Algebra Problems of the Day (Algebra Regents, January 2025 Part I)

This exam was adminstered in January 2025.

More Regents problems.

January 2025 Algebra Regents

Part I

Each correct answer will receive 2 credits. No partial credit.


9. When the formula p = 2l + 2w is solved for w, the result is

(1) w = (2l + p) / 2
(2) w = (p - 2l) / 2
(3) w = p/2 + l
(4) w = l - p/2

Answer:(2) w = (p - 2l) / 2

Use inverse operations to isolate w.

p = 2l + 2w

p - 2l = 2w

(p - 2l) = w

The correct answer is Choice (2).

10. Market Street Pizza kept a record of pizza sales for the month of February. The results are shown in the table below.

Of all the pizzas sold in February, what percent were plain, deep-dish pizzas?

(1) 20%
(2) 30%
(3) 40%
(4) 50%

Answer: (1) 20%

There were 200 plain, deep-dish pizzas sold. The percentage would be 200 divided by the total number of pizzas sold. Find the grand total of all pizzas in the table.

300 + 200 + 80 + 25 + 120 + 105 + 100 + 70 = 1000 pizzas sold.

200/1000 = 0.20 = 20%, which is Choice (1).

11. When solving -2(3x - 5) = 9/2 x - 2 for x, the solution is

(1) 8/7
(2) 10/11
(3) -16/21
(4) -16/3

Answer: (1) 8/7

You can solve this with the calculator but be sure to use parentheses when substituting.

-2(3x - 5) = 9/2 x - 2

-6x + 10 = 9/2 x - 2

-12/2 x + 10 = 9/2 x - 2

-21/2 x = -12

-21x = -24

x = -24/-21

x = 8/7

The correct Choice is Choice (1).

12.The expression x^{2a + b} is equivalent to

(1) x^2a + x^b
(2) x^a + x^{a + b}
(3) x^a * x^{a + b}
(4) x^{a + b} * x^{a + b}

Answer: (3) x^a * x^{a + b}

Terms with different exponents CANNOT be combined because they are not Like Terms. Terms with the same base can be multiplied. When multiplying terms with the same base, the exponents are added.

The first two choices cannot be added together because they are not like terms. Eliminate Choices (1) and (2).

In Choice (3), x^a * x^{a + b} = x^{2a + b}, which is the correct answer.

In Choice (4), x^{a + b} * x^{a + b} = x^{2a + 2b}. Eliminate Choice (4).

13. The inputs and outputs of a function are shown in the table below.

This function can best be described as

(1) linear
(2) quadratic
(3) exponential
(4) absolute value

Answer: (3) exponential

There is no common difference but there is a common ratio. You can see from the bottom three lines that 0.5 times 2 is 1 and 1 times 2 is 2. You can check the others as well. Going up the table, each decimal is half as large as the one below it.

Since the table has a common ratio, it is exponential, which is Choice (3).

14. Stephanie is solving the equation x² - 12 = 7x - 8. Her first step is shown below. Given: x² - 12 = 7x - 8
Step 1: x² - 4 = 7x

(1) associative property
(2) commutiative property
(3) distributive property
(4) addition property of equality

Answer: (4) addition property of equality

To get from the Given equation to the Step 1, Stephanie added 8 to both sides of the equation. This is possible because of the addition property of equality.

The correct answer is Choice (4).

15. What is the sum of 8√(3) and √(3)?

(1) 8√(6)
(2) 9√(6)
(3) 7√(3)
(4) 9√(3)

Answer: (4) 9√(3)

The sum of 8x and x is 9x. This is true whether x is apples, kittens, -27, or √(3).

Choice (4) is the correct answer.

16. The dot plots below represent test scores for 20 students on a math test.

The mode for this math test is 80 and the median is 85. Which dot plot correctly represents this data?

(1) I
(2) II
(3) III
(4) IV

Answer: (1) I

The mode of a dot plot is the number with the highest columns of dots. That eliminates Choices (2) and (4).

The median of 20 students is the average of the 10th and 11th score. In plot I, the 10th and 11th dots are both 85. In plot III, the 10th and 11th dots are in the 80 column.

Eliminate Choice (3).

Choice (1) is the correct answer.

More to come. Comments and questions welcome.

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