Free Printable Algebra 1

1.

A.2A - A part of a linear function is shown on the grid.

What is the range of the part of the linear function shown? The range is the set of all real numbers (a) and (b) .

Choose from the below words

greater than -4

less than or equal to 2

greater than or equal to -2

less than 3

2.

A.2A - The domain and range if part of linear function r are given.

$x>5$

$y<2$

a)

b)

c)

d)

3.

A.2C - The table represents some points on the graph of a linear function.

Which function represents the relationship?

a)

$y=-\frac{3}{2}x+4$

b)

$y=-\frac{3}{2}x-14$

c)

$y=-\frac{2}{3}x-9$

d)

$y=-\frac{2}{3}x-1$

4.

A.2C - Printer ink costs $18.99 per cartridge. The company that sells the ink cartridges charges a flat rate shipping fee of $7.95, no matter the number of cartridges purchased in a single order.

Which linear function models the total cost, t, for a single order of c cartridges?

a)

$c=26.94t$

b)

$x=18.99t+7.95$

c)

$t=26.94c$

d)

$t=18.99c+7.95$

5.

A.2E - The graph shows point P and line m.

Which equation best represent the slope-intercept form of the line that passes through point P and is parallel to line m?

a)

$y=\frac{3}{2}x+5$

b)

$y=\frac{3}{2}x-5$

c)

$y=-\frac{2}{3}x+\frac{2}{3}$

d)

$y=-\frac{2}{3}x-\frac{2}{3}$

6.

A.2G - A line is graphed on a coordinate grid.

Which statement about the line is true?

a)

The equation of the line is x = -4, and the slope is undefined.

b)

The equation of the line is y = -4, and the slope is equal to -4.

c)

The equation of the line is x = -4, and the slope is equal to -4.

d)

The equation of the line is y = -4, and the slope is undefined.

7.

A.3A - A line contains the points (-2, -2) and (4, 2).

What is the slope of the line/

a)

$-\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$-\frac{3}{2}$

d)

$\frac{2}{3}$

8.

A.3B - The water level in a tank is changing at a constant rate. The graph shows the relationship between time in hours, x, and the water level in meters, y.

Complete the statement that describes the rate of change of water level with respect to time.

The water level (a) at a rate of (b) m/h

Choose from the below words

decreases

0.25

increases

1

4

9.

A.3B - A construction worker built steps up to a home. The table shows the linear relationship between the height off the ground in inches and the number of steps.

What is the rate of change of height off the ground with respect to the number of steps?

a)

$14$ in. per step

b)

$\frac{1}{7}$ in. per step

c)

$7$ in. per step

d)

$\frac{1}{14}$ in. per step

10.

A.3C - The graph of linear function, f, is shown.

What is the zero of f.

a)

-3

b)

3

c)

2

d)

-6

11.

A.3C - The graph of a linear function is shown on the grid.

What are the x-intercept and the y-intercept of the line?

a)

x-intercept: (8, 0)

y-intercept: (0, -2)

b)

x-intercept: (-2, 0)

y-intercept: (0, 4)

c)

x-intercept: (-2, 0)

y-intercept: (0, 8)

d)

x-intercept: (4, 0)

y-intercept: (0, 8)

12.

A.3E - The graph of the function f(x) = x is transformed to a form function g(x) such that g(x) = 3f(x). Which graph represents f and g?

a)

b)

c)

d)

13.

A.4A - The table shows the number of species added to the United States endangered species list each year for several years. A linear function can be used to model the data.

Which correlation best describes the strength of the linear association between the number of species added to the United States endangered species list and the year?

a)

Weak negative correlation, because $r\approx-0.91$

b)

Weak negative correlation, because $r\approx-0.09$

c)

Strong negative correlation, because $r\approx-0.09$

d)

Strong negative correlation, because $r\approx-0.91$

14.

A.4C - The table shows the number of customers each hour for an online sale.

