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The Best Algebra 2 Regents Review Guide 2020

Posted by Hannah Muniz | Dec 16, 2019 11:00:00 AM

General Education

 

feature_algebra_2_regents_math_blackboard

If you're currently attending a public high school in New York State, then you'll have to pass one of three math Regents exams to earn your diploma. The Algebra 2 Regents exam, also called the Trig Regents exam due to its emphasis on trigonometry, tests you on numerous high-level math topics, from exponential functions and polynomials to conditional probability and complex numbers.

The next Algebra 2 Regents exam will take place on Thursday, January 23, 2020, at 1:15 pm.

This guide covers everything there is to know about Algebra 2 Regents, including the format of the exam, what its questions look like, the main topics it tests, and key tips for passing it.

 

What's the Format of the Algebra 2 Regents Exam?

On the Algebra 2 Regents exam you'll get a total of 37 questions spread out over four parts, which consist of a multiple-choice section (Part I) and three constructed-response sections (Parts II, III, and IV). You'll have three hours to complete the test, though most students finish more quickly than this.

Here's an overview of the Trig Regents format:

  # of Questions Question Type Points per Question Partial Credit Given? Total Points
Part I 24 (#1-24) Multiple choice 2 No 48
Part II 8 (#25-32) Short response 2 Yes 16
Part III 4 (#33-36) Medium response 4 Yes 16
Part IV 1 (#37) Long response 6 Yes 6
TOTAL 37 86

 

In Part I, you'll get four answer choices (labeled 1-4) for each multiple-choice question, and you'll choose just one of these by marking it on a separate answer sheet.

For the constructed-response questions in Parts II through IV, you must show your work in order to earn full credit. Specifically, you have to do the following, per the official Algebra II Test Guide:

"For constructed-response questions, students are required to clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, proofs, etc. In some cases, they may be required to provide written explanations or justifications to demonstrate conceptual understanding."

Just putting down the correct answer will net you 1 point, but you'll need to write more if you wish to get full credit (2-6 points, depending on the constructed-response question).

While you won't get any scrap paper to use during the exam, you may use any blank spaces in the test booklet for working through problems; these areas will not be graded. You'll get one sheet of scrap graph paper (located in the back of your booklet), which you can tear off and use as needed; anything written on this will not be scored.

The following tools must be made available to you during the Algebra 2 Regents exam:

  • A graphing calculator
  • A ruler

Lastly, in the back of your test booklet will be a "High School Math Reference Sheet" containing several formulas and conversions. You may use this at any time during the exam as a reference.

Here's what the sheet looks like:

body_geometry_regents_reference_sheet

 

body_math_formulas_numbers_collage

 

What Topics Does Algebra 2 Regents Cover?

Algebra 2 Regents covers high-level topics that are slightly more complicated than what's tested on Algebra 1 Regents, with a bigger focus on trigonometry (hence the reason the test is also commonly referred to as Trig Regents).

In addition to the topics covered on Algebra 1 Regents, you'll need to know the following (note that we've included links to our relevant SAT/ACT guides in case you'd like to review):

The chart below shows what percentage of NYS Algebra Regents each major category comprises:

Category Domain Topics Percentage of Test by Credit
Number & Quantity The Real Number System Extend the properties of exponents to rational exponents.  5-12%
Quantities Reason quantitatively and use units to solve problems.
The Complex Number System Perform arithmetic operations with complex numbers. Use complex numbers in polynomial identities and equations.
Algebra Seeing Structure in Expressions Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. 35-44%
Arithmetic with Polynomials and Rational Expressions Understand the relationship between zeros and factors of polynomials. Use polynomial identities to solve problems. Rewrite rational expressions.
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. Solve systems of equations. Represent and solve equations and inequalities graphically. 
Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section.
Functions Interpreting Functions Understand the concept of a function and use function notation. Interpret functions that arise in application in terms of the context. Analyze functions using different representations. 30-40%
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.
Trigonometric Functions Extend the domain of trigonometric functions using the unit circle. Model periodic phenomena with trigonometric functions. Prove and apply trigonometric identities.
Statistics & Probability Interpreting Categorical and Quantitative Data Summarize, represent and interpret data on a single count or measurement variable. Summarize, represent and interpret data on two categorical and quantitative variables. 14-21%
Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments. Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data. Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Source: Engage NY via the New York State Education Department

 

body_math_textbook_page

 

What Do Algebra 2 Regents Questions Look Like?

