The following questions appeared on the August 2022 Algebra 1 Regents Exam

More Regents problems.

*Algebra 1 Regents, August 2022*

Part I: Each correct answer will receive 2 credits.

**16.** When 3x^{2} + 7x - 6 + 2x^{3} is written in standard form, the leading
coefficient is

1) 7

2) 2

3) 3

4) -6

**Answer: 2) 2 **

The leading term in standard form is 2x

^{3}, so the leading coefficient is 2, which is Choice (2).

**17.** Which of the equations below have the same solution?

*I. 10(x - 5) = -15*

II. 4 + 2(x - 2) = 9

III. 1/3 x = 3/2

II. 4 + 2(x - 2) = 9

III. 1/3 x = 3/2

1) I and II, only

2) I and III, only

3) II and III, only

4) I, II, and III

1) I and II, only

2) I and III, only

3) II and III, only

4) I, II, and III

**Answer: 3) II and III, only **

Since the want to know the percent of all students, you need to find how many (males and females) are in the survey and the total that prefer Pizza.

10(x - 5) = -15

x - 5 = -15/10

x = 5 - 15/10 = 5 - 3/2 = 7/2 or 3 1/2 or 3.5

4 + 2(x - 2) = 9

2(x - 2) = 5

x - 2 = 5/2

x = 2 + 5/2 = 9/2 or 4 1/2 or 4.5

1/3 x = 3/2

x = 3(3/2) = 9/2 or 4 1/2 or 4.5

**18.** In an organism, the number of cells, C(d), after d days can be
represented by the function C(d) = 120 • 2^{3d}. This function can also
be expressed as

1) C(d) = 240^{3d}

2) C(d) = 9600 • 2^{d}

3) C(d) = 120 • 6^{d}

4) C(d) = 120 • 8^{d}

**Answer: 4) C(d) = 120 • 8 ^{d} **

The laws of exponents tell us that 2

^{3d}= (2

^{3})

^{d}.

And 2^{3} evaluates to 8.

So C(d) = 120 • 2^{3d} = C(d) = 120 • 8^{d}, which is Choice (4).

CHoice (3) shows s^{3} = 6, which is incorrect.

Choices (1) and (2) break the laws of exponents and the rules for the Order of Operations.

**19.** In the process of solving the equation 10x^{2} - 12x - 16x = 6, George wrote 2(5x^{2} - 14x) = 2(3), followed by 5x^{2} - 14x = 3. Which
properties justify George’s process?

*A. addition property of equality*

B. division property of equality

C. commutative property of addition

D. distributive property

B. division property of equality

C. commutative property of addition

D. distributive property

1) A and C

2) A and B

3) D and C

4) D and B

**Answer: 4) D and B **

First, George used the distributive property, in reverse, factoring out 2 from each expression. Then he used the division property, and divided both sides of the equation by 2.

Comibining -12x and -16x into -28x, which then became 2(-14x) is NOT the addition property of equality. That was just combining like terms.

**20.** a sequence is defined recursively by

*a*

a

_{1}= -2a

_{n}= 3a_{n - 1}+ 1

*What is the value of a _{4}?
1) -41
2) -14
3) 22
4) 67
*

**Answer: 1) -41 **

Use the formula, Luke!

a_{2} = 3a_{1} + 1 = 3(-2) + 1 = -5

a_{3} = 3a_{2} + 1 = 3(-5) + 1 = -14

a_{4} = 3a_{3} + 1 = 3(-14) + 1 = -41

The correct answer is Choice (1).

More to come. Comments and questions welcome.

More Regents problems.

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