Which function best models the data in the table?

a)

$f\left(x\right)=296-41x$

b)

$f\left(x\right)=337-41x$

c)

$f\left(x\right)=317-38x$

d)

$f\left(x\right)=296-38x$

15.

A.5A - A rectangle has a length of (5 + 2x) inches and a width of 10 inches. A triangle has a base of 30 inches and a height of (4x - 10) inches. The area in square inches of the rectangle is equal to the are in square inches of the triangle. What is the value of x?

a)

2.5

b)

3

c)

7.5

d)

5

16.

A.5A - What is the solution to the equation $5\left(2w+4\right)=4\left(2w+9\right)$

a)

$w=\frac{5}{2}$

b)

$w=8$

c)

$w=\frac{28}{9}$

d)

$w=5$

17.

A.12B - A function is shown.

$g\left(x\right)=6\left(2x+7\right)$

What is value of $g\left(20\right)$ ?

a)

167

b)

282

c)

324

d)

247

18.

A.12C - A sequence if defined by $f\left(1\right)=27$ and $f\left(n\right)=\frac{1}{3}f\left(n-1\right)$ for each whole number n, where as n > 1. What are the first four terms of the sequence?

a)

27, 9, 3, 1

b)

27, 81, 243, 729

c)

$\frac{1}{3},\frac{28}{3},\frac{55}{3},\frac{82}{3}$

d)

$\frac{1}{3},\frac{1}{81},\frac{1}{2,187},\frac{1}{59,049}$

19.

A.12E - Which equation is equivalent to $S=PH+2B$ when solved for B?

a)

$B=\frac{S-Ph}{2}$

b)

$B=\frac{2S}{Ph}$

c)

$B=\frac{SPh}{2}$

d)

$B=\frac{S-2}{Ph}$

20.

A.2H - A customer is ordering hats and T-shirts from an online store. Each hat costs $7, and each T-shirt costs $10. A customer receives free shipping if the amount of the order is over $100.

Write an inequality that represents all possible combinations of hats, x, and T-shirts, y, in order that qualifies for free shipping.

(a) x + (b) y (c) (d)

Choose from the below words

7

10

>

100

17

<

=

21.

A.2I - The tables of ordered pairs represent some points on the graph of two different lines.

Which system of equations represents the graph of these two lines?

a)

x - 6y = -90

x - 3y = 27

b)

x + 6y = 90

x + 3y = -27

c)

6x - y = -15

3x - y = 9

d)

6x + y = 15

3x + y = -9

22.

A.3D - Which ordered pair is in the solution set of

$y\le\frac{3}{5}x-6$

a)

(5, -4)

b)

(-2, -5)

c)

(9, 1)

d)

(-8, 3)

23.

A.3G - The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted ticket was 80% of the price of a standard ticket.

-- There were 153 standard tickets sold at the baseball game.

-- There were 47 discounted tickets sold at the baseball game.

-- The total amount of ticket sales from the standard and discounted tickets was $2,649.34

The line graphed on the grid represents the first equation in a system of linear equations for this situation.

If the second equation in the systems is y = 0.80x, what is the best estimate of the price of a discounted ticket?

a)

$13.95

b)

$14.55

c)

$13.25

d)

$11.15

24.

A.5C - What is the solution to this system of equations?

$-3x+5y=21$

$6x-y=-15$

a)

(2, 27)

b)

(-2, 3)

c)

(2,0)

d)

(-3, -3)

25.

A.5C - A company advertises on two websites. Each website charges a different amount based on the number of clicks on the advertisement. The table shows the number of clicks on each website and the total cost for each of two days.

What is the cost per click on Website 1?

a)

$1.85

b)

$5.38

c)

$2.20

d)

$2.70

26.

A.10B - Which expression is equivalent to

$\left(2a+5\right)\left(3a-2\right)$

a)

$17a-10$

b)

$6a^2-10$

c)

$6a^2+11a-10$

d)

$6a^2+19a+10$

27.

A.10C - What is the quotient represented by the expression $\frac{8w^2-20w-12}{2w+1}$ for all values of w where the expression is defined?

a)

4w + 12

b)

4w - 12

c)

w - 3

d)

w + 3

28.