It helps to be familiar with the different question types on the Algebra Regents exam before you sit down to take it. As mentioned, there are four types of questions you'll get on the test:

  • Multiple choice (Part I)
  • Short response (Part II)
  • Medium response (Part III)
  • Long response (Part IV)

We'll look at each of these question types in more detail below. All sample questions and student responses are from the August 2019 administration of the Algebra 2 Regents exam.

 

Multiple-Choice Sample Question (Part I)

body_algebra_2_regents_part_i_sample_question

Usually in math you'll be asked to either FOIL two binomials or factor a quadratic equation (that's $ax^2+bx+c$) into two binomialshere, though, we're being asked to do both in one problem!

Start by writing out the first set of parentheses as two binomials:

$(x+2)^2+4(x+2)+3$
$(x+2)(x+2)+4(x+2)+3$

Next, use FOIL to distribute these two binomials:

$x^2+2x+2x+4+4(x+2)+3$

Combine like terms until you're left with a basic quadratic equation. To simplify the $4(x+2)$ part, you'll have to use the distributive property:

$x^2+2x+2x+4+4x+8+3$
$x^2+4x+4+4x+11$
$x^2+8x+15$

Here's where we need to work in the opposite direction and factor the equation so that we get two binomials (the structure of every answer choice). We know that $x^2$ is simply $x$ multiplied by $x$, so the first terms in each of our binomials must be $x$:

$(x+\unknown)(x+\unknown)$

Next, to get the second term, $8x$, we'll need two numbers that add up to 8. At the same time, these two numbers must multiply together to give us our third term (15). The only numbers that do this are 5 and 3, giving us the following pair of binomials:

$(x+5)(x+3)$

The correct answer is answer choice 2.

If you'd like to review how to factor a quadratic equation into two binomials, check out this helpful YouTube video:

 

 

Short-Response Sample Question (Part II)

body_algebra_2_regents_part_ii_sample_question

To get this 2-credit question right, you'll need to know the rules of probability.

According to the description, students who have taken either AP World History or AP European History (but not both) are eligible to enroll in AP US History. Out of 825 seniors, 165 took World History and 66 took AP Euro; thus, the total number of eligible students is as follows:

$165+66=231$

But of these 231 seniors, 33 took both World History and AP Euro, making them unable to enroll in US History. Consequently, we must subtract 33 from 231:

$231-33=198$

So out of 825 total seniors, 198 are eligible to enroll in AP US History. Probability is shown using the following formula, in which $\bi P( \bi E)$ stands for the probability of a specific event happening:

$P(E)={\desired \outcome}/{\all \possible \outcomes}$

Our probability (and final answer) looks like this:

$198/825$

You can leave your answer as a fraction or convert it into either a decimal or a percentage:

$198/825=0.24=24%$

Here's one student's correct response to this question:

body_algebra_2_regents_part_ii_student_response

 

body_us_history_union_army"What do you mean you're not eligible to take AP US History???"

 

Medium-Response Sample Question (Part III)

body_algebra_2_regents_part_iii_sample_question_1

body_algebra_2_regents_part_iii_sample_question_2

To be able to answer this question, you'll need to know what a sine function is. Here's how a basic sine function, or $y=\sin(x)$, looks when graphed:

 

body_sine_function_graphPeo/Wikimedia Commons

 

And here's the general formula for any sine function:

$y=a\sin(bx)$

In this, $\bi a$ stands for the amplitude, that is, the vertical distance between the $x$-axis (when $x=0$) and the highest point on the $y$-axis. The higher the amplitude, the more vertically stretched the graph will be.

Meanwhile, $\bi b$ is the coefficient of $\bi x$; it is related to the period of a sine function, or the distance on the $x$-axis before the graph begins to repeat itself. The period of a basic sine function is $2π$, so $b$ represents the number of cycles the graph goes through between 0 and $2π$ (that's 1 in a basic sine function, or $y=\sin(x)$). Therefore, ${2π}/b$ is equal to the period of the function.

In this problem, we've been given both the amplitude and period for a sine function. We know that the amplitude is represented by a and that it comes right before the "sin" in the equation, so we can plug this number into our formula like this:

$y=a\sin(bx)$
$y=2\sin(bx)$

You might be tempted to plug in $b$ here as well, but remember that $\bi b$ itself doesn't represent the period; rather, the period is equal to ${2π}/b$. We are told that the period of the function is $π/2$. This means that ${2π}/b=π/2$. To find the value of $b$, then, we must use algebra and solve:

${2π}/b=π/2$
$2π={bπ}/2$
$4π=bπ$
$4=b$

Now that we have our values for both $a$ and $b$ we can write out the equation for our sine function:

$y=2\sin(4x)$

This is the answer to the first part of the question.

