Heart of Algebra: Key SAT Math Concepts



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This weekend is another SAT test date on Saturday, December 7. Good luck to all students that are registered for the exam and be sure to get plenty of rest the night before your test!


To help our students feel prepared and ready to reach high scores on the SAT, today's article will provide key strategies on the SAT Math section so that you can get as close as possible to an SAT Math 800. More specifically, we will give you detailed tactics on the very first section you should expect to see on the SAT Math section - Heart of Algebra.


We will reference practice problems from the real College Board SAT practice test (Practice Test #1).


In order to achieve the results that you want, you should first understand what the SAT Math is composed of.


What Is Tested On The SAT Math Section?


For starters, the SAT Math sections are assigned to students on the third and fourth sections of the entire SAT test. You are given twenty-five minutes during the first half, with NO aid from a calculator. Afterward, it is the fifty-five minute SAT Math section in which you are allowed to use a calculator.


It is guaranteed that the SAT Math sections will begin with multiple-choice questions, followed by the standard four potential answer options that you can choose from.


Students will then be asked for self-response answers, commonly known as "grid-ins." Although the bulk of the SAT Math test is multiple-choice, twenty-two percent are grid-ins. Student-produced responses (grind-ins) require that you first solve the problem and enter your answers into the grid provided on the answer sheet.


In total there are 58 questions, with 45 being multiple-choice and 13 as grid-ins.


The SAT Math exam is separated into four main component areas:

  1. Heart of Algebra (19 questions)

  2. Problem Solving and Data Analysis (17 questions)

  3. Passport to Advanced Math (16 questions)

  4. Additional Topics in Math (6 questions)


Now that you understand the general gist of what is tested on SAT Math, we will concentrate on dissecting and understanding crucial strategies for the Heart of Algebra section in detail.


What Is Heart of Algebra?


The first segment of the SAT Math that students can anticipate is the Heart of Algebra. It is the largest category of the SAT Math (thirty-three percent to be exact), so it is highly recommended that you are well-prepared for it.


As there are nineteen questions built off of the Heart of Algebra category, you will see eight questions in section 3 of the SAT Math test (the non-calculator portion) and eleven questions in section 4 (the calculator portion)


The College Board varies the style type that they will ask you of Heart of Algebra questions, meaning that you will see both multiple-choice and grid-in questions. They will either provide equation(s) that require you to solve for the answer, or you will be given a real-world case problem where you will need to personally develop equation(s) to find the resolution.


We will discuss what Heart of Algebra comprises, what question types you should expect, and overall strategies that you can use to ace this section.


As the name suggests, this SAT Math section will focus on algebra content such as:

  • Linear equations

  • System of equations

  • Absolute value

  • Graphing linear equations

  • Linear inequalities

  • Systems of Inequalities


The article will cover each subject areas below along with what you should know in each.


Linear Equations


The simple linear equation equations will ask you to solve a provided linear equation. The more challenging linear equations will require that you develop the linear equation given the situation.


In the case that you are given an easy linear equation, the College Board will typically ask you to solve for the answer without placing the linear equation into a real-world context.


It may look something like this:


TIP: For solving for the simpler linear equation is by plugging all the answer choices for x and seeing which worked. This is not an advisable method since it will take you more time versus solving the equation; use at your discretion only if you are really struggling with the linear equation!


In the case that you are given a challenging linear equation, the College Board will usually ask test-takers to develop a linear equation given a real-world situational context.


It may look something like this:

TIP: In order to successfully complete this linear equation question, be sure to take each step one at a time! You should first start by solving the total number of messages sent by each individual, then join the two totals into one expression.


Systems of Equations


Now that you have completed the linear equation questions, systems of equations are slightly more tricky since you will have to do additional steps and/or develop a second equation.


The simple systems of equations questions will request that you solve for a variable providing you with two equations and two variables. The challenging system of equations questions will ask you to formulate a system of equations to depict the real-world scenario, then using the equation to solve for a variable.


In the case that you are given an easy system of equation, the College Board will provide the equations for you and ask that you solve for the variable x.


It may look something like this:


In the case that you are given a challenging system of equation, the College Board may provide the equations for you but ask that you solve for not only one, but two variables.


It may look something like this:


TIP: In either cases, a tactic that can work is simply plugging in the answer choices (if provided). Again, be sure to take your time as you work through each question. If you mess up on step, you will get the wrong answer.


Here's a bonus, a super-tricky system of equation problem:

This question provides a real-world context that you are expected to create two separate equations out of and solve for the variable.


