Tag Archives: complete the square

SAT Math: Completing the Square Problems

Earlier this week, we wrote a post on Completing the Square. Understanding this concept will help you with problems involving both circles and parabolas. If you’ve read through that post and you’re ready to test your skills, you’ll find five problems below that you can try. The solutions can also be found in the links below.

Complete the Square Problems
Complete the Square Solutions

If you have any questions about these problems, completing the square in general, or anything else to do with the SAT, send us an email at info@cardinalec.com .

SAT Math: Completing the Square

When the new SAT came out in March 2016, it became clear that the test makers were looking to test some skills that hadn’t appeared on the previous version of the test. One of those skills is “completing the square,” which can be helpful when you are working on problems involving circles and parabolas.

So what is completing the square? Well, a perfect square trinomial x² + bx + c is one that can be rewritten in the form (x + k)², where k is some integer. For instance x² + 10x + 25 is a perfect square trinomial because is can be factored into (x + 5)(x + 5) = (x + 5)².

When you are asked to complete the square, you need to find that value of c (there is always only one possible value) that will make the trinomial a perfect square. For instance, suppose you were asked this question:

What number will complete the square for x²  + 6x + ___ ?

Continue reading SAT Math: Completing the Square