Free Printable Algebra I

1.

Based on these data, which statement is a valid conclusion?

a)

The ball lands on the ground at 4 seconds.

b)

The ball reaches a maximum height of 11 feet.

c)

The ball was launched from a height of 0 feet.

d)

The ball reaches its maximum height at 2 seconds.

2.

A tour bus can seat, at most, 48 passengers. An adult ticket costs $18 and a child ticket costs$ 12. The bus company must collect at least $650 to make a profit. If a represents the number of adult tickets sold and c represents the number of child tickets sold, which system of inequalities models this situation if they make a profit?

a)

(1) a + c < 48 18a + 12c > 650

b)

(2) a + c ≤ 48 18a + 12c ≥ 650

c)

(3) a + c < 48 18a + 12c < 650

d)

(4) a + c ≤ 48 18a + 12c ≤ 650

3.

Which equation is always true?

a)

$x^2 \cdot x^3 = x^5$

b)

$3^x · 3^2 = 9^{2x}$

c)

$-x^2 = z^2$

d)

$7^a · 7^b = 7^{ab}$

4.

The expression −2(x² − 2x + 1) + (3x² + 3x − 5) is equivalent to

a)

x² + x − 4

b)

x² − x − 7

c)

x² + 7x − 4

d)

x² + 7x − 7

5.

Which sum is irrational?

a)

−2√12 + √100

b)

−√4 + 1/3√900

c)

1/2√25 + √64

d)

√49 + 3√121

6.

The solution to 4(x − 5)/3 + 2 = 14 is

a)

15

b)

14

c)

6

d)

4

7.

On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?

a)

linear growth

b)

linear decay

c)

exponential growth

d)

exponential decay

8.

What is the degree of the polynomial 2x − x² + 4x³?

a)

1

b)

2

c)

3

d)

4

9.

The zeros of the function f(x) = x(x − 5)(3x + 6) are

a)

0, −5, and 2

b)

0, 5, and −2

c)

−5 and 2, only

d)

5 and −2, only

10.

What is the y-intercept of the line that passes through the points (−1,5) and (2,−1)?

a)

−1

b)

−2

c)

3

d)

5

11.

Which pay plan should Nancy choose in order to have the highest salary in her eighth year?

a)

a(t)

b)

b(t)

c)

c(t)

d)

d(t)

12.

The third term in a sequence is 25 and the fifth term is 625. Which number could be the common ratio of the sequence?

a)

1/5

b)

5

c)

1/25

d)

25

13.

The box plot below summarizes the data for the amount of snowfall, in inches, during the winter of 2021 for 12 locations in western New York. What is the interquartile range?

a)

30

b)

50

c)

80

d)

110

14.

Four quadratic functions are represented below. Which function has the smallest minimum value?

a)

I

b)

II

c)

III

d)

IV

15.

The equation that represents the sequence -2, -5, -8, -11, -14, ... is

a)

a_n = -3 + (-2)(n - 1)

b)

a_n = -2 + (-3)(n - 1)

c)

a_n = 3 + (-2)(n - 1)

d)

a_n = -2 + (3)(n - 1)

16.

The dot plot below shows the number of goals Jessica scored in each lacrosse game last season. Which statement about the dot plot is correct?

a)

mean > mode

b)

mean = median

c)

mode = median

d)

median > mean

17.

The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = $2(x - 3)^2$ compared to the graph of f(x) = $x^2$ . Which student response is correct? (1) Ashley said that the graph of g(x) is wider and shifted left 3 units. (2) Beth said that the graph of g(x) is narrower and shifted left 3 units. (3) Carl said that the graph of g(x) is wider and shifted right 3 units. (4) Don said that the graph of g(x) is narrower and shifted right 3 units.

a)

Ashley said that the graph of g(x) is wider and shifted left 3 units.

b)

Beth said that the graph of g(x) is narrower and shifted left 3 units.

c)

Carl said that the graph of g(x) is wider and shifted right 3 units.

d)

Don said that the graph of g(x) is narrower and shifted right 3 units.

18.

What was Dave’s average rate of change, in miles per hour, on this trip?

a)

10

b)

11

c)

11.6

d)

14.5

19.

Which expression is equivalent to $(x - 5)(2x + 7) - (x + 5)$ ?

a)

$2x^2 - 2x - 30$

b)

$2x^2 - 2x - 40$

c)

$2x^2 - 4x - 30$

d)

$2x^2 - 4x - 40$

20.

The functions f(x) and g(x) are graphed on the set of axes below. What is the solution to the equation f(x) = g(x)?

a)

1 and 5

b)

-5 and 0

c)

-3 and 5

d)

0 and 4

21.