TIP: Define your x and y variables for the number of salads and drinks and create your two equations. Be sure to properly write out the equation for the truck's revenue and then solve it.


Absolute Value


Normally, students can expect to see only one Absolute Value question on the SAT Math section. It is not intended to be challenging and is usually straight-forward.


However, this means that you must know the rules of absolute value in order to answer the question correctly.


Any value that is within an absolute value will be bracketed with the signs.


For example,

  • | - 7 |

  • | x - 7 |


The absolute value is a depiction of distance along a number line, both forward and backward.


This leads you to the first rule that you need to remember: whatever is in the absolute value sign will become positive since it stands for a distance along a number line (and it is not possible to have a negative distance).


With that in mind, another rule that you need to know for absolute value is that an absolute value equation will always have two answers.


For example, | x - 2 | = 4 will have two possible answers:

  • x - 2 = 4

and

  • x - 2 = -4


You should have two solutions, x = 6, -2.


It may look something like this:

TIP: When you stumble upon an absolute value question, be sure to always create two separate solutions (positive and negative).



Graphing Linear Equations


The College Board hopes to test students' ability to read a graph and translate it into the y = mx + b form.


For the students that need a refresher, y = mx + b is the slope-intercept equation of a line where m represents the slope and b represents the y-intercept.


Typically, you will find that the College Board asks imposes these questions with a picture of a line graph where you will need to first decipher what the slope and y-intercept values are in order to develop the equation of the line.


TIP: The best way of solving graphing linear equation problems is to have the slope-intercept form and slope equation memorized. If you understand what the variables stand for in each equation, you will surely ace the graphing linear equation problems on SAT Math.


Slope-intercept form:

y = mx + b


Slope equation:




Linear Inequalities and Systems of Linear Inequalities


This category of the SAT Math is considered the most challenging portion of the Heart of Algebra. As they are more challenging for student test-takers, these usually show up later or at the end of the section.


The College Board won't ask students to create and set up the inequalities nor will they present students with a real-world case using inequalities. But because these are the more tough Heart of Algebra questions - you need to take your time when solving these problems.


It may look something like this:


TIP: Remember the rules of inequalities. See below.


These things do not affect the direction of the inequality:

  • Add (or subtract) a number from both sides

  • Multiply (or divide) both sides by a positive number

  • Simplify a side

These things do change the direction of the inequality:

  • Multiply (or divide) both sides a by a negative number

  • Swapping left and right hand sides


7EDU's Essential Strategies For Heart of Algebra on SAT Math


We know that was a lot to read, so if you ever prefer a live online class - check out our event calendar to register for free webinars. These are led by professional instructors that have years of experience tutoring and teaching for the SAT, ACT, AP exams, and more.


This Friday (December 6), we have Aimee as our guest instructor. Register to receive the webinar link; and if you can't make it, register anyway to receive a recording!


Essential Strategy #1: Plug-In The Answer Options


For all the SAT Math multiple-choice problems, we highly advise that you always check your answer by plugging in the answer choices to the provided equation(s). This can sometimes be time-consuming so be strategic about employing this tactic. In some cases, this approach may be much simpler than trying to solve the problem.


Whether or not you are trying to use this strategy to find the answer, you should still consider plugging in your answer option to double-verify that your response is correct.


Essential Strategy #2: Remember Core Rules and Formulas


If you wish to do well and get an 800 on the SAT Math test, one of the very first things you need to establish is a solid foundation of the core math rules and formulas.


For the Heart of Algebra section, you should know the rules of absolute value, the formulas we mentioned in this article, and the rules of inequalities in order to answer the SAT algebra questions correctly.


Without a strong basis of the algebra formulas and rules, these math problems are impossible to solve. So brush up on your fundamentals and be sure that you know how to strategically apply them when necessary!


Essential Strategy #3: Take Your Time Through Each Problem


This is one of our favorite advice to give students that perplexes both parents and learners: remember to take your time when working through each SAT Math problem. Yes it is important to get through each question on the exam, but you also need to answer the questions correctly.


You can only solve for the right answers for the Heart of Algebra category if you are working through each step. Take your time to ensure that you aren't making a minor mistake that can result in an incorrect answer or maybe requiring you to start over and waste more time.

7EDU Impact Academy offers many college preparation services including one-on-ones, counseling, and specific courses.


Schedule your free 30-minute consultation

with one of our academic counselors at (408) 216-9109

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