Algebra Problems of the Day (Algebra 1 Regents, January 2023)

The following questions appeared on the January 2023 Algebra 1 Regents Exam

More Regents problems.

Algebra 1 Regents, January 2023

Part I: Each correct answer will receive 2 credits.


1. When the expression 2x(x − 4) − 3(x + 5) is written in simplest form, the result is

1) 2x² − 11x − 15
2) 2x² − 11x + 5
3) 2x² − 3x − 19
4) 2x² − 3x + 1

Answer: 1) 2x² − 11x − 15

Multiply and then combine like terms.

2x(x − 4) − 3(x + 5)
2x² − 8x − 3x - 15
2x² − 11x - 15

Choice (1) is the correct answer.

2. The point (3,w) is on the graph of y = 2x + 7. What is the value of w?

1) -2
2) -4
3) 10
4) 13

Answer: 4) 13

What is the value of y when x = 3?

2(3) + 7 = 6 + 7 = 13, which is Choice (4).

3. Students were asked to write 2x³ + 3x + 4x² + 1 in standard form. Four student responses are shown below.

Alexa: 4x² + 3x + 2x³ + 1
Carol: 2x³ + 3x + 4x² + 1
Ryan: 2x³ + 4x² + 3x + 1
Eric: 1 + 2x³ + 3x + 4x²
Which student’s response is correct?

1) Alexa
2) Carol
3) Ryan
4) Eric

Answer: 3) Ryan

Standard for of a polynomial is that the leading term has the highest exponent, the second term has the next highest exponent, and so forth. The coefficients are not relevant in finding the leading term.

Ryan has the exponents in descending order. This is Choice (3).

4. Given f(x) = −3x² + 10, what is the value of f(−2)?

1) -26
2) -2
3) 22
4) 46

Answer: 3) 22

Substitute x = -2 and evaluate. Remember Order of Operations.

f(-2) = 3(-2)² + 10 = 3(4) + 10 = 22.

This is Choice (3).

5. Which relation is a function?

Answer: 1) {(1,3,(2,1),(3,1)(4,7)}

In a function, there can only be one y-value for every x-value. There can only be one output for any input. On a graph, this gives us the Vertical Line Test.

In Choice (1), none of the x-values repeat. This is the correct choice.

In Choice (2), the input 7 has two different outputs, so it is not a function.

In Choice (3), the graph fails the vertical line test. A vertical line, such as the y-axis, can be drawn through the circle and touch it in more than one place.

In Choice (4), the relation map shows that 6 in the domain maps to both 5 and 7 in the range. This means that it is not a function.

6. What is the value of the third quartile in the box plot shown below?

1) 18
2) 22
3) 36
4) 46

Answer: 3) 36

The Five Number Summary that creates the Box and Whisker Plot is made up of (in order): the minimum, the first quartile, the median, the third quartile, and the maximum.

The right edge of the box is the third quartile, and it has a value of 36, which is Choice (3).

7. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?

1) 1/7
2) 1/3
3) -3/7
4) -1/3

Answer: 2) 1/3

Isolate the variable. Get all the a terms on the left and all the numbers on the right.

2 + 3(2a + 1) = 3(a + 2)
2 + 6a + 3 = 3a + 6
3a = 1
a = 1/3

This is Choice (2).

8. One Saturday afternoon, three friends decided to keep track of the number of text messages they received each hour from 8 a.m. to noon.
The results are shown below.

Emily said that the number of messages she received increased by 8 each hour.
Jessica said that the number of messages she received doubled every hour.
Chris said that he received 3 messages the first hour, 10 the second hour, none the third hour, and 15 the last hour.

Which of the friends’ responses best classifies the number of messages they received each hour as a linear function?

1) Emily, only
2) Jessica, only
3) Emily and Chris
4) Jessica and Chris

Answer: 1) Emily, only

A linear function has a constant rate of change.

- Emily's messages increased by the same about each hour.

- Jessica's messages doubled, which is exponential, not linear.

- Chris's messages do not change at a constant rate, so it is not linear.

So the answer is Choice (1).

More to come. Comments and questions welcome.

More Regents problems.

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