## Wednesday, January 25, 2023

### Algebra Problems of the Day (Algebra 1 Regents, August 2022)

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

More Regents problems.

### Algebra 1 Regents, August 2022

16. When 3x2 + 7x - 6 + 2x3 is written in standard form, the leading coefficient is

1) 7
2) 2
3) 3
4) -6

The leading term in standard form is 2x3, 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

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 • 23d. This function can also be expressed as

1) C(d) = 2403d
2) C(d) = 9600 • 2d
3) C(d) = 120 • 6d
4) C(d) = 120 • 8d

Answer: 4) C(d) = 120 • 8d

The laws of exponents tell us that 23d = (23)d.

And 23 evaluates to 8.

So C(d) = 120 • 23d = C(d) = 120 • 8d, which is Choice (4).

CHoice (3) shows s3 = 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 10x2 - 12x - 16x = 6, George wrote 2(5x2 - 14x) = 2(3), followed by 5x2 - 14x = 3. Which properties justify George’s process?

B. division property of equality
D. distributive property

1) A and C
2) A and B
3) D and C
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

a1 = -2
an = 3an - 1 + 1

What is the value of a4?

1) -41
2) -14
3) 22
4) 67

Use the formula, Luke!

a2 = 3a1 + 1 = 3(-2) + 1 = -5

a3 = 3a2 + 1 = 3(-5) + 1 = -14

a4 = 3a3 + 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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