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.
1. The graph below represents a dog walker’s speed during his 30-minute
walk around the neighborhood.
Which statement best describes what the dog walker was doing during
the 12-18 minute interval of his walk?
1) He was walking at a constant rate.
2) He was increasing his speed.
3) He was decreasing his speed.
4) He was standing still.
Answer: 1) He was walking at a constant rate.
He is walking at a constant rate of 1.5 miles per hour. Were he standing still, his speed would be zero. Increasing his speed causing the graph to have a positive slope, and decreasing his speed will give it a negative slope.
2. Given the relation: {(0,4), (2,6), (4,8), (x,7)}
Which value of x will make this relation a function?
1) 0
2) 2
3) 6
4) 4
Answer: 3) 6
It can only be a function if none of the x values repeat. The domain already has 0, 2, and 4 in it, so they cannot be repeated. The only possible choice given is 6.
3. The Speedy Jet Ski Rental Company charges an insurance fee and an hourly rental rate. The total cost is modeled by the function
R(x) = 30 + 40x. Based on this model, which statements are true?
II. x is the number of hours rented.
III. $40 is the insurance fee.
IV. $30 is the hourly rental rate.
1) I, only
2) I and II, only
3) I, III, and IV, only
4) I, II, III, and IV
Answer: 2) I and II, only
The total cost is modeled by the function R(x), so statement I is true.
The cost has an hourly rate and the number of hours is the variable, x. So statement II is also true.
The insurance fee is charge a single time and does not get multiplied by the number of hours. So the insurance fee must be $30, not $40. Statement III is false.
The hourly rental rate gets the variable for the number of hours, so it must be $40 and not $30. Statement IV is false.
4. The eleventh term of the sequence 3, -6, 12, -24, …, is
1) -3072
2) -6144
3) 3072
4) 6144
Answer: 3) 3072
You can see that the numbers are doubling except that the sign is also changing. This is a geometric sequence with a common ratio of -2. You can see that the odd terms are positive and the even terms are negative, so Choices (1) and (2) can be eliminated.
You could put -24 into your calculator and multiply by -2 to find the fifth term and then multiply the answer six more times.
48, -96, 192, -384, 768, -1536, 3072
Choice (3) is the correct answer.
You could also use the formula to find the nth term of a geometric sequence: an = a1rn - 1.
a11 = (3)(2)(11-1) = 3072.
5. Which situation represents exponential growth?
1) Aidan adds $10 to a jar each week.
2) A pine tree grows 1.5 feet per year.
3) Ella earns $20 per hour babysitting.
4) The number of people majoring in computer science doubles every 5 years.
Answer: 4) The number of people majoring in computer science doubles every 5 years.
Exponential growth means that it has a common ratio. There is a some number that is multiplied from term to term. It is not growing by a constant amount.
Adding $10 per week is constant. It's a linear equation. Eliminate Choice (1).
Growing 1.5 feet per year is constant. It's also linear. Eliminate Choice (2).
Earning $20 per hour is a constant amount. Linear. Eliminate Choice (3).
Doubling every 5 years has a constant rate of growth but the amount changes each time. Choice (4) is the answer.
6. The expression (-x2 + 3x - 7) - (4x2 + 5x - 2) is equivalent to
1) -5x2 - 2x - 9
2) -5x2 - 2x - 5
3) -5x2 + 8x - 9
4) -5x2 + 8x - 5
Answer: 2) -5x2 - 2x - 5
Combine the like terms. Make sure to distribute the subtraction to all the terms in the second polynomial.
(-x2 + 3x - 7) - (4x2 + 5x - 2)
-x2 + 3x - 7 - 4x2 - 5x + 2
-5x2 - 2x - 5
This is Choice (2).
7. If f(x) = x2, which function is the result of shifting f(x) 3 units left and 2 units down?
1) g(x) = (x + 2)2 - 3
2) h(x) = (x - 2)2 + 3
3) j(x) = (x + 3)2 - 2
4) k(x) = (x - 3)2 + 2
Answer: 3) j(x) = (x + 3)2 - 2
If the graph is being shifted down 2 units, there there will be a -2 at the end. There is only one choice, and that's Choice (3).
When the graph is shifted to the left, that means you are adding a value to the inside of the parentheses which gets squared.
8. An equation used to find the velocity of an object is given as
v2 = u2 + 2as,where u is the initial velocity, v is the final velocity,
a is the acceleration of the object, and s is the distance traveled.
When this equation is solved for a, the result is
1) a = (v2 u2) / (2s)
2) a = (v2 - u2) / (2s)
3) a = v2 - u2 - 2s
4) a = 2s(v2 - u2)
Answer: 4) the number of time periods
Use inverse operations to isolate the varaible, which is a in this case.
v2 = u2 + 2as
v2 - u2 = 2as
(v2 - u2) / (2s) = a
This is Choice (2).
More to come. Comments and questions welcome.
More Regents problems.
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