Help: Some Really Hard Questions for the SAT Math II!

Test Preparation SAT Subject Test Preparation
1

<p>These are some questions I didn't understand from my practice test. I know it is a lot but I was hoping some could help me explain some of them to me. I think this is also good practice for anyone else who might be taking the Math II subject test soon.</p>

<ol>
<li><p>The set of points (x,y,z) such that x² + y² + z² = 1 is
A) empty
B) a point
C) a sphere
D) a circle
E) a plane</p></li>
<li><p>What is the sum of the infinite geometric series
(1/4 + 1/8 + 1/16 + 1/32 + ...)?
A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2</p></li>
<li><p>The only prime factors of a number n are 2,5,7, and 17. Which of the following could NOT be a factor of n?
A) 10
B) 20
C) 25
D) 30
E) 34</p></li>
</ol>

<p>38) If f(x) = 5√(2x), what is the value of f-1 (10)? (the -1 is above the f)
A) 0.04
B) 0.89
C) 2
D) 2.23
E) 22.36</p>

<p>39) The Fibonacci sequence can be defined recursively as
a1 = 1
a2 = 1
an = an-1 + an-2 for n>3.</p>

<p>What is the 10th term of this sequence?
A) 21
B) 34
C) 55
D) 89
E) 144</p>

<p>42) The set of all real numbers x such that √(x²) = -x consists of
A) zero only
B) nonpositive real numbers only
C) positive real numbers only
D) all real numbers
E) no real numbers</p>

<p>45) If log a 3 = x and log a 5 = y, then log a 45 =
A) 2x+y
B) x² + y
C) x²y
D) x + y
E) 9x + y</p>

2

<ol>
<li><p>C) Sphere.</p></li>
<li><p>This is equal to (1/2)(1/2 + 1/4 + 1/8 + …). The sum 1/2 + 1/4 + 1/8 + … is equal to 1, so the answer is A) 1/2.</p></li>
<li><p>If 30 is a factor of n, then 3 is a factor of n. This cannot be true, D).</p></li>
<li><p>Solve f(k) = 10:</p></li>
</ol>

<p>5sqrt(2x) = 10 → x = 2, C).</p>

<ol>
<li>Might help to write the terms out (if you haven’t memorized the sequence):
1,1,2,3,5,8,13,21,34,55</li>
</ol>

<p>The tenth term is 55, C).</p>

<ol>
<li>It helps to know that the absolute value of x is sometimes defined as</li>
</ol>

<p>|x| = sqrt(x^2).</p>

<p>Here, you’re essentially solving |x| = -x, in which the solution is the set of non-positive real numbers, B).</p>

<ol>
<li>Apply logarithm identities:
log 45 = log 9 + log 5
= 2 log 3 + log 5
= 2x + y, A).</li>
</ol>

3

<p>^Thanks, I understand them all now. A lot of it was because I didn’t know some of the rules needed for the question^</p>

4

<p>Great! Yeah, especially 12, 18, 45. For 12 it just helps to know that (alternatively, x^2 + y^2 + z^2 = radius^2 = 1, sphere). For 18 it helps to know how to sum a geometric series, and for 45 you pretty much need properties of logarithms (you could crank everything out on a calculator but that’d take too much time).</p>