When babysitting, Nicole charges an hourly rate and an additional charge for gas. She uses the function C(h) = 6h + 5 to determine how much to charge for babysitting. The constant term of this function represents

a)

the additional charge for gas

b)

the hourly rate Nicole charges

c)

the number of hours Nicole babysits

d)

the total Nicole earns from babysitting

22.

When solved for x in terms of a, the solution to the equation 3x - 7 = ax + 5 is

a)

12/3a

b)

12/(3 - a)

c)

3a/12

d)

(3 - a)/12

23.

Wayde van Niekerk, a runner from South Africa, ran 400 meters in 43.03 seconds to set a world record. Which calculation would determine his average speed, in miles per hour?

a)

$\frac{400 \text{ m}}{43.03 \text{ sec}} \times \frac{1000 \text{ m}}{0.62 \text{ mi}} \times \frac{1 \text{ hr}}{3600 \text{ sec}}$

b)

$\frac{400 \text{ m}}{43.03 \text{ sec}} \times \frac{0.62 \text{ mi}}{1000 \text{ m}} \times \frac{1 \text{ hr}}{3600 \text{ sec}}$

c)

$\frac{400 \text{ m}}{43.03 \text{ sec}} \times \frac{0.62 \text{ mi}}{1000 \text{ m}} \times \frac{3600 \text{ sec}}{1 \text{ hr}}$

d)

$\frac{400 \text{ m}}{43.03 \text{ sec}} \times \frac{1000 \text{ m}}{0.62 \text{ mi}} \times \frac{3600 \text{ sec}}{1 \text{ hr}}$

24.

Which function has a domain of all real numbers and a range greater than or equal to three?

a)

f(x) = -x + 3

b)

$g(x) = x^2 + 3$

c)

$h(x) = 3^x$

d)

m(x) = |x + 3|

25.

Solve $5(x - 2) \leq 3x + 20$ algebraically.

a)

x \leq 15

b)

x \geq 15

c)

x \leq 10

d)

x \geq 10

26.

Given g(x) = $x^3 + 2x^2 - x$ , what is the value of g(-3)?

a)

-36

b)

-54

c)

-72

d)

-90

27.

Given the relation R = {(-1,1), (0,3), (-2,-4), (x,5)}. State a value for x that will make this relation a function.

a)

1

b)

2

c)

3

d)

4

28.

Given the relation R = {(-1,1), (0,3), (-2,-4), (x,5)}. Explain why your answer makes this a function.

a)

Because each x-value is unique and maps to only one y-value.

b)

Because there are multiple y-values for a single x-value.

c)

Because the relation includes negative numbers.

d)

Because the relation is not defined for all real numbers.

29.

A survey of 150 students was taken. It was determined that $\frac{2}{3}$ of the students play video games. Of the students that play video games, 85 also use social media. Of the students that do not play video games, 20% do not use social media. What is the number of students who do not play video games and use social media?

a)

10

b)

15

c)

20

d)

25

30.

Use the method of completing the square to determine the exact values of x for the equation $x^2 + 10x - 30 = 0$ .

a)

x = -5 ± √55

b)

x = 5 ± √55

c)

x = -5 ± √30

d)

x = 5 ± √30

31.

Factor $20x^3 - 45x$ completely.

a)

$5x(4x^2 - 9)$

b)

$5x(4x^2 + 9)$

c)

5x(2x - 3)(2x + 3)

d)

5x(2x + 3)(2x - 3)

32.

Graph the following system of equations on the set of axes below. $y = x^2 - 3x - 6$ $y = x - 1$ What are the coordinates of all solutions?

a)

(2, 1) and (-3, -4)

b)

(3, 2) and (-2, -5)

c)

(1, -2) and (4, 3)

d)

(0, -1) and (5, 4)

33.

The table below shows the amount of money a popular movie earned, in millions of dollars, during its first six weeks in theaters. | Week (x) | 1 | 2 | 3 | 4 | 5 | 6 | |----------------|---|---|---|---|---|---| | Dollars Earned, in Millions (y) | 185 | 150 | 90 | 50 | 25 | 5 | What is the linear regression equation for this data set, rounding all values to the nearest hundredth?

a)

y = -30x + 215

b)

y = -29.5x + 190

c)

y = -28.33x + 200

d)

y = -27.5x + 185

34.

