Quiz about ALG1 STAAR Prep

Question 1

(2023.1) The table represents some points on the graph of a linear functions.

Which function represents this relationship?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

(2023.3) The graph of quadratic function h is shown.

Which function best represents h?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

(2023.4) 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 area in square inches of the triangle.

What is the value of x?

Accepted Answer

5

Answer

2.5

Answer

3

Answer

7.5

Question 4

(2023.5) Which expression is a factor of $$30x^2-4x-16$$ ?

Accepted Answer

$$5x-4$$

Answer

$$5x+4$$

Answer

$$3x-2$$

Answer

$$3x-4$$

Question 5

(2023.6) 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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

(2023.8) Which statement about $$f\left(x\right)=4x^2-36x+81$$ is true?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

(2023.10) Which expression is equivalent to $$\left(x^{\frac{3}{7}}\right)^2$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

(2023.11) Which statement about the function $$n\left(x\right)=5x^2-20x+12$$ is true?

Accepted Answer

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

Answer

The domain of the function is $$x\ge2$$ .

Answer

The domain of the function is $$x\ge0$$ .

Answer

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

Question 9

(2023.13) 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 per hour?

Accepted Answer

27.9

Answer

31.0

Answer

40.2

Answer

24.9

Question 10

(2023.14) Researchers studied the population of a town over time and modeled the data useing an exponential function.

The initial estimated population was 48,000.

After the first year, the population of the 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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

(2023.15) The graph of the function $$f\left(x\right)=x$$ is transformed to form function $$g\left(x\right)$$ such that $$g\left(x\right)=3f\left(x\right)$$ . Which graph represents $$f$$ and $$g$$ ?

Accepted Answer

Question 12

(2023.16) What is the quotient represented by the expression $$\frac{8w^2-20w-12}{2w+1}$$ ?

Accepted Answer

$$4w-12$$

Answer

$$4w+12$$

Answer

$$w-3$$

Answer

$$w+3$$

Question 13

(2023.17) Which ordered pair is in the solution set of $$y\le\frac{3}{5}x-6$$ ?

Accepted Answer

$$\left(5,\ -4\right)$$

Answer

$$\left(-2,\ -5\right)$$

Answer

$$\left(9,\ 1\right)$$

Answer

$$\left(-8,\ 3\right)$$

Question 14

(2023.18) Which statement about $$p\left(x\right)=-7\left(4\right)^x$$ is true?

Accepted Answer

The range is all real numbers less than 0.

Answer

The domain is all real numbers greater than for equal to 4.

Answer

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

Answer

The range is all real numbers.

Question 15

(2023.19) The graph of a quadratic function is shown on the grid.

Which statement appears to be true?

Accepted Answer

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

Answer

The function has 3 zeroes.

Answer

The maximum value of the function is 3.

Answer

The vertex of the graph of the function is $$\left(4,\ 1\right)$$ .

Question 16

(2023.20) Which expression is equivalent to $$\sqrt{600}$$ ?

Accepted Answer

$$10\sqrt{6}$$

Answer

$$6\sqrt{10}$$

Answer

$$24\sqrt{25}$$

Answer

$$25\sqrt{24}$$

Question 17

(2023.21) A line is graphed on a coordinate grid.

Which statement about the line is true?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 18

(2023.22) The graph of a linear function, $$f$$ , is shown.

What is the zero of $$f$$ ?

Accepted Answer

2

Answer

-3

Answer

3

Answer

-6

Question 19

(2023.23) What is the solution to this system of linear equations?

$$-3x+5y=21$$

$$6x-y=-15$$

Accepted Answer

$$\left(-2,\ 3\right)$$

Answer

$$\left(2,\ 27\right)$$

Answer

$$\left(2,\ 0\right)$$

Answer

$$\left(-3,\ -3\right)$$

Question 20

(2023.24) Which expressions are equivalent to $$12x^2-48x+48$$ ?

Select TWO correct answers.

Accepted Answer

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

(2023.25) Which quadratic function in vertex form can be represented by the graph that has a vertex at $$\left(1,\ 46\right)$$ and passes through the point $$\left(3,\ 10\right)$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

(2023.26) The table shows the number of customers each hour for an online sale.

