SAT Math: Algebraic Operations

Now more than ever, with the focus of the New SAT Math test being on algebra and functions, you need to make sure that you are an ace at algebraic operations. This includes things like simplifying algebraic expressions, solving linear and quadratic equations, and solving for a variable in a formula.

At the bottom of the page, we have links to 10 SAT practice problems that involve these topics, along with their solutions.

But first, a few friendly reminders (things you’ll probably remember your algebra teacher saying many times over!):

  • You can combine terms that have the same variable raised to the same power. For example, 3x² – 8x + 4x² + 5x = 7x² – 3x. Those are called like terms.
  • You need to be very good at translating between words and algebra. The SAT will give you a word problem that you’ll need to write an equation for and then solve in order to find some unknown quantity.
  • When solving an equation use opposite operations to solve for the variable. Need to get rid of a +3 in the equation? Then you should subtract 3. The variable is being multiplied by 2? To undo that, divide by 2.
  • Whatever you do to one side of the equation when solving, you must do to the other side as well.
  • Be very, very careful with signs. The most common error I run into when reviewing a student’s work is a negative sign that gets “lost” somewhere along the way. And can we all agree that there’s no such thing as a “small” sign mistake?

OK then, here are the problems. Give them a try!

Additional Practice — Algebraic Operations
Solutions — Algebraic Operations

If you have questions about these problems or anything at all to do with the SAT, send us an email at info@cardinalec.com .

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