The table below shows the amount of money a popular movie earned, in millions of dollars, during its first six weeks in theaters. | Week (x) | 1 | 2 | 3 | 4 | 5 | 6 | |----------------|---|---|---|---|---|---| | Dollars Earned, in Millions (y) | 185 | 150 | 90 | 50 | 25 | 5 | What is the correlation coefficient to the nearest hundredth?

a)

-0.98

b)

-0.92

c)

-0.85

d)

-0.75

35.

State what this correlation coefficient indicates about the linear fit of the data.

a)

The correlation coefficient indicates a perfect positive linear relationship.

b)

The correlation coefficient indicates a strong negative linear relationship.

c)

The correlation coefficient indicates no linear relationship.

d)

The correlation coefficient indicates a weak positive linear relationship.

36.

Use the quadratic formula to solve the equation $3x^2 - 10x + 5 = 0$ . Express the answer in simplest radical form.

a)

x = (5 + √5)/3 or x = (5 - √5)/3

b)

x = (10 + √10)/6 or x = (10 - √10)/6

c)

x = (5 + √10)/3 or x = (5 - √10)/3

d)

x = (10 + √5)/6 or x = (10 - √5)/6

37.

Graph the system of inequalities on the set of axes below. 3y + 2x ≤ 15 y - x > 1 Which of the following coordinates is a point in the solution to this system?

a)

(0, 0)

b)

(5, 5)

c)

(3, 2)

d)

(6, 1)

38.

Courtney went to a coffee shop to purchase lattes and donuts for her friends. One day she spent a total of $15.50 on four lattes and two donuts. The next day she spent a total of$ 18.10 on three lattes and five donuts. All prices included tax. If x represents the cost of one latte and y represents the cost of one donut, which of the following systems of equations can be used to model this situation?

a)

4x + 2y = 15.50, 3x + 5y = 18.10

b)

4x + 2y = 18.10, 3x + 5y = 15.50

c)

4x + 5y = 15.50, 3x + 2y = 18.10

d)

2x + 4y = 15.50, 5x + 3y = 18.10

39.

Courtney thinks that one latte costs $2.75 and one donut costs$ 2.25. Is Courtney correct? Justify your answer. Use your equations to determine algebraically the exact cost of one latte and the exact cost of one donut.

a)

Yes, Courtney is correct.

b)

No, Courtney is not correct.

c)

The cost of a latte is $2.75 and a donut is $2.25.

d)

The cost of a latte and a donut cannot be determined.

40.

What is the conversion of 1 mile to feet?

a)

5280 feet

b)

5000 feet

c)

6000 feet

d)

5500 feet

41.

Convert 1 pound to ounces.

a)

16 ounces

b)

12 ounces

c)

14 ounces

d)

18 ounces

42.

How many yards are there in a mile?

a)

1760

b)

1500

c)

2000

d)

1600

43.

What is the formula for the Quadratic Equation?

a)

The formula for the Quadratic Equation is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients.

b)

The formula for the Quadratic Equation is given by x = (b ± √(b² + 4ac)) / (2a), where a, b, and c are coefficients.

c)

The formula for the Quadratic Equation is given by x = (-b ± √(b² - 2ac)) / (2a), where a, b, and c are coefficients.

d)

The formula for the Quadratic Equation is given by x = (-b ± √(b² - 4ac)) / (a), where a, b, and c are coefficients.

44.

What is the formula for the Quadratic Formula?

a)

x = (-b ± √(b²-4ac)) / 2a

b)

x = (b ± √(b²-4ac)) / 2a

c)

x = (-b ± √(b²+4ac)) / 2a

d)

x = (-b ± √(b²-4ac)) / a

45.

What is the formula for the Equation of the Axis of Symmetry?

a)

x = -b/(2a)

b)

x = b/(2a)

c)

x = -2a/b

d)

x = 2a/b

46.

What is the formula for Slope?

a)

m = (y2 - y1) / (x2 - x1)

b)

m = (x2 - x1) / (y2 - y1)

c)

m = (y1 - y2) / (x1 - x2)

d)

m = (x1 - x2) / (y1 - y2)

47.

What is the formula for Linear Equation Slope Intercept?

a)

y = mx + b

b)

y = m + bx

c)

y = x + mb

d)

y = b + mx

48.

What is the formula for Linear Equation Point Slope?

a)

y - y₁ = m(x - x₁)

b)

y = mx + b

c)

ax + by = c

d)

x = my + b

49.

What is the formula for Exponential Equation?

a)

$y = ab^x$

b)

y = mx + c

c)

$y = ax^2 + bx + c$

d)

y = a/x

50.

What is the formula for Annual Compound Interest?

a)

A = $P(1 + r/n)^{(nt)}$

b)

A = P(1 + rt)

c)

A = $P(1 - r/n)^{(nt)}$

d)

$A = P(1 + r)^{t}$

51.

