What is Heart of Algebra?
The new SAT has named it’s math topics a little strangely. For example, one of the math topics is called Heart of Algebra. You might wonder what that means and what it covers exactly. Well, after looking at the criteria outlined by CollegeBoard, it includes things such as Linear Equations and everything that is associated with them – which is basically what Algebra is all about. If you remember from Grades 9 and 10, they introduced Algebra to you by having you solve for variables. That is essentially what Heart of Algebra is – representing relationships between variables and solving for those variables. For the SAT, Heart of algebra focuses on mastery of the following topics:
– Linear Equations (Single and Systems)
– Linear Functions
– Linear Equalities
The point of this category is to see if students can demonstrate both procedural skill and a thorough understanding of the concepts. This is accomplished by asking the student to solve straightforward questions or challenging questions. The challenging questions ask the student to interpret relationships between graphical and algebraic representations.
Let’s take a further look at what this means.
When you use algebra in everyday life, you have to come up with algebraic expressions. For example:
Example 1 (Linear Equation):
If the price of 1lb of apples increases every year by 25 cents, how much will they be 10 years from now (if they are $2.25/lb this year). This would involve you to define certain variables, such as n for the number of years and r for the rate.
Current Price + (price increase x number of years) = price in 10 years for 1lb of apples
Current Price = $2.25
Price Increase = 0.25
Number of Years = 10
Therefore, 2.25 + 0.25(10) = $4.75 lb/apples
Example 2 (System of Linear Equations):
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let’s define x to be the T/F questions; y to be the MC questions
There are two relationships:
x + y = 20 The total amount of questions has to be 20.
3x + 11y = 100 The total amount of points has to be 100.
Example 3 (Linear Inequality):
Rakim has $1500 in his bank account at the beginning of the year. He wants to have at least $200 left by the end of the year. He withdraws $50 each week for his expenses. How many weeks can Rakim withdraw money from his account?
Let w be the number of weeks
We know that Rakim starts with 1500 and each week this amount decreases by 20. We also know that we can keep withdrawing 20 every week until the amount in the bank reaches below 200. So, our algebraic expression is as follows:
1500 – 20w ≥ 200
If we solve for w, we get: w ≤ 26 and we can plug this back into the original equation to see that we are correct.
From these examples, you can see that many Heart of Algebra questions will ask the student to solve using the following steps:
1.) Define one or more variables
2.) Determine the algebraic relationship between the variables
3.) Solve for the required variable
4.) Interpret the results to answer what the question is specifically asking
When practicing for the Heart of Algebra section for the SAT, make sure to practice many questions for the same concept. This is because the same concepts will be tested in several different ways. Practicing a variety of questions, with different contexts, is a good way to ensure that you’ll be ready for anything the new SAT throws at you. Heart of Algebra also covers topics such as Absolute Value and Coordinate Planes, which we will cover in the next blog entry, so stay tuned.
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