Here’s another challenging problem for you, this one involving circles. You’ll need to use concepts you’ve learned in both Algebra and Geometry to get this one right. Good luck!
In the circle below with center at Point O, the length of chord AB is 30 units. The radius in the diagram is perpendicular to the chord AB, which cuts the radius into two pieces with lengths of x units and x + 1 units as labeled in the diagram. What is the length, in units, of the radius of the circle?
Continue reading ACT Math: A Challenging Circle Problem
Are you up for another challenging ACT Math problem? This one will require you to use concepts you’ve learned in both Algebra and Geometry.
The equation of the parabola in the figure below is f(x) = -12/25 x2 + 12. Point A is a vertex of the triangle and the y-intercept of the parabola. Points B and C are also vertices of the triangle and the x-intercepts of the parabola. What is the perimeter of triangle ABC ?
Continue reading A Challenging Algebra & Geometry Problem
After successfully launching the Kindle version of the “SAT Math Challenge Problem Workbook” three weeks ago, we got to work on the print version of the book.
You can now purchase the paperback version via Amazon. It has the same content as the Kindle version but with the added benefit that you can write in it, marking up the diagrams as you work on the Geometry problems (and we all know you should definitely be marking up the diagrams on the geometry problems!), writing and solving your own equations right there next to the problems, and making notes as you go along.
To preview the book or make a purchase, simply click on the book cover to the left
One of our students, a very highly-motivated student who is on his way to Cornell University in the fall, spent a lot of time preparing for the SAT. He asked early on for some additional problems “like those you’d see at the end of the Math sections.” Each week, I had to make him a new set of five problems. I was always proud if I made a problem that actually stumped him — it didn’t happen often!
Those problems — and more — have been collected into a new book, “SAT Math Challenge Problem Workbook,” available now for Kindle and downloadable to iPads and tablets with the free Kindle Reading app. The price ($4.99) has been kept low so that as many students as possible can have access to this material.
To preview the book or make a purchase, just click on the book cover above. If you need the Kindle Reading app, you can learn more here.
It’s been a while since we’ve updated our series of SAT Math Challenge Problems (you can see all of the problems here). Here are five more problems designed to resemble those you’d find at the end of an SAT Math section. Give your brain a workout and let us know what you think. The solutions appear at the bottom of this post.
1) Let the functions f and g be defined completely by the table below. If f(a) < a for some number a, what is the value of g(a)?
Continue reading SAT Math: Challenging Problems #10