

a)

$12x^3y^4$

b)

$27x^2y^3$

c)

$4x^2y^3$

d)

$6x^3y^4$

28.

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

a)

$14x^{10}$

b)

$49x^{10}$

c)

$14x^7$

d)

$49x^7$

29.

Which value of x is a solution to this equation?

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

a)

x= -12

b)

x= -4

c)

x= -2

d)

x= -6

30.

What is the positive solution to this equation?

$4x^2+12x=135$

Your answer should be a rational number with a decimal.

(a)

31.

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

Which inequality best represtns the domain of the part shown?

a)

$-9<x\le2$

b)

$-9\le x<2$

c)

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

d)

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

32.

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?

a)

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

b)

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

c)

{0, 2, 4, 6}

d)

{4, 44, 84, 124}

33.

What is the y-intercept of the graph of $g\left(x\right)=73\left(\frac{4}{5}\right)^x$ ?

Your answer should be a whole number.

(a)

34.

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?

a)

b)

c)

d)

35.

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?

a)

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

b)

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

c)

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

d)

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

36.

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

a)

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

b)

$7r^2+12r+8$

c)

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

d)

$7r^2+2r-8$

37.

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

a)

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

b)

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

c)

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

d)

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

38.

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

a)

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

b)

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

c)

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

d)

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

39.

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?

a)

$6x+2y<120$

b)

$2x+6y\le120$

c)

$6x+2y>120$

d)

$2x+6y\ge120$

40.

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?

a)

$y=-1.6x+111$

b)

$y=3.5x+85$

c)

$y=2.5x+90$

d)

$y=-3.3x+130$

41.

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

a)

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

b)

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

c)

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

d)

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

42.

Given $f\left(x\right)=6\left(1-x\right)$ , what is the value of $f\left(-8\right)$ ?

Your answer should be a whole number.

(a)

43.

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

a)

b)

c)

d)

44.

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

a)

b)

c)

d)

45.

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

a)

x = 7

b)

y = -2

c)

x = -2

d)

y = 7

46.

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?

a)

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

b)

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

c)

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

d)

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

47.

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

$x+y<1$

$x-y\le2$

a)

b)

c)

d)

48.

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?

a)

$a_n=-6n+18$

b)

$a_n=-18n+6$

c)

$a_n=6n-18$

d)

$a_n=18n-6$

49.

What is the solution to this equation?

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

a)

32

b)

46

c)

-6.4

d)

-40.75

50.

What is the solution to $-\left(6m+8\right)=4\left(17-m\right)$ ?

Your answer should be an integer.

(a)

Spring 2023 Algebra I Benchmark Review

Total questions: 50

Worksheet time: 3hrs 37mins

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