For the second part, we need to graph this function. In sine functions with a positive amplitude, the curve passes through the origin $(0, 0)$ and continues upward. We also know the following about our function:

  • The amplitude is 2, so the highest and lowest points of every curve will be $y=2$ and $y=-2$.
  • The period is $π/2$, so a whole cycle must happen between 0 and $π/2$, or every half pi

Here's a student's correctly drawn graph:

body_algebra_2_regents_part_iii_student_response

 

body_light_sine_waveLook deep into the pretty sine wave ...

 

Long-Response Sample Question (Part IV)

body_algebra_2_regents_part_iv_sample_question_1body_algebra_2_regents_part_iv_sample_question_2body_algebra_2_regents_part_iv_sample_question_3

This 6-credit problem can be divided into three parts, so let's look at how to solve each one.

 

Part 1

This part deals with simple substitution. The s stands for the speed of the wind in mph. Therefore, if the wind has a speed of 30 mph, we just need to plug this number into our equation for the Beaufort Wind Scale as $\bi s$ and solve for $\bi B$:

$B=1.69√{30+4.45}-3.49$
$B=1.69√{34.45}-3.49$
$B=1.69(5.869412)-3.49$
$B=9.919307-3.49$
$B=6.429307$

A Beaufort number of 6.4293 rounds down to 6 on the Beaufort Wind Scale, translating to a "steady breeze."

Here's an example of a student's full-credit response to this question:

body_algebra_2_regents_part_iv_student_response_1

 

Part 2

This part is essentially the opposite of Part 1 in that we're given the value of $B$ (15, which isn't even on the chart because it's so high!) and need to solve for $s$ to the nearest mile per hour.

So let's plug 15 as $\bi B$ into our equation and solve for $\bi s$:

$15=1.69√{s+4.45}-3.49$
$18.49=1.69√{s+4.45}$
$10.9408284=√{s+4.45}$
${10.9408284}^2=(√{s+4.45})^2$
$119.701726078=s+4.45$
$s=115.251726078$

As we can see, $\bi s$ equals 115.251726, meaning it would round down to 115 mph.

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

body_algebra_2_regents_part_iv_student_response_2

 

Part 3

In this part, we must find the range of values of $s$ that all have a Beaufort number of 10. While you might be tempted to just solve for $s$ when $B=10$, this would only yield the value of $s$ that equals exactly 10 on the Beaufort Wind Scale instead of all numbers that round down or up to 10.

To find this range, we need to plug in the lowest possible number that rounds up to 10 (9.5) and the highest possible number that rounds down to 10 (10.49). This will give us the lowest possible and highest possible values of $s$ with a Beaufort number that rounds to 10.

Here's the lowest possible value of $\bi s$ (when $\bi B$ = 9.5):

$9.5=1.69√{s+4.45}-3.49$
$12.99=1.69√{s+4.45}$
$7.686391=√{s+4.45}$
$59.0805994188=s+4.45$
$s=54.6305994$

And here's the highest possible value of $\bi s$ (when $\bi B \bo =\bo 10.49$):

$10.49=1.69√{s+4.45}-3.49$
$13.98=1.69√{s+4.45}$
$8.27218935=√{s+4.45}$
$68.4291166423=s+4.45$
$s=63.9791166$

Because 54.631 rounds up to 55 mph and 63.979 rounds up to 64 mph, the range of values of $\bi s$ that have a Beaufort number of 10 is 55 to 64 mph, or 55 $\bo ≤ \bi s \bo ≤$ 64.

Here's an example of a correct response written by a real student:

body_algebra_2_regents_part_iv_student_response_3

 

body_girl_graduate_throwing_capRemember, being able to take a cool-but-sort-of-cliched graduation pic is your main goal when it comes to passing Algebra 2 Regents.

 

How to Pass Algebra 2 Regents: 6 Crucial Tips

If you've decided to take Algebra 2 Regents for your math graduation requirement, it'll help you to know what it actually takes to pass the exam.

To pass Algebra 2 Regents, you'll need to get a scaled score of 65, or about 26 credits (out of 86 total). Looking at the official Algebra 2 Regents score conversion charts for past exams can give you a better sense of how credits translate into scaled scores. Every administration is different, so the exact number of credits you'll need to pass and get a scaled score of 65 can vary slightly.

Here are six tips to help you raise your chances of passing Algebra 2 Regents.

 

#1: Check Your Progress With Practice Tests

The best way to prepare for Algebra 2 Regents is to practice with previously administered tests, which will give you the most realistic test-taking practice and help you learn exactly what to expect on the exam. You can download past exams for free on the official NYSED Regents website.

