Tag Archives: ACT

ACT Math: A Challenging Circle Problem

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?

Challenge 4-15A

A.  13
B.  15
C.  17
D.  18
E.  20

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A Challenging Algebra & Geometry 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 ?

Challenge 4-10A

A.  24
B.  28
C.  30
D.  32
E.  36

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ACT Math: Finding an Angle Measure in a Right Triangle

When I look at which posts people are viewing on this blog, inevitably one of the most popular posts is the one about Right Triangle Trigonometry (SOH-CAH-TOA) and its follow-up post with more practice problems. Today, we’ll expand on that topic by looking at how you can determine the measure of an angle in a right triangle.

Consider this problem:

In the right triangle ABC below, what is the measure, to the nearest degree, of Angle A?

Trig Angle A

A.  38
B.  44
C.  46
D.  49
E.  53

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April 2016 College & Testing Newsletter (Vol. 1 Issue 1)

The April 2016 Cardinal Educational Consulting College & Testing Newsletter is out! In this issue:

  • SAT & ACT registration deadlines
  • ACT Math tips and strategies
  • Wait list advice from the admissions staff at Georgia Tech
  • Admissions statistics from the Ivy League and other elite universities
  • A visit to Connecticut College

To see the newsletter click here.

To get the newsletter delivered straight to your inbox, just type your email address into the box over in the right sidebar.

ACT Math: A Challenging Shaded Region Problem

Our latest book, 200 Challenging ACT Math Problems, is in the proofreading stage and should be ready for publication in a couple of weeks. In the meantime, here’s a taste of the type of problem you’ll find in the book. See if you can figure out the answer to this challenging shaded region problem (Scroll down for the solution).

The large square in the diagram below has an area of 64 square units. A circle is inscribed in the large square and then a smaller square is inscribed in the circle. What is the total area, rounded to the nearest tenth of a square unit, of the shaded regions?

Shaded Challenge A

A.  16.0
B.  17.1
C.  18.3
D.  32.0
E.  34.3

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