A square and a regular hexagon have the same perimeter. If the area of the square is 2.25, what is the area of the hexagon?
A) 2.250
B) 2.598
C) 2.838
D) 3.464
E) 3.375
In figure 2, AB=BC. If the area of triangle ABE is x, what is the area of triangle ACD?
A) x sqrt2
B) x sqrt3
C) 2x
D) 3x
E) 4x
In the figure above, the length of each edge of the cube is 2. If P, Q, R, and S are the centres of faces ABFE, BCGF, DCGH, and ADHE, respectively, what is the perimeter of quadrilateral PQRS?
A) 4
B) 4 sqrt2
C) 6
D) 4 sqrt 3
E) 8
What is the area of a triangle whose sides are 5,5, and 6?
A) 6
B) 12
C) 16
D) 18
E) 24
A large cube with edge of length 3 units is built from 6 small blue unit cubes and 21 small white unit cubes. What is the greatest possible fraction of the surface area of the large cube that could be blue?
A) 1/9
B) 2/9
C) 1/3
D) 4/9
E) 2/3
Even though very little information has been released to date—not even a full practice test yet!—I’m hard at work trying to get a head start on the next iteration of the Math Guide for the new SAT (coming about a year from now—March 2016). When I write questions, I have a very hard time keeping (more…)
College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have (more…)
College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have (more…)
College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have (more…)
College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have (more…)
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How’s everyone else doing on this quiz?
All this talk about the new SAT is interesting and all, but we’ve still got two years to live with the old one, so let’s get back to our regularly scheduled PWNing. Here’s a minorly important circle fact that I find a lot of students don’t know: when a wheel is rolling—without slipping—it makes travels (more…)
I was just noodling around with Geometer’s Sketchpad today, you know—like a totally normal person, and I made this figure, which I thought would make an awesome challenge question. Wasn’t even planning to post a challenge question, and then BAM! Inspiration. In the figure above, equilateral triangle DEF is partially obscured by a semicircle with (more…)
This morning I was lying in bed waiting for my alarm to go off, and a question just popped into my head. This happens to me fairly often, but usually I’m too lazy to write it down, then I forget it, then I spend the rest of the day trying to convince myself that it (more…)