We recommend taking a full-length practice test at 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 see whether you're close to passing or whether you might need to buckle down and prep harder.

With every Algebra Regents practice test, make sure to abide by the official time limit (three hours) and take it in a quiet place where nobody will bother you. It's important to mimic real testing conditions as closely as possible; doing this will give you the most accurate indicator of your abilities and where you're currently scoring.

Once you've finished taking a practice test, use the answer key to score your exam and determine whether you passed. You can also refer to the student responses on the NYSED site to get a clearer idea of what types of answers earn full credit.

 

#2: Review Key Topics Using Class Materials

You'll most likely take the Algebra 2 Regents exam once you've completed (or are at least close to completing) your high school trigonometry or advanced algebra class. Therefore, you can use old homework assignments, graded tests and quizzes, or your math textbook to help you review the major topics tested on the exam.

Try to figure out whether there are any concepts you still struggle to understand. It might also help to use practice problems from your trig textbook to review.

 

#3: Get Help From Your Math Teacher

Your math teacher wants you to do well on the Algebra 2 Regents test so you can get your diploma and graduate; therefore, don't be afraid to meet with your teacher and ask them if they have any advice for the exam or if they would be willing to help you with understanding some of those trickier algebra concepts and strategies.

You can also ask your teacher what graders typically look for in constructed-response questions.

 

#4: When in Doubt, Plug In Answers and Numbers

Plugging in answers and plugging in numbers are some of the best strategies to know for Algebra 2 Regents (and Algebra 1 Regents) and are most helpful for the multiple-choice questions.

These methods involve the use of substitution of either one of the four answer choices or an easy-to-use number, such as 2 or 3, for a variable. If you're not sure how to approach a math problem or want to use the process of elimination, these two strategies should be your next move.

You can also use these methods to check your work and ensure that the equations give you the right answer(s).

 

#5: Make Good Use of Your Time

The Part I multiple-choice section is arguably the easiest of the four sections (and its questions are worth fewer points than those in Parts III and IV), so you'll want to save most of your time for the constructed-response questions.

Because you'll have a total of three hours for Trig Regents, you should aim to spend no more than an hour on Part I (that's about two and a half minutes per question)—this will give you two whole hours for Parts II through IV, ideally with some extra time at the end to check your answers.

 

#6: Answer Every Question!

There's no penalty for incorrect answers on Algebra 2 Regents, so it's in your best interest to put down an answer for every single question, regardless of how stumped you might be.

In Part I, try to use the process of elimination to figure out which answer choices might be more logical or appropriate than others. Doing this could raise your chances of getting the question right from 25% to 33% or even 50%.

Another option is to choose a guessing number (1-4), which you'll use whenever you have no idea how to solve a multiple-choice problem or are running out of time. For instance, if my guessing number were 2, I'd choose answer choice 2 for every multiple-choice question I didn't know how to solve.

For all constructed-response questions, you can get partial credit for showing at least some correct work, so be sure to write down whatever you can!

 

Conclusion: What to Know About Algebra 2 Regents

Algebra 2 Regents, also known as Trig Regents due to its emphasis on trigonometry, is one of three math Regents tests that's required for graduation from a public high school in New York State. The three-hour exam consists of 37 questions spread out across one multiple-choice section and three constructed-response sections.

You must pass Algebra 2 Regents to get your high school diploma (if this exam is your chosen math test). A passing score is 65, equal to about 26 (out of 86) credits. Topics tested include high-level algebra and trig concepts, from quadratic functions to logarithms, matrices, and probability.

The best way to ensure you pass the exam is to take real practice tests, review previous homework assignments and quizzes from your math class, and get help from your math teacher. On test day, remember to use key strategies (such as plugging in answers and numbers), spend more time on constructed-response questions, and answer every single question.

 

What's Next?

Algebra 2 Regents isn't the only math Regents exam you can take to graduate. Check out our expert review guides to the Geometry Regents and Algebra 1 Regents to learn more about your other options.

What exactly are the New York State Regents Examinations? Why were these tests created, and which ones do you need to pass in order to graduate? Learn everything there is to know in our introductory guide to the Regents exams.

Also taking the SAT or ACT? Then you'll want to get a great math section score. Take a look at our in-depth guides to getting a perfect score on SAT Math and ACT Math.

 

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Hannah Muniz
About the Author

Hannah received her MA in Japanese Studies from the University of Michigan and holds a bachelor's degree from the University of Southern California. From 2013 to 2015, she taught English in Japan via the JET Program. She is passionate about education, writing, and travel.



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