## Friday, January 20, 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

6. The expression 1/3 x(6x2 − 3x + 9) is equivalent to

1) 2x2 − x + 3
2) 2x2 + 3x + 3
3) 2x3 − x2 + 3x
4) 2x3 + 3x2 + 3x

Multiplying the polynomial by 1/3 decreases all the coefficients by a factor of 3. Multiplying the polynomial by x increases the exponent on each term (with the constant term getting x1, which is simply x.)

1/3 x(6x2 − 3x + 9) = 1/3 (6x3 − 3x2 + 9x) = 2x3 − x2 + 3x.

This is Choice (3).

7. The graphs below represent four polynomial functions. Which of these functions has zeros of 2 and -3?

If the function has zeroes of 2 and -3, then the function crosses the x-axis at x = 2 and x = -3.

Only Choice (3) shows this.

Choice (1) has zeroes of -2 and 3. Choice (2) has zeroes of -2 and -3. Choice (4) has zeroes of 2 and 3.

8. What is the constant term of the polynomial 4d + 6 + 3d2?
1) 6
2) 2
3) 3
4) 4

The constant term has no variable. It's just a number. In this case that number is 6.

2 is the exponent of the variable in the leading term, and the highest power in the polynomial.

4 is a coefficient of x, but not the leading coefficient. The polynomial is not written in standard form, which would have the highest power first.

9. Emily was given \$600 for her high school graduation. She invested it in an account that earns 2.4% interest per year. If she does not make any deposits or withdrawals, which expression can be used to determine the amount of money that will be in the account after 4 years?

1) 600(1 + 0.24)4
2) 600(1 - 0.24)4
3) 600(1 + 0.024)4
4) 600(1 - 0.024)4

Interest adds to your balance, so subtraction is silly. Eliminate Choices (2) and (4).

The interest rate of 2.4% is written as 0.024, in decimal form. This is shown in Choice (3), which is the Correct answer.

Choice (1) shows 24% interest, which would be great if you can get it!

The only possibility here is Choice (4), 0.

10. Different ways to represent data are shown below.

Which data representations have a median of 2?

1) I and II, only
2) I and III, only
3) II and III, only
4) I, II, and III

Answer: 1) I and II, only

The median in the box and whisper plot is the line over the number 2, so II is correct. That eliminates Choice (2).

There are 15 dots in graph I, so the median is the 8th dot, which is over the number 2, so I is correct. This eliminates choice (3).

In the bar chart, there are 1 + 3 + 5 + 3 + 4 + 5 + 2 = 23 pieces of data. The medain is the 12th piece of data. 1 + 3 + 5 = 9. The 12th piece of data is NOT over the number 2. Eliminate Choice (4).

Choice (1) is the correct answer.

More to come. Comments and questions welcome.

More Regents problems.

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