SAT Math: A Challenging Quadratic Function Problem

As you prepare for the SAT, you’ll definitely want to review quadratic functions. You’ll need to know how to solve quadratic equations, as well as understand the properties of the graphs of these functions.

Here’s a challenging problem involving a quadratic function. Give it a try and then scroll down for the solution.

f(x) = a(x + b)(x – 8)

The equation above represents a quadratic function where a and b are constants. If the function is graphed in the xy-plane, its vertex is at the point (2, -54). What is the value of a + b?

(A)  4
(B)  5.5
(C)  6
(D)  7.5

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ACT Math: A Challenging Polygons Problem

We’ve listed this problem under “ACT Math,” but you could just as easily see a problem like this on the SAT Math test as well. Give the problem a try, and then scroll down for the solution.

A regular polygon is covered by a piece of paper so that only one of its interior angles is visible. You are able to determine that the interior angle is four times as large as the exterior angle. How many sides does the polygon have?


A.  8

B.  9
C.  10
D.  11
E.  12

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SAT Math: Focus on Lines & Systems of Equations

We’ve just published another new book, SAT Math: Focus on Lines & Systems of Equations, that can be downloaded to read on your Kindle, iPad, or tablet.

This book is the second in a series that addresses the topics that appear most frequently in the Math section of the New SAT. You’ll review the properties of lines, including their graphs, and look at the different methods for solving systems of linear equations. Then you’ll apply what you know as you solve 25 problems — some done without your calculator and some with, just as it is on test day. Each problem comes with a full explanation of how to arrive at the correct answer.

We’d like to help as many students as possible achieve success on the SAT, so we’ve made the price of each of the volumes in this series just $0.99.

The book can be purchased on Amazon by clicking on the image to the left or going here.

 

SAT Math: Focus on Quadratics & Parabolas

We’ve just published a new book, SAT Math: Focus on Quadratics & Parabolas, that can be downloaded to read on your Kindle, iPad, or tablet.

This book will be the first in a series that addresses the topics that appear most frequently in the Math section of the New SAT. You’ll get a chance to review the most important concepts of quadratic equations and the graphs of parabolas. Then you’ll apply what you know to 25 problems — some done without your calculator and some with, just as it is on test day. Each problem comes with a full explanation of how to arrive at the correct answer.

We’d like to help as many students as possible achieve success on the SAT, so we’ve made the price of this volume just $0.99.

The book can be purchased on Amazon by clicking on the image to the left or going here.

 

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 .