Which function best models the data in the table?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

(2023.27) 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 $$t$$ years. What does $$1.029$$ represent in the function?

Accepted Answer

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

Answer

The initial number of whales in the North Atlantic Ocean.

Answer

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

Answer

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

Question 24

(2023.28) A line contains the points $$\left(-2,\ -2\right)$$ and $$\left(4,\ 2\right)$$ .

What is the slope of the line?

Accepted Answer

$$\frac{2}{3}$$

Answer

$$-\frac{2}{3}$$

Answer

$$\frac{3}{2}$$

Answer

$$-\frac{3}{2}$$

Question 25

(2023.29) What is the solution to the equation $$5\left(2w+4\right)=4\left(2w+9\right)$$ ?

Accepted Answer

$$w=8$$

Answer

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

Answer

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

Answer

$$w=5$$

Question 26

(2023.30) The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted tickets 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.

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

Accepted Answer

$11.15

Answer

$13.95

Answer

$14.55

Answer

$13.25

Question 27

(2023.31) A sequence is 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 $$n>1$$ . What are the first four terms of the sequence?

Accepted Answer

$$27,\ 9\ ,\ 3,\ 1$$

Answer

$$27,\ 81,\ 243,\ 729$$

Answer

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

Answer

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

Question 28

(2023.32) The table represents some points on the graph of quadratic function $$g$$ .

What is the range of $$g$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

(2023.33) Which expression is equivalent to $$\left(2a+5\right)\left(3a-2\right)$$ ?

Accepted Answer

$$6a^2+11a-10$$

Answer

$$17a-10$$

Answer

$$6a^2-10$$

Answer

$$6a^2+19a+10$$

Question 30

(2023.34) Printer ink costs $18.99 per cartridge. The company that sells the ink cartridges charges a flat 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.

Accepted Answer

$$t=18.99c+7.95$$

Answer

$$c=26.94t$$

Answer

$$c=18.99t+7.95$$

Answer

$$t=26.49c$$

Question 31

(2023.36) This year the number of students who participated in a sport was 317. Each year, the number of students who participate in a sport increases by 4%.

Which function can be used to model the number of students participating in sports after $$x$$ year.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

(2023.37) The table of ordered pairs represent some points on the graph of two different lines.

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

Accepted Answer

$$6x+y=15$$

$$3x+y=-9$$

Answer

$$x-6y=-90$$

$$x-3y+27$$

Answer

$$x+6y=90$$

$$x+3y=-27$$

Answer

$$6x-y=-15$$

$$3x-y=9$$

Question 33

(2023.39) Which expression is equivalent to $$24gh-12g^2+18g$$ ?

Accepted Answer

$$6g\left(4h-2g+3\right)$$

Answer

$$6g\left(4h-12g+18\right)$$

Answer

$$12g\left(2h-12g+18\right)$$

Answer

$$12g\left(2h-g+3\right)$$

Question 34

(2023.40) 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?

Accepted Answer

$2.70

Answer

$1.85

Answer

$5.38

Answer

$2.20

Question 35

(2023.41) Function $$k$$ is defined as $$k\left(x\right)=x^2+32x+248$$ . What are the solutions to $$k\left(x\right)=0$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

(2023.42) 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?

Accepted Answer

The y-intercept of the graph is 650.

Answer

The y-intercept of the graph is 455.

Answer

The graph has a vertical asymptote at $$x=0$$ .

Answer

The graph has a horizontal asymptote at $$y=30$$ .

Question 37

(2023.44) The graph shows point $$P$$ and line $$m$$ .

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

(2023.45) Which equation is equivalent to $$S=Ph+2B$$ when solved for $$B$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

(2023.46) The domain and range of part of linear function $$r$$ are given.

$$x>5$$

$$y<2$$

Which graph could represent this part of linear function $$r$$ ?

Accepted Answer

Question 40

(2023.47) A function is shown.

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

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

Accepted Answer

282

Answer

167

Answer

324

Answer

247

Question 41

(2023.48) The graph of a linear function is shown on a grid.

