Quiz about Algebra I – June '24

Question 1

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

Accepted Answer

The ball lands on the ground at 4 seconds.

Accepted Answer

The ball reaches its maximum height at 2 seconds.

Answer

The ball reaches a maximum height of 11 feet.

Answer

The ball was launched from a height of 0 feet.

Question 2

Which equation is always true?

Accepted Answer

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

Accepted Answer

$$3^x · 3^2 = 9^{2x}$$

Accepted Answer

$$7^a · 7^b = 7^{ab}$$

Answer

$$-x^2 = z^2$$

Question 3

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?

Accepted Answer

exponential decay

Answer

linear growth

Answer

linear decay

Answer

exponential growth

Question 4

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

Accepted Answer

a(t)

Answer

b(t)

Answer

c(t)

Answer

d(t)

Question 5

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

Accepted Answer

5

Answer

1/5

Answer

1/25

Answer

25

Question 6

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?

Accepted Answer

30

Answer

50

Answer

80

Answer

110

Question 7

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

Accepted Answer

I

Answer

II

Answer

III

Answer

IV

Question 8

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

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?

Accepted Answer

mean > mode

Answer

mean = median

Answer

mode = median

Answer

median > mean

Question 10

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

Accepted Answer

$$2x^2 - 4x - 40$$

Answer

$$2x^2 - 2x - 30$$

Answer

$$2x^2 - 2x - 40$$

Answer

$$2x^2 - 4x - 30$$

Question 11

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)?

Accepted Answer

1 and 5

Answer

-5 and 0

Answer

-3 and 5

Answer

0 and 4

Question 12

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

Accepted Answer

the additional charge for gas

Answer

the hourly rate Nicole charges

Answer

the number of hours Nicole babysits

Answer

the total Nicole earns from babysitting

Question 13

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

Accepted Answer

12/(3 - a)

Answer

12/3a

Answer

3a/12

Answer

(3 - a)/12

Question 14

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?

Accepted Answer

$$\frac{400 ext{ m}}{43.03 ext{ sec}} imes \frac{0.62 ext{ mi}}{1000 ext{ m}} imes \frac{1 ext{ hr}}{3600 ext{ sec}}$$

Accepted Answer

$$\frac{400 ext{ m}}{43.03 ext{ sec}} imes \frac{1000 ext{ m}}{0.62 ext{ mi}} imes \frac{3600 ext{ sec}}{1 ext{ hr}}$$

Answer

$$\frac{400 ext{ m}}{43.03 ext{ sec}} imes \frac{1000 ext{ m}}{0.62 ext{ mi}} imes \frac{1 ext{ hr}}{3600 ext{ sec}}$$

Answer

$$\frac{400 ext{ m}}{43.03 ext{ sec}} imes \frac{0.62 ext{ mi}}{1000 ext{ m}} imes \frac{3600 ext{ sec}}{1 ext{ hr}}$$

Question 15

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

Accepted Answer

$$h(x) = 3^x$$

Answer

f(x) = -x + 3

Answer

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

Answer

m(x) = |x + 3|

Question 16

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

Accepted Answer

x \leq 15

Answer

x \geq 15

Answer

x \leq 10

Answer

x \geq 10

Question 17

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

Accepted Answer

-54

Answer

-36

Answer

-72

Answer

-90

Question 18

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

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 19

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

Accepted Answer

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

Answer

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

Answer

Because the relation includes negative numbers.

Answer

Because the relation is not defined for all real numbers.

Question 20

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?

Accepted Answer

15

Answer

10

Answer

20

Answer

25

Question 21

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

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?

Accepted Answer

y = -28.33x + 200

Answer

y = -30x + 215

Answer

y = -29.5x + 190

Answer

y = -27.5x + 185

Question 24

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?

Accepted Answer

-0.98

Answer

-0.92

Answer

-0.85

Answer

-0.75

Question 25

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

Accepted Answer

The correlation coefficient indicates a perfect positive linear relationship.

Answer

The correlation coefficient indicates a strong negative linear relationship.

Answer

The correlation coefficient indicates no linear relationship.

Answer

The correlation coefficient indicates a weak positive linear relationship.

