Top 5 SAT Algebra Questions

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Roughly 90% of the math section of the SAT is comprised of questions spanning a few categories: Heart of Algebra, Passport to Advanced Math, and Problem Solving and Data Analysis.

While no category is more important than another, in order to do well on the SAT Math section, you are going to need to prepare for the Heart of Algebra questions that will appear on the test.

Here are five of the top SAT Heart of Algebra questions, taken from the College Board, that you should study to prepare for your test:

1. Creating linear expressions

You will see some math questions in the Heart of Algebra category that ask you to create a linear expression that can be applied to a real-world situation.

Here is an example of this type of algebra question:

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional one-time untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights?

  1. (99.5 + 0.08x)+5
  2. 1.08 (99.95x)+5
  3. 1.08 (99.95x+5)
  4. 1.08(99.5+5)x

In order to find the right answer, which is “B” by the way, you will need to come up with an expression that accounts for the room rate, the fixed fee, and the room tax.

2. Creating inequalities

The Heart of Algebra questions on the SAT will also include questions that ask you to create and solve inequalities.

For example:

A company’s manager estimated that the cost C, in dollars, of producing n items is C=yn +350. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?

  1. n<70
  2. n<84
  3. n>70
  4. n>84

You can solve this question by creating the inequality 12n> 7n+350 and solving this inequality to get “C” n>70.

3. Creating functions

You will likely encounter several problems on the SAT Math section that require you to create functions.

Here is a sample question:

The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?

  1. f(t) = 17 – (21/50t)
  2. f(t) = 17- (50t/21)
  3. f(t) = ((17-21t)/50)
  4. f(t)= ((17-50t)/21)

In order to find that the correct answer is “B,” you will need to find the function that adequately represents time and gas mileage.

4. Analyzing graphs

Some SAT Algebra questions will require you to be able to graph a particular equation.

For example:

If k is a positive constant different from 1, which of the following could be the graph of y minus x equals k left parenthesis x space plus space y right parenthesis in the xy-plane?

The graph that accurately depicts this equation looks like the image below.

To reach this conclusion, you have to manipulate the equation and solve for y.

5. Calculating slope

The Heart of Algebra category of the SAT Math section has questions that will require you to use the equation for slope, y=mx+b, in order to find the slope of an equation and apply it to a real-world situation.

For example:

The mean number of students per classroom, y, at Central High School can be estimated using the equation y=0.8636x + 27.227 where x represents the number of years since 2004 and x≤10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

  1. The estimated mean number of students per classroom in 2004
  2. The estimated mean number of students per classroom in 2014
  3. The estimated yearly decrease in the mean number of students per classroom
  4. The estimated yearly increase in the mean number of students per classroom

The answer in this case would be “D.”

Using Prep Expert to prepare for Heart of Algebra questions

In addition to reviewing these five types of algebra questions, the best way for you to prepare for Heart of Algebra questions on the SAT is to take an SAT prep course.

Prep Expert offers high-quality, flexible SAT prep courses that will help you learn how to solve the Heart of Algebra questions you will see on the test. Learn more about Prep Expert and sign up for a Prep Expert SAT prep course when you visit our website.

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