Algebra regents questions by topic

Algebra regents questions by topic DEFAULT

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Are you a student at a public high school in New York State? Then you must pass a math Regents exam in order to graduate and get your diploma. One of these exams is Algebra 1 Regents, which tests your understanding of an array of algebra-related concepts and laws, from exponents and equations to functions and probability.

The next NYS Algebra regents exam will be held on Wednesday, June 23, 2021, at 9:15 am.

Read on to learn exactly what the Algebra 1 Regents exam entails, what kinds of questions you can expect, what topics you should know, and how you can ensure you pass it.


What's the Format of Algebra 1 Regents?

The Algebra 1 Regents exam is a three-hour math test consisting of 37 questions across four parts. Here's an overview of the structure of the test:

 # of QuestionsQuestion TypePoints per QuestionPartial Credit Given?Total Points
Part I24 (#1-24)Multiple choice2No48
Part II8 (#25-32)Short response2Yes16
Part III4 (#33-36)Medium response4Yes16
Part IV1 (#37)Long response6Yes6


Part I consists of all multiple-choice questions, whereas Parts II through IV have what are called constructed-response questions for which you write out your work to show how you found the correct answer.

For each multiple-choice question, you'll get four answer choices (labeled 1-4) to pick from. To get full points for each constructed-response question, you must do the following per the official instructions:

"Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale."

Basically, you have to show your work! If you put down just the correct answer, you'll net 1 point—but that's it.

You won't get scrap paper to use, but you may use any blank spaces in the test booklet. You will be given one sheet of scrap graph paper. Note that anything written on this paper will not be scored.

The following equipment must be provided to you for the Algebra 1 Regents exam:

  • A graphing calculator
  • A ruler

In the back of the test booklet will be a "High School Math Reference Sheet" containing common formulas and conversions. Here's what this sheet looks like:



body_math_easy_additionUnfortunately, Algebra 1 Regents questions won't be this simple!


What Do Algebra 1 Regents Questions Look Like?

In this section, we look at some sample questions from the Algebra 1 Regents test. All questions and student responses are taken from the August 2019 administration of the Algebra 1 Regents exam.


Multiple-Choice Sample Question (Part I)


The cost of jerseys is $\$23$ per jersey. So if there were, say, 10 people on Bryan's hockey team, that would be ten $\$23$ jerseys, or $10*23$. We could therefore write 23$\bi x$ to show this same idea algebraically, with $\bi x$ representing the number of jerseys.

There's also a $\$250$ onetime set-up fee, but because this fee doesn't depend on any particular number of jerseys—you could by 10 or 100 jerseys and it would still be a $\$250$ set-up fee—we would just write it as a constant that's being added to the $\bi x$.

This means that our final algebraic expression should look like this:


Answer choice 3 matches this and is therefore the correct answer.


Short-Response Sample Question (Part II)


For this short-response question, you must plug -2 into the equation and solve. In other words, you're being asked to solve the equation if $x=-2$ (that's what $g(-2)$ means):


The correct answer is -8. Be sure to use PEMDAS. To solve it, you have to deal with the exponent first (the $-2^2$ part) and then multiply everything else from left to right. Finally, you add it all together to get the correct answer (-8).

This student response got full credit for having both the correct setup and answer:



Medium-Response Sample Question (Part III)


There are two things you need to do for this question:

  • Graph the snowfall
  • Calculate the average rate of snowfall per hour

Before you start graphing anything, make sure that you read the graph closely and understand what the $\bi x$-axis and $\bi y$-axis mean. Whereas the $x$-axis represents the number of hours that have passed, the $y$-axis represents the total amount of snowfall in inches. As a result, the $x$-axis is divided up by hour, while the $y$-axis is divided up by half inch.

So how do you graph this? Let's do it together, step by step, based on the information above.

"For the first 4 hours, it snowed at an average rate of one-half inch per hour."

Starting from the origin of the graph, or $(0, 0)$, draw an increasing line so that it goes up one-half inch every hour until hour 4; this should place you at a total of 2 inches of snowfall (that's $0.5*4$), or coordinates $(4, 2)$.