What is the formula for Arithmetic Sequence?

a)

a_n = a_1 + (n - 1)d

b)

$a_n = a_1 * r^{(n-1)}$

c)

$a_n = a_1 + n^2$

d)

a_n = a_1 - (n - 1)d

52.

What is the formula for Geometric Sequence?

a)

The formula for a geometric sequence is given by: $a_n = a_1 * r^{(n-1)}$ , where $a_n$ is the nth term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.

b)

The formula for a geometric sequence is given by: a_n = a_1 + (n-1) * d, where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the term number.

c)

The formula for a geometric sequence is given by: $a_n = a_1 * n^r$ , where $a_n$ is the nth term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.

d)

The formula for a geometric sequence is given by: $a_n = a_1 / r^{(n-1)}$ , where $a_n$ is the nth term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.

53.

What is the formula for Interquartile Range (IQR)?

a)

Q3 - Q1

b)

Q3 + Q1

c)

Q3 * Q1

d)

Q3 / Q1

54.

What is the formula for Lower Outlier Boundary?

a)

Q1 - 1.5 * IQR

b)

Q1 + 1.5 * IQR

c)

Q3 - 1.5 * IQR

d)

Q3 + 1.5 * IQR

55.

What is the formula for Upper Outlier Boundary?

a)

Q3 + 1.5 * IQR

b)

Q1 - 1.5 * IQR

c)

Q3 - 1.5 * IQR

d)

Q1 + 1.5 * IQR

56.

What is the purpose of the procedures mentioned in the 'Mechanics of Rating' document?

a)

To provide guidelines for rating

b)

To describe the rating process

c)

To outline the objectives of rating

d)

To explain the benefits of rating

57.

According to the 'Mechanics of Rating', how many mathematics teachers are required to score a student's answer paper?

4 lines

58.

True or False: Schools are permitted to rescore any of the constructed-response questions on this exam after each question has been rated once.

a)

True

b)

False

59.

What are the general principles for rating constructed-response questions on the Regents Examination in Algebra I?

a)

The principles include clarity, consistency, and fairness.

b)

The principles include speed, accuracy, and efficiency.

c)

The principles include creativity, originality, and innovation.

d)

The principles include complexity, difficulty, and challenge.

60.

What should raters do if specific rubrics for each question are not addressed in the guidelines?

a)

Follow their own judgment

b)

Refer to general guidelines

c)

Skip the question

d)

Ask for clarification

61.

A response is considered a full-credit response when it includes:

a)

a detailed explanation

b)

a brief summary

c)

a list of key points

d)

an unrelated answer

62.

What should be done if a full-credit response includes one or more examples of an acceptable method for solving the question?

a)

Provide additional examples

b)

Acknowledge the method as correct

c)

Ignore the examples

d)

Request a different method

63.

The types of errors that can result in a 1-credit deduction are:

a)

Syntax errors

b)

Logical errors

c)

Runtime errors

d)

All of the above

64.

A conceptual error is different from computational, graphing, or rounding errors because it involves:

a)

a misunderstanding of the problem or concept.

b)

a mistake in calculation.

c)

an error in plotting a graph.

d)

a minor mistake in approximation.

65.

How should repeated occurrences of the same conceptual error be treated in responses to other questions?

a)

They should be ignored.

b)

They should be corrected each time.

c)

They should be noted but not corrected.

d)

They should be corrected only once.

66.

For each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (25) x ≤ 15, and correct algebraic work is shown. [2]

a)

x ≤ 15 and correct algebraic work is shown

b)

x > 15 and correct algebraic work is shown

c)

x ≤ 15 and no algebraic work is shown

d)

x > 15 and no algebraic work is shown

67.

For each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (26) −6, and correct work is shown. [2]

a)

Award 2 credits

b)

Award 1 credit

c)

Award 0 credits

d)

Award 3 credits

68.

A correct value is stated, and a correct explanation is written.

a)

[2]

b)

[1]

c)

[0]

69.

The frequency table is completed correctly.

a)

Appropriate work is shown, but one computational error is made.

b)

Appropriate work is shown, but one conceptual error is made.

c)

Either 100 or 10 is written correctly in the table, and no further correct work is shown.

d)

Only the given information of 150 and 85 is written in the table.

e)

A zero response does not contain enough relevant course-level work to receive any credit, does not satisfy the criteria for one or more credits, or is a correct response that was obtained by an obviously incorrect procedure.

Algebra I – June '24

Total questions: 69

Worksheet time: 37mins

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