# Compass Math Pool 2

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

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)

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

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

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

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.

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

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.

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

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.

#### If g(x) = 4x - 4x, what is the value of g(3/2)?

Substituting 3/2 into the function, we get 4(3/2) - 4(3/2) = 6 - 4(1/2)3 = 6 - 23 = 6 - 8 = -2. This is response A.

#### If q and r are positive odd integers, which of the following is greatest?

Since r and q are positive odd integers, and a negative integer raised to a positive odd integer power is negative, two of the expressions are negative and three are positive. The greatest of the five choices must be one of the three positive expressions, which are qr, (-q)2r, (-2q)2r . Since qr<q2r<(2q)2r it follows by substitution that qr<(-q)2r<(-2q)2r. Thus, the greatest of the five expressions is (-2q)2r.

#### The line in the xy-coordinate system is the graph of the equation y=mx+b. Which of the following must be true?

The slope and y -intercept of the graph of y=mx+b are m and b respectively. From the graph, it can be seen that the line has a negative slope and a positive y-intercept. Therefore, m0 so mb<0.

#### If f(x) = x + 9, which of the following is a solution of f(5a) + 3 = f(3a) + 11? In other words, what might be the value of ‘a’?

Substituting both 5a and 3a into f(x) and then using the second equation, we get 5a + 9 + 3 = 3a + 9 + 11 . This simplifies to 5a + 12 = 3a + 20, and then we get 2a = 8 . Finally, we get a = 4. This is response E.

#### Jamal ran a distance of 360 feet. Lonnie ran a distance of 30 yards. What is the ratio of the distance Jamal ran to the distance Lonnie ran?

Choice (A) is correct. Jamal ran 360 feet, which is equal to 120 yards. Thus, the ratio of Jamal's distance to Lonnie's distance is 120 yards to 30 yards, which is the same as 4:1