"The snow then started to fall at an average rate of one inch per hour for the next 6 hours."

From $(4, 2)$, draw an increasing line until hour 10 that goes up a whole inch every hour. You should end at $(10, 8)$, indicating a total snowfall of 8 inches over the course of 10 hours.

"Then it stopped snowing for 3 hours."

No new snow means nothing changes vertically (on the y-axis), giving us a horizontal line. From your current location at $(10, 8)$, draw a flat horizontal line from hour 10 until hour 13.

"Then it started snowing again at an average rate of one-half inch per hour for the next 4 hours until the storm was over."

From the point at $(10, 8)$, draw an increasing line so that it goes up one-half inch every hour until hour 17. This line will have the same slope as the first line you drew. You should end up at $(17, 10)$, meaning it snowed a total of 10 inches over 17 hours.

Here's what a correctly drawn graph looks like. The student put down points at each hour mark to show where the total snowfall was every hour; they also connected the dots, which you must do if you want to get full points for this question!


Once you've graphed the word problem, it's time to figure out the overall average rate of snowfall over the length of the storm. To do this, we'll have to divide the total amount of accumulated average snowfall (10 inches) by the total number of hours it snowed (17):


Round your answer to the nearest hundredth of an inch, per the instructions in the problem. This gives us a total average snowfall of 0.59 inches.


body_fox_snowIs 10 inches of snow enough for a fox to submerge its head in?


Long-Response Sample Question (Part IV)



This long-response question is worth 6 credits and can be divided into three parts.


Part 1

Here, we're being asked to come up with a system of equations (likely two equations) that can be used to describe the situation. While A stands for the number of Americana chickens Allysa bought, D stands for the number of Delaware chickens she bought.

Allysa bought a total of 12 chickens, consisting of both Americana chickens and Delaware chickens. Therefore, we can conclude that the number of Americana chickens bought + the number of Delaware chickens bought = 12 total chickens. In algebra, this would look like this:


That's just one equation in our system of equations. So what's the other?

We know that Allysa paid a total of $\$35$ for her chickens. We also know that each Americana chicken is $\$3.75$, while each Delaware chicken is $\$2.50$. Therefore, the number of Americana chickens bought at 3.75 each + the number of Delaware chickens bought at 2.50 each = 35 dollars. In other words:


Our system of equations, then, looks like this:



Part 2

This second part of the problem is asking us to solve for the exact values of both $A$ and $D$ using the system of equations we found. To do this, we must set up the two equations in such a way that one of them contains only one variable (either $\bi A$ or $\bi D$).

Because the first of our equations is the simpler one, let's use this one to solve for $A$ in terms of $D$:


We know that $A$ is equal to 12 subtracted by $D$. Now, we can plug this into our other equation as $\bi A$, giving us only the variable $\bi D$ to work with:


Solve for $D$ to find the number of Delaware chickens Allysa bought:


Now that we have the value of $D$, we can plug this value of 8 into our equation and solve for $A$:


The algebra shows that Allysa bought 8 Delaware chickens and 4 Americana chickens.

Here's an example of a student's correct response:



Part 3

This part isn't as tricky as it looks and mostly consists of easy addition, multiplication, and division.

To start, we must find out how many total eggs Allysa can expect her 12 chickens to lay each week. Based on what we found in Part 2 above, we know that Allysa has 8 Delaware chickens and 4 Americana chickens.

As Part 3's instructions tell us, Delaware chickens lay 1 egg a day, whereas Americana chickens lay 2 eggs a day.

Per day, then, Allysa's 8 Delaware chickens lay a total of 8 eggs (because 8 chickens multiplied by 1 egg each per day = 8 eggs a day). And her 4 Americana chickens lay 8 total eggs as well (as 4 chickens multiplied by 2 eggs each per day = 8 eggs each day). This means that Allysa takes in 16 eggs in total per day from both types of chickens she owns (since $8+8=16$).