A.10D - Which expression is equivalent to

$24gh-12g^2+18g$

a)

6g (4h - 12g + 18)

b)

12g (2h - 12g + 18)

c)

6g (4h - 2g + 3)

d)

12g (2h - g + 3)

29.

A.10E - Which expression is a factor of

$30x^2-4x-16$

a)

5x + 4

b)

3x - 2

c)

5x - 4

d)

3x - 4

30.

A.10E - Which expressions are equivalent to

$12x^2-48x+48$

Select TWO correct answers.

a)

$12\left(x-2\right)^2$

b)

$-12\left(x^2-4x+4\right)$

c)

$12\left(x-4\right)\left(x-1\right)$

d)

$-12\left(x-2\right)^2$

e)

$12\left(x^2-4x+4\right)$

31.

A.11A - Which expression is equivalent to $\sqrt[]{600}$

a)

$6\ \sqrt[]{10}$

b)

$10\ \sqrt[]{6}$

c)

$24\ \sqrt[]{25}$

d)

$25\ \sqrt[]{24}$

32.

A.11B - Which expression is equivalent to

$\left(x^{\frac{3}{7}}\right)^2$

a)

$x^{\frac{6}{14}}$

b)

$x^{\frac{17}{7}}$

c)

$x^{\frac{6}{7}}$

d)

$x^{\frac{5}{7}}$

33.

A.11B - The expression $x^6y^4\div\left(\frac{x^2}{y}\right)$ can be written as a product of two exponential terms with bases x and y with all values of x and y where the expression is defined. Choose the correct value of the exponent for each term.

_x (a) _y (b)

Choose from the below words

4

5

-3

2

8

34.

A.6A - Which statement about the function $n\left(x\right)=5x^2-20x+12$

a)

The domain of the function is $x\ge2$

b)

The range of the function is $n\left(x\right)\ge-8$

c)

The domain of the function is $x\ge0$

d)

The range of the function $n\left(x\right)\le12$

35.

A.6A - The table represents some points on the graph of quadratic function g.

What is the range of g?

a)

All real numbers less than or equal to $\frac{3}{2}$

b)

All real numbers less than or equal to $\frac{19}{4}$

c)

All real numbers greater than or equal to $\frac{3}{2}$

d)

All real numbers greater than or equal to $\frac{19}{4}$

36.

A.6B - Which quadratic function in vertex form can be represented by the graph that has a vertex at (1, 46) and passes through the point (3, 10)?

a)

$y=9\left(x-3\right)^2+10$

b)

$y=9\left(x-1\right)^2+46$

c)

$y=-9\left(x-3\right)^2+10$

d)

$y=-9\left(x-1\right)^2+46$

37.

A.6C - The graph of quadratic function h is shown.

Which function best represents h?

a)

$h\left(x\right)=x^2+2x-3$

b)

$h\left(x\right)=x^2-2x-3$

c)

$h\left(x\right)=x^2+4x+3$

d)

$h\left(x\right)=x^2-4x+3$

38.

A.7A - The graph of a quadratic function is shown on the grid.

Which statement appears to be true?

a)

The function has 3 zeros.

b)

The maximum value of the function is 3.

c)

THe vertex of the graph of the function is (4, 1)

d)

The equation of the axis of symmetry of the graph of the function is x=1

39.

A.7A - The graph of a quadratic function is shown.

Which values best represent the zeros of the function? Select TWO correct answers.

a)

x = 1

b)

x = -4

c)

x = -1

d)

x = 3

e)

x = -3

40.

A.7B - Which statement about $f\left(x\right)=4x^2-36x+81$ is true?

a)

The zeros are $\frac{3}{4}$ and -27 because $f\left(x\right)=\left(4x-3\right)\left(x-27\right)$

b)

The zeros are $-\frac{3}{2}$ and $\frac{27}{2}$ because $f\left(x\right)=\left(2x+3\right)\left(2x+27\right)$

c)

The zeros are $\pm\frac{9}{2}$ because $f\left(x\right)=\left(2x-9\right)\left(2x+9\right)$

d)

The zero is $\frac{9}{2}$ because $f\left(x\right)=\left(2x-9\right)^2$

41.

