## Thursday, January 19, 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

1. If f(x) = (3x + 4)/2, then f(8) is

1) 21
2) 16
3) 14
4) 4

This is a simple substitution and evaluation question. However, on the test it was written as a fraction without parentheses. Be careful entering it into your calculator.

(3(8) + 4)/2 = 28/2 = 14, which is Choice (3).

If you didn't use the parentheses, they you got 24 + 4/2 = 26. Luckily, that isn't one of the choices.

Offhand, I couldn't tell you where they got the incorrect choices from.

2. If x ≠ 0, then the common ratio of the sequence x, 2x2, 4x3, 8x4, 16x5, ... is

1) 2x
2) 2
3) x
4) 1/2 x

Divide 2x2 by x. The quotient is 2x. Repeat for (4x3)/(2x2. You will get the same result: 2x.

3. The expression 36x2 - 9 is equivalent to
1) (6x - 3)2
2) (18x - 4.5)2
3) (6x + 3)(6x - 3)
4) (18x + 4.5)(18x - 4.5)

Answer: 3) (6x + 3)(6x - 3)

The Difference of Two Perfect Squares Rule states that the two factors will be conjugates. That is, the binomials will be the same except that one has a plus sign and one has a minus sign. Also the coefficient will be the square roots of the original, not the numbers divided by 2.

They like to use "divided by 2" in thiese kinds of problems. However, as long as my students make this mistake (along with other students across the state), they'll continue to use this. It makes the question easy to answer for everyone else!

The correct answer is Choice (3), (6x + 3)(6x - 3).

Expended, it becomes 36x2 - 18x + 18x - 36. The two middle terms are a zero pair.

4. Given the relation R = {(-4,2), (3,6), (x,8), (-1,4)}
Which value of x would make this relation a function?

1) -4
2) -1
3) 3
4) 0

For the relation to be a function, no x value can be repeated. This eliminates -4, 3, and -1. Any other number could stand in for x except those three.

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

5. If the point (K,-5) lies on the line whose equation is 3x + y = 7, then the value of K is

1) -8
2) -4
3) 22
4) 4

Substitute y = -5 and solve for x.

3x + y = 7
3x + -5 = 7
3x = 12
x = 4

Choice (4) is 4, which is the correct answer.

More to come. Comments and questions welcome.

More Regents problems.

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