Now how many eggs do Allysa's chickens lay in a week? To find this, multiply the number of eggs her chickens lay each day (that's 16) by 7 days:


Allysa's chickens lay 112 eggs a week. But Allysa can only sell her eggs by the dozen, or in groups of 12, so we need to divide this total by 12 to see how many full dozens that gives her:


You'll need to round down to the nearest whole number since we can't have anything less than a full dozen. In other words, 9 dozens fit into 112. (To make 10 dozens, we would need 120 eggs.)

Finally, multiply these 9 dozens by the price per dozen eggs ($\$2.50$) to see how much money Allysa would make by the end of the week:


Allysa would make $\$\bo 22.50$.

This sample student response earned full points:





What Topics Does Algebra 1 Regents Cover?

The Algebra 1 Regents exam covers the basic skills and laws taught in algebra before you get into trigonometry. Below is a more in-depth list of the topics tested with links to our relevant SAT/ACT guides in case you're looking to review any concepts:

This chart shows what percentage of Algebra 1 Regents each major category tested comprises:

CategoryDomainTopicsPercentage of Test by Credit
Number & QuantityQuantitiesReason quantitatively and use units to solve problems2-8%
The Real Number SystemUse properties of rational and irrational numbers
AlgebraSeeing Structure in ExpressionsInterpret the structure of expressions50-56%
Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational ExpressionsPerform arithmetic operations on polynomials
Understand the relationship between zeros and factors of polynomials
Creating EquationsCreate equations that describe numbers or relationships
Reasoning with Equations and InequalitiesUnderstand solving equations as a process of reasoning and explain the reasoning
Solve equations and inequalities in one variable
Represent and solve equations and inequalities graphically
Solve systems of equations
FunctionsInterpreting FunctionsUnderstand the concept of a function and use function notation32-38%
Interpret functions that arise in application in terms of the context
Analyze functions using different representations
Building FunctionsBuild a function that models a relationship between two quantities
Build new functions from existing functions
Linear, Quadratic and Exponential ModelsConstruct and compare linear, quadratic, and exponential models and solve problems
Interpret expressions for functions in terms of the situation they model
Statistics & ProbabilityInterpreting Categorical and Quantitative DataInterpret linear models5-10%
Summarize, represent and interpret data on two categorical and quantitative variables
Summarize, represent and interpret data on a single count or measurement variable

Source:Engage NY via the New York State Education Department


body_high_school_diplomaIn order to get your high school diploma, you'll need to pass NYS Algebra Regents.


How to Pass Algebra Regents: 6 Essential Tips

If you're taking the Algebra 1 Regents exam to fulfill your math test requirement, then you need to ensure that you will pass the test. To pass, you must earn a scaled score of 65 or higher, which comes out to about 27 credits/points (out of 86).

You can use official Algebra 1 Regents conversion charts for past tests to get a better sense of how credits translate into scaled scores. Every administration is different, though, so the number of points you need to get a certain score can vary slightly from test to test.

Here are six useful tips—both for your prep and test day—to help you pass Algebra Regents.


#1: Monitor Your Progress With Real Practice Tests

One of the best ways you can prepare for the Algebra 1 Regents exam is to use real, previously administered tests, which are available for free on the New York State Education Department website. Because these are actual exams administered by the NYSED, you know you'll be getting the most realistic test-taking experience possible when you use them.

It's most effective to take one practice test in the beginning of your prep, one in the middle of your prep, and one right before test day. This way you can monitor your progress and figure out which topics, if any, you're still struggling with.

Every time you take a practice test, be sure to time yourself as you'll be timed on the actual exam (three hours); you should also take the test in a quiet room away from others. You'll want to mimic real testing conditions as closely as possible so you can get a highly accurate indicator of where you're scoring and whether you're on track to passing.

After you finish taking a test, score it using its answer key and refer to the student responses to see what kinds of answers earned full points and what graders were looking for.


#2: Review Topics Using Class Materials

All the topics tested on the Algebra 1 Regents exam should be topics you already studied in depth in your algebra class, so if you still have any old homework assignments, graded tests/quizzes, or an algebra textbook, use these to review for the Algebra 1 Regents exam and to get a clearer sense of what areas you used to struggle with (and whether you still struggle with them).

