The following questions appeared on the une 2023 Algebra 1 Regents Exam

More Regents problems.

*Algebra 1 Regents, June 2023*

Part I: Each correct answer will receive 2 credits.

**17.** Some adults were surveyed to find out if they would prefer to buy a
sports utility vehicle (SUV) or a sports car. The results of the survey
are summarized in the table below.

Of the number of adults that preferred sports cars, approximately what percent were males?

1) 15.8

2) 45.2

3) 64.4

4) 82.6

Of the number of adults that preferred sports cars, approximately what percent were males?

1) 15.8

2) 45.2

3) 64.4

4) 82.6

**Answer: 2) 45.2 **

84 adults preferred sports cars, and 38 of them were male, which is less than half, so eliminate Choices (3) and (4).

Divide 38/84 = 0.452..., which is about 45.2%, which is **Choice (2)**.

**18.** The solution to 2x^{2} = 72 is

1) {9,4}

2) {-4. 9}

3) {6}

4) {__+__6}

**Answer: 4) { +6} **

You could test 4, 6 and 9 and see which numbers work.

Or you can solve it as follows:

2x^{2} = 72

x^{2} = 36

x = __+__6.

The correct answer is **Choice (4)**.

While (4)(9) = 36, neither 4^{2} nor 9^{2} equal 36.

It's important to remember the negative solution. Positive 6 isn't the ONLY solution.

**19.** Three quadratic functions are given below.

Which of these functions have the same vertex?

1) I and II, only

2) II and III, only

3) I and III, only

4) I, II, and III

Which of these functions have the same vertex?

1) I and II, only

2) II and III, only

3) I and III, only

4) I, II, and III

**Answer: 3) I and III, only **

The vertex for function III can be seen to be (-2,5). Function I is written in vertex form, and the vertex for I is (-2,5). So I and III are the same. Eliminate Choices (1) and (2).

Next, determine if the vertex for function II is also (-2,5). You can see in the table that (-2,5) is a point in the function. HOWEVER, it is NOT the vertex. There is another point at (-1,5). That means that the Axis of Symmetry for function II occurs at x = -1.5. And the vertex of the function is on the Axis of Symmetry. Eliminate Choice (4).

The correct answer is** Choice (3)**.

**20.** The domain of the function f(x) = x^{2} + x - 12 is

1) (-∞,-4]

2) (-∞,∞)

3) {-4,3]

4) [3,∞)

**Answer: 2) (-∞,∞) **

The domain is the set of all x values that are valid for the function. In this example, every value of x is valid, from negative infinity to positive infinity, which is

**Choice (2)**.

If the funtion contained, for example, a variable in the denominator of a fraction, or a variable under a square root symbol, then there would be values of x for which the function would not make sense and they would be outside of the function's domain.

The function has ZEROES at x = -4 and x = 3, but that is not the domain.

Choices (1) and (4) are portions of the function where the range (the y value) is non-negative. But these have nothing to do with the domain.

**21.** A father makes a deal with his son regarding his weekly allowance.
The first year, he agrees to pay his son a weekly allowance of $10.
Every subsequent year, the allowance is recalculated by doubling
the previous year’s weekly allowance and then subtracting 8. Which
recursive formula could be used to calculate the son’s weekly allowance
in future years?

1) a_{n} = 2n - 8

2) a_{n} = 2(n + 1) - 8

3) a_{1} = 10,
a_{n+1} = 2a_{n} - 8

4) a_{1} = 10,
a_{n+1} = 2(a_{n} - 8)

**Answer: 3) a _{1} = 10,
a_{n+1} = 2a_{n} - 8 **

A recursive formula needs a beginning, which is a

_{1}. Each value after that is calculated from the one before it. Eliminate Choice (1) and (2).

The difference between Choices (3) and (4) is that in (3) the value is doubled and then 8 is subtracted. In (4), 8 is subtracted first and then the amount is doubled.

The definition of the formula agrees with **Choice (3), which is the correct answer**.

**22.** AWhat is the solution to the inequality below?

*4 - 2/5 x*

__>__1/3 x + 15

1) x

2) x

3) x

4) x

1) x

__<__112) x

__>__113) x

__<__-154) x

__>__-15

**Answer: 3) x < -15 **

You could put each half of the equation into your graphing calculator to find where they are equal and see where the left side is greater than the right side.

__>__1/3 x + 15

-2/5 x

__>__1/3 x + 11

-2/5 x - 1/3 x

__>__11

-6/15 x - 5/15 x

__>__11

-11/15 x

__>__11

1x

__<__(-15/11)11

x

__<__-15

**Choice (3) is the correct answer.**

Remember to multiply by the reciprocal of the fraction. Remember that when you multiply an inequality by a fraction, you have to flip the inequality symbol the other direction.

**23.** Which statement is correct about the polynomial 3x^{2} + 5x -2?

1) It is a third-degree polynomial with a constant term of 22.

2) It is a third-degree polynomial with a leading coefficient of 3.

3) It is a second-degree polynomial with a constant term of 2.

4) It is a second-degree polynomial with a leading coefficient of 3.

**Answer: 4) It is a second-degree polynomial with a leading coefficient of 3. **

The degree of the polynomial has to do with the highest exponent in the expression, not the number of terms it contains. The leading coefficient is the coefficient of the term with the highest exponent. The constant is the term without a variable and the sign in front of it is part of the constant.

The polynomial 3x^{2} + 5x -2 is second degree with a leading coefficient of 3 and a constant of -2. The only choice that does not contradict any of this is **Choice (4)**.

**24.** A store manager is trying to determine if they should continue to sell
a particular brand of nails. To model their profit, they use the function
p(n), where n is the number of boxes of these nails sold in a day. A
reasonable domain for this function would be

1) nonnegative integers

2) rational numbers

3) real numbers

4) integers

**Answer: 1) nonnegative integers **

The store manager cannot sell fractions of boxes of nails and he can't sell negative boxes of nails. Irrational boxes is right out.

He can sell zero boxes.

Nonnegative integers is the reasonable domain for this function. **The correct answer is choice (1)**.

End of Part I. How did you do?

More to come. Comments and questions welcome.

More Regents problems.

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