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

Accepted Answer

x-intercept: $$\left(-2,\ 0\right)$$

y-intercept: $$\left(0,\ 8\right)$$

Answer

x-intercept: $$\left(8,\ 0\right)$$

y-intercept: $$\left(0,\ -2\right)$$

Answer

x-intercept: $$\left(-2,\ 0\right)$$

y-intercept: $$\left(0,\ 4\right)$$

Answer

x-intercept: $$\left(4,\ 0\right)$$

y-intercept: $$\left(0,\ 8\right)$$

Question 42

(2023.49) The graph of a quadratic function is shown.

Which values best represent the zeroes of the function?

Select TWO correct answers.

Accepted Answer

$$x=-1$$

Accepted Answer

$$x=3$$

Answer

$$x=1$$

Answer

$$x=-3$$

Answer

$$x=0$$

Question 43

(2023.50) 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?

Accepted Answer

$$7$$ in. per step

Answer

$$14$$ in. per step

Answer

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

Answer

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

Question 44

(2022.1) The graph of quadratic function $$r$$ is shown on the grid.

Which answer choice best represents the intercepts of the graph of $$r$$ ?

Accepted Answer

x-intercepts: (-10, 0) and (2, 0)

y-intercept: (0, -5)

Answer

x-intercept: (5, 0)

y-intercepts: (0, 10) and (0, -2)

Answer

x-intercepts: (0, -10) and (0, 2)

y-intercept: (-5, 0)

Answer

x-intercept: (0, 5)

y-intercepts: (10, 0) and (-2, 0)

Question 45

(2022.2) A worker is packing items in boxes. The table shows the linear relationship between the number of items the worker has packed in boxes after different amounts of time.

Which statement describes the rate of change of the number of items the worker packed in boxes with respect to the number of minutes the worker has been packing items in boxes?

Accepted Answer

The worker packed 4 items in boxes per minute.

Answer

The worker packed 8 items in boxes per minute.

Answer

The worker packed 37 items in boxes per minute.

Answer

The worker packed 15 items in boxes per minute.

Question 46

(2022.3) A system of equations is graphed on the grid.

Which system of equations is best represented by the graph?

Accepted Answer

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

$$y=-\frac{3}{5}x-8$$

Answer

$$y=\frac{2}{5}x-8$$

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

Answer

$$y=\frac{5}{2}x-8$$

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

Answer

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

$$y=-\frac{5}{3}x-8$$

Question 47

(2022.4) Which graph represents $$y$$ as a function of $$x$$ ?

Accepted Answer

Question 48

(2022.5) What is the solution to this system of equations?

$$2x+y=40$$

$$x-2y=-20$$

Accepted Answer

(12, 16)

Answer

(15, 17.5)

Answer

There is no solution.

Answer

There are an infinite number of solutions.

Question 49

(2022.6) Which graph best represents a quadratic function with a range of all real numbers greater than or equal to 3?

Accepted Answer

Question 50

(2022.7) The value of $$y$$ is directly proportional to the value of $$x$$ . When $$x=512$$ , $$y=128$$ .

What is the value of $$y$$ when $$x=64$$

Accepted Answer

16

Answer

256

Answer

32

Answer

8

Question 51

(2022.8) A customer is buying bath towels and hand towels and can spend no more than $100. Each bath towel costs $8, and each hand towel costs $5. The inequality $$8x+5y\le100$$ represents all possible combinations of $$x$$ , the number of bath towels, and $$y$$ , the number of hand towels the customer can buy.

Which graph best represents the solution set for this inequality?

Accepted Answer

Question 52

(2022.9) An exponential function is graphed on the grid.

Which function is best represented by the grid?

Accepted Answer

$$p\left(x\right)=\left(0.25\right)^x$$

Answer

$$p\left(x\right)=2\left(0.5\right)^x$$

Answer

$$p\left(x\right)=\left(1.25\right)^x$$

Answer

$$p\left(x\right)=\left(25\right)^x$$

Question 53

Which expression is equivalent to $$\left(n-4\right)\left(2n+7\right)$$ ?