I recommend trying out some of the practice math questions from your algebra textbook that you didn't already do for homework or in-class practice.


#3: Consult Your Math Teacher as Needed

If you have any questions about a particular exam topic, a question type, or the scoring system, don't be afraid to talk to your algebra teacher. They want you to pass Algebra 1 Regents and get your high school diploma, after all!

See whether your teacher has any time after class to go over tricky concepts with you or give you advice on what graders look for when it comes to the constructed-response questions.


#4: Plug In Answers and Numbers

These two strategies—plugging in answers and plugging in numbers—are great ones to know for the Algebra 1 Regents exam, particularly for the multiple-choice questions in Part I.

If you don't know how to approach an algebra problem, you can use these tricks to help you figure out what the answer could be.

Both strategies involve the use of substitution of either one of the four answer choices or any easy-to-use number for a variable in an equation/system of equations. You can also use these strategies to check your answer and make sure that it actually works with the equation(s) provided.


#5: Use Your Time Wisely

As you know, Algebra 1 Regents consists of four parts, the first of which is a long multiple-choice section. But since this is arguably the easiest of the four sections, you'll want to make sure that you're not spending too much time on Part I. And since Parts II, III, and IV are harder and worth more points, you'll want to save as much time as you can for the constructed-response questions.

You'll get three hours for the exam, so try to spend no more than an hour on Part I—this gives you about two and a half minutes per multiple-choice question. Ideally, you'll also have plenty of time at the end of the exam to check your answers.


#6: Answer Every Single Question

Since there's no guessing penalty on the Algebra 1 Regents exam, you should put down an answer for every question, even if you're completely stumped as to how to solve it.

With the multiple-choice questions, use the process of elimination first to see if you can whittle down the number of answer choices to three or even two, thereby raising your chances of getting the correct answer from 25% to 33% or 50%.

Another tactic is to choose a guessing number (1-4) you can use when a multiple-choice problem stumps you. For instance, if your guessing number was 3, then you would pick answer choice 3 for any multiple-choice problem you had absolutely no idea how to solve.

For the Part II, III, and IV constructed-response questions, you can get partial credit for showing at least some correct work—even if it's just a small part of what the problem asks you to do—so put down whatever you can!




Key Takeaways: What to Know About Algebra 1 Regents

The Algebra 1 Regents exam is one of three math Regents exams that high school students in New York can choose from to fulfill their graduation requirements. The test has 37 questions spread out across four sections: the first is a multiple-choice section, and the other three are constructed-response sections that require you to show your work in order to earn credit.

A passing score on Algebra Regents is a 65, equal to about 27 credits. In terms of topics tested, the NYS Algebra Regents test covers a broad range of algebra fundamentals, from equations and inequalities to functions and polynomials.

To give yourself your best shot at passing, be sure to take real practice tests, review old homework assignments and materials from your algebra class, and get help from your algebra teacher if you have any questions or need additional guidance.

On the day of the test, make sure to answer every question, use different strategies such as the process of elimination and plugging in answers/numbers, and organize your time so that you have more time for the constructed-response questions.

Good luck!


What's Next?

Not a fan of Algebra 1 Regents? No problem. If you'd rather take a different math Regents exam for your high school graduation requirements, then check out our guides to the Geometry Regents test and the Algebra 2 Regents test.

Want to learn more about the New York Regents Examinations?Our in-depth guide goes over what these tests are for and who must take them.

You'll have to take a science Regents exam in addition to a math one. Learn about these tests with our expert articles on Earth Science Regents, Chemistry Regents, and Living Environment Regents.


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Regents Exam Questions by Topic Page 1 LINEAR EQUATIONS ...