A.7C - The function $f\left(x\right)=x^2$ was transformed to create the function $g\left(x\right)=f\left(x-3\right)-9$ .

What are the coordinates of the vertex of the graph of g?

( (a) , (b) )

Choose from the below words

3

9

-9

-3

0

42.

A.8A - Function k is defined as $k\left(x\right)=x^2+32x+248$ .

What are the solutions to k(x) = 0

a)

$x=-16+2\ \sqrt[]{2}$ and $x=-16-2\ \sqrt[]{2}$

b)

$x=16+2\ \sqrt[]{2}$ and $x=16-2\ \sqrt[]{2}$

c)

$x=-32+4\ \sqrt[]{2}$ and $x=-32-4\ \sqrt[]{2}$

d)

$x=32+4\ \sqrt[]{2}$ and $x=32-4\ \sqrt[]{2}$

43.

A.8B - An experiment examined the relationship between the number of miles a car traveled, y, per gallon of gasoline and the speed of the car, x, in miles per hour. The table displays the data collected.

A quadratic function can be used to model the data in the table. Which value best estimates the miles per gallon when the speed is 65 miles perhour?

a)

27.9

b)

31.0

c)

40.2

d)

24.9

44.

A.9A - Which statement about $p\left(x\right)=-7\left(4\right)^x$ is true?

a)

The domain s all real numbers greater than or equal to 4.

b)

The range is all real numbers less than 0.

c)

THe domain is all real numbers less than or equal to 0.

d)

The range is all real numbers.

45.

A.9B - The function $w\left(t\right)=270\left(1.029\right)^t$ can be used to estimate the number of whales in the North Atlantic Ocean at the end of t year. What does 1.029 represent in this function?

a)

The initial number of whales in the North Atlantic Ocean

b)

The decay factor of the number of whales in the North Atlantic Ocean

c)

The number of whales in the North Atlantic Ocean at the end of the first year

d)

The growth factor of the number of whales in the North Atlantic Ocean

46.

A.9C - Researchers studied the population of a town over time and modeled the data using an exponential function.

-- The initial estimated population was 48,000

-- After the first year, the population of town was 50,400

If the population of the town continues to grow at this rate each year, which function can be used to model the population x years after the researchers began their study?

a)

$p\left(x\right)=48,000\left(\frac{50,400}{48,000}\right)^x$

b)

$p\left(x\right)=50,400\left(\frac{50400}{48000}\right)^x$

c)

$p\left(x\right)=50,400\left(\frac{1}{48,000}\right)^x$

d)

$p\left(x\right)=48,000\left(\frac{1}{50,400}\right)^x$

47.

A.9C - This year the number of students who participated in sports was 317. Each year the number of students who participate in sports increases by 4%.

Which function can be used to model the number of students participating in sports after x years?

a)

$f\left(x\right)=317\left(4\right)^x$

b)

$f\left(x\right)=4x+317$

c)

$f\left(x\right)=317\left(1.04\right)^x$

d)

$f\left(x\right)=1.04x+317$

48.

A.9D - What is the equation of the asymptote of the graph of the function $y=16\left(0.75\right)^x$

(a) = (b)

Choose from the below words

y

0

x

0.75

12

16

49.

A.9D - A customer purchases an electronic device for $650. Each year the value of the electronic device decreases by 30%.

Which statement is true about the graph that represents the relationship between the value of the device in dollars y, and the number of years, x, since the device was purchased?

a)

The y-intercept of the graph is 650.

b)

The y-intercept of the graph is 455

c)

The graph has a vertical asymptote at

x = 0

d)

The graph has a horizontal asymptote at y = 30

Algebra 1 - STAAR 2023

Total questions: 49

Worksheet time: 2hrs 27mins

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