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 algebrarelated 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 threehour math test consisting of 37 questions across four parts. Here’s an overview of the structure of the test:
# of Questions 
Question Type 
Points per Question 
Partial Credit Given? 
Total Points 

Part I 
24 (#124)  Multiple choice  2  No  48 
Part II 
8 (#2532)  Short response  2  Yes  16 
Part III 
4 (#3336)  Medium response  4  Yes  16 
Part IV 
1 (#37)  Long response  6  Yes  6 
TOTAL 
37 
— 
— 
— 
86 
Part I consists of all
multiplechoice questions
, whereas Parts II through IV have what are called
constructedresponse questions
for which you write out your work to show how you found the correct answer.
For each multiplechoice question,
you’ll get four answer choices (labeled 14)
to pick from. To get full points for each constructedresponse 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:
Unfortunately, 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
.
MultipleChoice 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 setup 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 $\$250$ setup 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:
$23x+250$
Answer choice 3 matches this and is therefore the correct answer.
ShortResponse Sample Question (Part II)
For this shortresponse 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):
$g(2)=4(2)^23(2)+2$
$g(2)=4(4)3(2)+2$
$g(2)=16+6+2$
$g(2)=8$
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:
MediumResponse 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 onehalf inch per hour.”
Starting from the origin of the graph, or $(0, 0)$,
draw an increasing line so that it goes up onehalf 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 yaxis), 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 onehalf 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 onehalf 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)
:
$10/17=0.58823529411=0.59$
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
.
Is 10 inches of snow enough for a fox to submerge its head in?
LongResponse Sample Question (Part IV)
This longresponse 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:
$A+D=12$
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:
$3.75A+2.50D=35$
Our system of equations, then, looks like this:
$A+D=12$
$3.75A+2.50D=35$
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 $D$:
$A+D=12$
$A=12D$
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
:
$3.75A+2.50D=35$
$3.75(12D)+2.50D=35$
Solve for $D$ to find the number of Delaware chickens Allysa bought:
$3.75(12D)+2.50D=35$
$453.75D+2.50D=35$
$451.25D=35$
$1.25D=10$
$1.25D=10$
$D=8$
Now that we have the value of $D$, we can plug this value of 8 into our equation and solve for $A$:
$A+D=12$
$A+8=12$
$A=128$
$A=4$
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
:
$16*7=112$
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:
$112/12=9.3333=9$
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:
$9*2.50=22.50$
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 indepth list of the topics tested with links to our relevant SAT/ACT guides in case you’re looking to review any concepts:

Basics of algebra
 Balancing equations

Order of operations/
PEMDAS
 Substitution

Formulas

Inequalities

Systems of equations

Exponents
 Laws of exponents
 Negative exponents
 Reciprocals
 Square roots
 Cube roots
 Factoring

Functions

Linear equations

Logarithms

Polynomials
 Quadratic equations

Sequences and series

Simplifying
 Equations
 Fractions
 Cross multiplying

Associative, commutative, and
distributive laws

Word problems
This chart shows what percentage of Algebra 1 Regents each major category tested comprises:
Category 
Domain 
Topics 
Percentage of Test by Credit 
Number & Quantity  Quantities  Reason quantitatively and use units to solve problems  28% 
The Real Number System  Use properties of rational and irrational numbers  
Algebra  Seeing Structure in Expressions  Interpret the structure of expressions  5056% 
Write expressions in equivalent forms to solve problems  
Arithmetic with Polynomials and Rational Expressions  Perform arithmetic operations on polynomials  
Understand the relationship between zeros and factors of polynomials  
Creating Equations  Create equations that describe numbers or relationships  
Reasoning with Equations and Inequalities  Understand 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  
Functions  Interpreting Functions  Understand the concept of a function and use function notation  3238% 
Interpret functions that arise in application in terms of the context  
Analyze functions using different representations  
Building Functions  Build a function that models a relationship between two quantities  
Build new functions from existing functions  
Linear, Quadratic and Exponential Models  Construct and compare linear, quadratic, and exponential models and solve problems  
Interpret expressions for functions in terms of the situation they model  
Statistics & Probability  Interpreting Categorical and Quantitative Data  Interpret linear models  510% 
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
In 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 testtaking 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 inclass 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 constructedresponse 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 multiplechoice 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 easytouse 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 multiplechoice 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 constructedresponse 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 multiplechoice 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 multiplechoice 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 (14)
you can use when a multiplechoice problem stumps you. For instance, if your guessing number was 3, then you would pick answer choice 3 for any multiplechoice problem you had absolutely no idea how to solve.
For the Part II, III, and IV constructedresponse 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 multiplechoice section, and the other three are constructedresponse 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 constructedresponse 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 indepth 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
.