RegentsExamQuestionsbyTopicPage 1LINEAREQUATIONS: Parallel and Perpendicular Lines-GEwww.jmap.orgNAME:_____________________________1. fall0828ge, P.I. G.G.62What is the slope of a line perpendicular tothe line whose equation is 5x3y 8?4. 080630a, P.I. G.G.63Which line is perpendicular to the line whoseequation is 5y6 3x?[A] 5 3[B] 5 3[C] 3 5[D] 3 5[A] y 355x7 [B] y x7353[C] y x7 [D] y x7352. 060926ge, P.I. G.G.63Which equation represents a lineperpendicular to the line whose equation is2x3y 12?[A] 2y3x 6 [B] 6y4x12[C] 3y2x 12 [D] 2y3x65. fall9925b, P.I. G.G.64Given two lines whose equations are3x y8 0 and 2xby 90,determine the value of b such that the twolines will be perpendicular.3. 060528a, P.I. G.G.63Which equation represents a line that isperpendicular to the line whose equation is2y 3x 7?[A] y [C] y 2332x3 [B] y x7x3 [D] 2y3x36. fall0812ge, P.I. G.G.65What is the equation of a line that passesthrough the point ( 3, 11 ) and is parallel tothe line whose equation is 2x y 4?[A] y 12[C] y x12252x252[B] y 2x5[D] y 2x5

RegentsExamQuestionsbyTopicPage 2LINEAREQUATIONS: Parallel and Perpendicular Lines-GEwww.jmap.orgNAME:_____________________________7. 060931ge, P.I. G.G.65Find an equation of the line passing throughthe point (5,4) and parallel to the line whoseequation is 2x y 3.8. 060907ge, P.I. G.G.64What is an equation of the line that passesthrough the point (-2,5) and is perpendicular1to the line whose equation is y x5?2[A] y 2x9 [B] y 2x9[C] y 2x1 [D] y 2x19. 010834a, P.I. G.G.64Write an equation of a line that is2perpendicular to the line y x5 and that3passes through the point (0,4).11. 060722a, P.I. G.G.63Which statement describes the lines whose1equations are y x12 and 6y2x 6?3[A] They are perpendicular to each other.[B] They are parallel to each other.[C] They intersect each other.[D] They are segments.12. fall0822ge, P.I. G.G.63The lines 3y16x 4 and 2y1 x9are[A] perpendicular [B] parallel[C] neither parallel nor perpendicular[D] the same line13. 060729aIf the product of x and 1 m is 1,m 0,thenx is equivalent to10. 080130a, P.I. G.G.63Shanaya graphed the line represented by theequation y x6. Write an equation for aline that is parallel to the given line. Write anequation for a line that is perpendicular to thegiven line. Write an equation for a line that isidentical to the given line but has differentcoefficients.[A] m[B] 1 m[C] 1 m[D] m

RegentsExamQuestionsbyTopicPage 1LINEAREQUATIONS: Parallel and Perpendicular[1] C[2] D[3] A[4] B[5][6] D[7][2] b = 6 by determining the slopes of bothlines, sets 2 negative reciprocal slope ofb 3 (i.e. 1 3 ).or [2] b = 6 by determining the product of theslopes = -1.[1] Sets 2 2 3 and solves for b b 3 .or [1] Finds slope of perpendicular as 1 3 , butdoes not solve b.or [1] b = 6 and no work shown.[0] Does not identify slopes.or [0] A zero response is completelyincorrect, irrelevant, or incoherent; or is acorrect response that was obtained by anobviously incorrect procedure.[2] y4 2( x5) or an equivalentequation, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as leaving theanswer as y 4x 2, which has a domain5 1restriction.or [1] y4 2( x5) or an equivalentequation, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[9][10][11] B[12] C[13] A[2] A correct equation is written, such as33y x4 or ( y4) ( x0).22[1] An appropriate equation is written, butone computational error is made or oneincorrect substitution is made.[1] An appropriate equation is written, butone conceptual error is made, such as writingan equation for a parallel line going through(0,4) or for a perpendicular line that does notgo through (0,4).or [1] The slope is identified correctly as 3 2or the y-intercept as 4, but no equation or anincorrect equation is written.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[3] Three correct equations are shown, suchas y x7, y x6, and 2y2x 12.[2] Only two correct equations are shown.[1] Only one correct equation is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[8] C

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Magazine: Regents Exam Questions by Topic Page 1 LINEAR EQUATIONS ...

June 2016 Algebra I CC Regents Questions #34

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