Math Questions

Test Preparation SAT Preparation
1

<ol>
<li>If abs(x)<y, which=“” of=“” the=“” following=“” must=“” be=“” true?=“” i.=“” y=“”>x
II. x>0
III. y>0</y,></li>
</ol>

<p>A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III</p>

<ol>
<li>The figure above (not shown) depicts a regular pentagon. If the pentagon is rotated clockwise about its center by x degrees, it will appear exactly the same. Which of the following could be the value of x?</li>
</ol>

<p>A. 136
B. 144
C. 150
D. 172
E. 180</p>

<ol>
<li>A deck of 52 cards contains 4 suits. Jonah picks two cards without replacement from the deck of cards, which goes from 1 to 13. What is the probability the sum of his cards will be 3?</li>
</ol>

<p>A. 2/13
B. 2/156
C. 2/169
D. 4/663
E. 8/663</p>

<ol>
<li>Christine walked 20 yards in a straight line. She then turned and walked 7 yards in another straight line. During the last 7 yards, she neither continued in her original direction nor retraced her steps. What is a possible distance, in yards, from Christie’s starting point to her ending point? (this one was a grid-in)</li>
</ol>

<p>5.Ginny must choose a password for her school account. She decides to use a 5 character password consisting of an arrangement of her 3 initials, GJN, followed by an arrangement of the digits in her age, 17. How many passwords are possible? (also free-response)</p>

<ol>
<li>Three circle lie in the xy-coordinate plane as above (basically, there’s a small circle in Quadrant II, a huge circle in Quadrant III, and a medium-size circle in Quadrant IV). if there is no line tangent to all 3 circles, how many different lines can be drawn so that each line is tangent to exactly two different circles?</li>
</ol>

2

<ol>
<li><p>I is true (casework based on whether x > 0, x < 0, or x = 0).
II is not always true (x could be negative).
III is true, because 0 <= |x| < y. Answer is D) I and III.</p></li>
<li><p>360/5 = 72, so rotating the pentagon by any multiple of 72 degrees yields the same shape, by symmetry. B) 144 is the only multiple of 72 listed.</p></li>
<li><p>You need a 1 and a 2. There are 4<em>4</em>2 = 32 ways to choose a 1 and a 2, and 5251 = 2652 ways to choose two cards without replacement (both assume that order matters, that’s why I multiplied by 2 to get 32). The probability is 32/2652 = E) 8/663.</p></li>
<li><p>By the triangle inequality, any distance strictly between 13 and 27 works (but don’t answer 13 or 27).</p></li>
<li><p>There are 3! = 6 ways to arrange “GJN” and 2! = 2 ways to arrange “17.” 62 = 12.</p></li>
<li><p>For any two circles, there are 4 lines tangent to them (try this yourself). 3C2 = 3, so the number of lines is 4*3 = 12.</p></li>
</ol>