Algebra Problems of the Day (Algebra Regents, June 2025 Part II)

This exam was adminstered in June 2025.

June 2025 Algebra, Part II

Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.

25. A survey was taken to determine whether students preferred to watch videos or listen to music. Of the 100 students surveyed, 44 were seniors. Of the 65 students who preferred to watch videos, 42 were juniors. Use this information to complete the frequency table below.

Answer:

Fill in what you know and the add or subtract to find the remaining boxes.

26. Solve the inequality for y:

5(2 - y) > -11y - 8

Answer:

Solve the same way that you solve an equation with variables on both sides, but by mindful if you have to multiply or divide by a negative number. Isolate the variable on one side of the inequality.

5(2 - y) > -11y - 8
10 - 5y > -11y - 8
10 + 6y > -8
6y > -18
y > -3

27. Express (5x - 3)(-2x + 7) as a trinomial in standard form.

Answer:

Standard form means to combine all like terms and then arrange the three terms in order of the highest exponent to the lowest (which could be 0 if there is no variable).

You can use FOIL or the Box (Lattice/Area) Method:

(5x - 3)(-2x + 7)
-10x² + 35x + 6x - 21

-10x² + 41x - 21

28. The first and fourth terms in an arithmetic sequence are given below.

-20, _____, _____, -2
Determine the eighth term.

Answer:

Find the differnce between each term and then find the eight term.

(-2) - (-20) = 18 over 3 terms, so each term is increasing by +6.

The eighth term is 4 past the fourth term, so 4(6) = 24. Add -2 + 24 = 22 is the eighth term.

Check: -20, -14, -8, -2, 4, 10, 16, 22.

29. Write an equation in slope-intercept form for the line that passes through (-2,5) and has a slope of -3. [Use of the set of axes below is optional.]

Answer:
If you point the plots on the graph, you should have (-2,5), (-1,2), and (0,-1). That gives the equation y = -3x - 1.

If you start with Point-Slope form, it's

y - 5 = -3(x + 2)
y - 5 = -3x - 6
y = -3x - 1

30. Factor the expression x³ - 36x completely.

Answer:
Any time you see the words "factor" and "completely", you can be sure that there will be multiple steps. Usually, it will involve factoring out the Greatest Common Factor first before factoring what remains. Sometimes it's using the Difference of Squares rule multiple times.

x³ - 36x

x(x² - 36)

x(x - 6)(x + 6)

End of Part II

How did you do?

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