Compass Math Pool 2

Question 1

Two sides of a triangle have sides 4 and 8. The length of the third side must be greater than_____ and less than____.

Accepted Answer

4, 12

Answer

The third side of the triangle must be greater than the smallest side (4) and less than the sum of the two sides (4+8=12)

Question 2

If 4x+1 = 64,  what is the value of  x?

Accepted Answer

2

Answer

Since 64=4x4x4 = 43, it follows that 4x+1 = 43, or x+1=3.  Therefore x=2.

Question 3

If the length of the side of the square is 84, what is the radius, r, of the circle in the figure?

Accepted Answer

42

Answer

If the side of the square is 84, then the diameter of the circle is also 84.  The diameter of a circle is twice the radius, therefore the radius is 84/2 or 42.

Question 4

Eddie is 7 years older than Brian. If Brian is x years old, then how old was Eddie 11 years ago?

Accepted Answer

x-4

Answer

We can model this by getting Eddie’s age now and then figuring out how old he was 11 years ago. Right now, he is x+7 . Eleven years ago, Eddie was x + 7 -11 = x - 4 years old. This is answer B.
a. The correct calculation should be x+ 7 (to get Eddie’s age now) - 11 , which is x - 4 .
b. Correct
c. This is an incorrect calculation of Eddie’s present age.
d. This response does not relate their ages properly.
e. This also does not express their age relationship properly.

Question 5

In the figure, AD || BC. mAC = 13. mBC = 5. If mBD = 15, what is mAD?

Accepted Answer

9

Answer

Correct answer: B. To find AD , we first need to know AB. Since AB belongs to both triangles, we’ll use what we know about triangle ABC to find AB, using the Pythagorean Theorem. AB is a short side, so we’ll call it a. The Pythagorean Theorem is a2 + b2 = c2 (a and b are the shorter sides, c is the hypotenuse) Plugging in gives  a2 + 52 = 132. Squaring gives a2 + 25 = 169. Subtracting 25  on each side gives a2 = 144 . Taking the square roots gives a=12 . This means AB = 12. To find AD, we’ll use the Pythagorean Theorem again, with a representing  AD this time. Plugging in gives a2 + 122 = 152. Squaring gives  a2 + 144 = 225.Subtracting  144 from each side gives a2 = 81. Taking the square root gives a = 9, which is length of AD.

COMPASS Practice Test

COMPASS Practice Test

Compass Math Pool 2