Accepted Answer

$$2n^2-n-28$$

Answer

$$3n+3$$

Answer

$$n-28$$

Answer

$$2n^2-15n-28$$

Question 54

(2022.11) Which situation shows causation?

Accepted Answer

When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.

Answer

When the number of people in a bus increases, the number of animals in the zoo also increases.

Answer

When the amount of a discount for a sale increases, the number of items sold for the sale decreases.

Answer

When the number of bike trails in a city decreases, the amount of rainfall in the city increases.

Question 55

(2022.12) A system of linear equations is represented by line h and line j. A table is representing some points on line h and the graph of line j are shown.

Which system of equations is best represented by lines h and j?

Accepted Answer

$$y=-\frac{3}{4}x-5$$

$$y=-\frac{5}{4}x+1$$

Answer

$$y=\frac{4}{3}x-5$$

$$y=\frac{4}{5}x+1$$

Answer

$$y=\frac{3}{4}x-5$$

$$y=\frac{5}{4}x+1$$

Answer

$$y=-\frac{4}{3}x-5$$

$$y=-\frac{4}{5}x+1$$

Question 56

(2022.13) Which answer choice describes how the graph of $$f\left(x\right)=x^2$$ was transformed to create the graph of $$n\left(x\right)=x^2-1$$ ?

Accepted Answer

A vertical shift down.

Answer

A vertical shift up.

Answer

A horizontal shift to the left.

Answer

A horizontal shift to the right.

Question 57

(2022.15) The graph of a linear function is shown on the grid.

Which equation is best represented by this graph?

Accepted Answer

$$y=-\frac{7}{4}x+7$$

Answer

$$y=-\frac{7}{4}x+4$$

Answer

$$y=-\frac{4}{7}x+4$$

Answer

$$y=-\frac{4}{7}x+7$$

Question 58

(2022.16) Which expression is equivalent to $$\frac{c^8\left(d^6\right)^3}{c^2}$$ ?

Accepted Answer

$$c^6d^{18}$$

Answer

$$c^4d^9$$

Answer

$$c^4d^{18}$$

Answer

$$c^6d^9$$

Question 59

(2022.17) Which value of $$x$$ is the solution to this equation?

$$5x^2=30x-45$$

Accepted Answer

$$x=3$$

Answer

$$x=-3$$

Answer

$$x=5$$

Answer

$$x=-5$$

Question 60

(2022.18) A florist is making bouquets of flowers for a wedding. Each bouquet will have 9 flowers. The graph shows the linear relationship between $$y$$ , the number of flowers used, and $$x$$ , the number of bouquets.

The florist will use no more than 8 bouquets for the wedding. Which set best represents the domain of the function for this situation?

Accepted Answer

$$\left\{0,\ 9,\ 18,\ 27,\ 36,\ 45,\ 54,\ 63,\ 72\right\}$$

Answer

$$\left\{0,\ 2,\ 4,\ 6,\ 8,\ 10\right\}$$

Answer

$$\left\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\right\}$$

Answer

$$\left\{0,\ 18,\ 36,\ 54,\ 72,\ 90\right\}$$

Question 61

(2022.19) The graph of a line is show on the grid. The coordinates of both points indicated on the graph of the line are integers.

What is the rate of change of $$y$$ with respect to $$x$$ for this line? graph missing. answer = -5/6

Accepted Answer

$$-\frac{5}{6}$$

Answer

$$\frac{5}{2}$$

Answer

$$-\frac{6}{5}$$

Answer

$$\frac{2}{3}$$

Question 62

(2022.21) Which expression is equivalent to $$\frac{8.8\cdot10^9}{2.2\cdot10^{-3}}$$ ?

Accepted Answer

$$4\cdot10^6$$

Answer

$$4\cdot10^{12}$$

Answer

$$4\cdot10^{-3}$$

Answer

$$4\cdot10^{-6}$$

Question 63

(2022.22) A person dives into a pool from its edge to swim to the other side. The table shows the depth in feet of the person from the surface of the water after $$x$$ second. The data can be modeled by a quadratic function.