Category Archives: ACT

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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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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ACT Math Strategy: Picking Numbers

For some of the more difficult, abstract questions on the ACT Math test, the “real” math that the test takers have in mind can be quite tricky. But for some of these problems, there might be a way to make the rather abstract problem more concrete, and thus easier. That leads us to an important ACT Math strategy: Picking Numbers.

Consider the following difficult problem which has previously appeared on the ACT.

For every positive two-digit number, x, with tens digit t and units digit u, let y be the two-digit number formed by reversing the digits of x. Which of the following is equivalent to x – y?

A.  9(t – u)
B.  9(u – t)
C.  9tu
D.  9ut
E.  0

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ACT Math: The Triangle Inequality

We all know that a triangle is made up of three sides. But do the lengths of those sides matter? Or can any three side lengths make up a triangle?

You might remember your Geometry teacher talking about the Triangle Inequality Theorem. It tells us that some triangles just aren’t possible. Imagine if I gave you three sticks with lengths of 10 inches, 2 inches and 5 inches and I told you to make a triangle. Try as hard as you’d like; you won’t be able to do it. You’ll end up instead with something that looks like this:

Triangle Inequality

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