Question 26

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

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.

Accepted Answer

No, Courtney is not correct.

Answer

Yes, Courtney is correct.

Answer

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

Answer

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

Question 28

What is the conversion of 1 mile to feet?

Accepted Answer

5280 feet

Answer

5000 feet

Answer

6000 feet

Answer

5500 feet

Question 29

Convert 1 pound to ounces.

Accepted Answer

16 ounces

Answer

12 ounces

Answer

14 ounces

Answer

18 ounces

Question 30

How many yards are there in a mile?

Accepted Answer

1760

Answer

1500

Answer

2000

Answer

1600

Question 31

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

Accepted Answer

x = -b/(2a)

Answer

x = b/(2a)

Answer

x = -2a/b

Answer

x = 2a/b

Question 32

What is the formula for Slope?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 33

What is the formula for Linear Equation Slope Intercept?

Accepted Answer

y = mx + b

Answer

y = m + bx

Answer

y = x + mb

Answer

y = b + mx

Question 34

What is the formula for Exponential Equation?

Accepted Answer

$$y = ab^x$$

Answer

y = mx + c

Answer

$$y = ax^2 + bx + c$$

Answer

y = a/x

Question 35

What is the formula for Annual Compound Interest?

Accepted Answer

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

Answer

A = P(1 + rt)

Answer

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

Answer

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

Question 36

What is the formula for Arithmetic Sequence?

Accepted Answer

a_n = a_1 + (n - 1)d

Answer

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

Answer

$$a_n = a_1 + n^2$$

Answer

a_n = a_1 - (n - 1)d

Question 37

What is the formula for Geometric Sequence?

Accepted Answer

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.

Answer

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.

Answer

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.

Answer

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.

Question 38

What is the formula for Interquartile Range (IQR)?

Accepted Answer

Q3 - Q1

Answer

Q3 + Q1

Answer

Q3 * Q1

Answer

Q3 / Q1

Question 39

What is the formula for Lower Outlier Boundary?

Accepted Answer

Q1 - 1.5 * IQR

Answer

Q1 + 1.5 * IQR

Answer

Q3 - 1.5 * IQR

Answer

Q3 + 1.5 * IQR

Question 40

What is the formula for Upper Outlier Boundary?

Accepted Answer

Q3 + 1.5 * IQR

Answer

Q1 - 1.5 * IQR

Answer

Q3 - 1.5 * IQR

Answer

Q1 + 1.5 * IQR

Question 41

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

Accepted Answer

To describe the rating process

Answer

To provide guidelines for rating

Answer

To outline the objectives of rating

Answer

To explain the benefits of rating

Question 42

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

Accepted Answer

True

Answer

False

Question 43

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

Accepted Answer

The principles include clarity, consistency, and fairness.

Answer

The principles include speed, accuracy, and efficiency.

Answer

The principles include creativity, originality, and innovation.

Answer

The principles include complexity, difficulty, and challenge.

Question 44

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

Accepted Answer

Refer to general guidelines

Answer

Follow their own judgment

Answer

Skip the question

Answer

Ask for clarification

Question 45

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

Accepted Answer

a detailed explanation

Answer

a brief summary

Answer

a list of key points

Answer

an unrelated answer

Question 46

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

Accepted Answer

Acknowledge the method as correct

Answer

Provide additional examples

Answer

Ignore the examples

Answer

Request a different method

Question 47

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

Accepted Answer

All of the above

Answer

Syntax errors

Answer

Logical errors

Answer

Runtime errors

Question 48

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

Accepted Answer

a misunderstanding of the problem or concept.

Answer

a mistake in calculation.

Answer

an error in plotting a graph.

Answer

a minor mistake in approximation.

Question 49

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

Accepted Answer

They should be corrected each time.

Answer

They should be ignored.

Answer

They should be noted but not corrected.

Answer

They should be corrected only once.

Question 50

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

Accepted Answer

[2]

Answer

[1]

Answer

[0]

Question 51

The frequency table is completed correctly.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

69 questions

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

Which equation is always true?

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

Which sum is irrational?

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

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?

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

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

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

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