The following questions appeared on the January 2024 Algebra 1 Regents Exam
More Regents problems.
Algebra 1 Regents, January 2024
Part I: Each correct answer will receive 2 credits.
9. Mrs. Smith’s math class surveyed students to determine their favorite
flavors of soft ice cream. The results are shown in the table below.
Chocolate Vanilla Twist Juniors 42 27 45 Juniors 67 42 21
Of the students who preferred chocolate, approximately what
percentage were seniors?
1) 27.5
2) 44.7
3) 51.5
4) 61.5
Answer: 4) 61.5
There were 42 + 67 = 109 who preferred Chocolate. Of those, 67/109 were seniors. Even without a calculator, you can see that there is only one possible answer, which is 61.5.
You don't need to know the number of juniors and seniors in the survey. You only need to know how many liked chocolate.
10. If f(x) = x2 + 2x + 1 and g(x) = 3x + 5, then what is the value of
f(1) - g(3)?
1) 10
2) 8
3) -10
4) -8
Answer: 3) -10
Substitute into each function and evaluate.
f(1) - g(3) = (1)2 + 2(1) + 1 - (3(3) + 5) = 1 + 2 + 1 - 9 - 5 = -10, which is Choice (3).
11. Which function has the largest y-intercept?
Answer: 3) g(x) = |x| + 3
The y-intercept is the value of y when x = 0.
In Choice (1), the y-intercept is -1.
In Choice (2), the y-intercept is 2.
In Choice (3), the y-intercept is 3.
In Choice (4), the y-intercept is 1.
The largest of these is 3, which is Choice (3).
12. Two texting plans are advertised. Plan A has a monthly fee of $15
with a charge of $0.08 per text. Plan B has a monthly fee of $3 with
a charge of $0.12 per text. If t represents the number of text messages
in a month, which inequality should be used to show that the cost of
Plan A is less than the cost of Plan B?
1) 15 + 0.08t < 3 + 0.12t
2) 15 + 0.08t > 3 + 0.12t
3) 15t + 0.08 < 3t + 0.12
4) 15t + 0.08 > 3t + 0.12
Answer: 1) 15 + 0.08t < 3 + 0.12t
The monthly fee is charged once and the per text charge gets the variable. Eliminate Choices (3) and (4).
Plan A < Plan B is Choice (1).
13. The function f(x) is graphed on the set of axes below.
What is the equation of the axis of symmetry for f(x)?
1) x = -1
2) x = -3
3) y = -1
4) y = -3
Answer: 1) x = -1
The axis of symmetry is a vertical line that goes through the vertex and cuts the parabola in half so that the left side is a mirror image of the right side.
The equation for any vertical line starts with "x =", so eliminate Choices (3) and (4).
The vertex is at (-1,-3), so the axis of symmetry is x = -1, which is the x-coordinate of the vertex. This is Choice (1).
14. What is the degree of the polynomial 5x - 3x2 - 1 + 7x3?
1) 1
2) 2
3) 3
4) 5
Answer: 3) 3
The degree of a polynomial is the largest exponent. (Note: it is not the exponent of the first term unless the polynomial is written in standard form.)
The largest exponent is 3, which is Choice (3).
15. The product of (x2 + 3x + 9) and (x - 3) is
1) x3 -27
2) x2 + 4x + 6
3) x3 - 6x2 - 18x - 27
4) -6x4 + x3 - 18x2 - 27
Answer:1) x3 -27
You can use the Distributive Property or the Area Model/Box Method to find the solution, but you don't need to.
If you look at the first terms of the two expressions, you have (x2)(x) which is x3, which will be the leading term of the product.
This means you can eliminate Choices (2) and (4).
Using the box method gets you this:
When the graph is shifted to the left, that means you are adding a value to the inside of the parentheses which gets squared.
| x2 | 3x | 9 | |
| x | x3 | 3x2 | 9x |
| -3 | -3x2 | -9x | -27 |
Adding like terms gets you x3 + 0 x2 + 0x - 27, which is Choice (1).
16. The solution to (2/3)(3 - 2x) = 3/4 is
1) -11/8
2) 5/8
3) -33/16
4) 15/16
Answer: 4) 15/16
Use inverse operations to isolate the varaible.
(2/3)(3 - 2x) = 3/4
3 - 2x = (3/4)(3/2)
-2x = 9/8 - 3
x = (9/8 - 24/8) / (-2)
x = (-15/8) / (-2) = (-15/-16) = 15/16
This is Choice (4).
More to come. Comments and questions welcome.
More Regents problems.
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