SAT Math Question Help

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1

<p>I ran into these 2 questions and I looked at the explanations provided in the book but I still don’t quite understand them.</p>

<ol>
<li>If f(x) = x^2 + 2, which of the following could be a value of f(x)?
A: -2
B: -1
C: 0
D: 1
E: 2</li>
</ol>

<p>Answer: E</p>

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<ol>
<li>In rectangle PQRS above, what is a + b in terms of x?
A: 90 + x
B: 90 - x
C: 180 + x
D: 270 - x
E: 360 - x</li>
</ol>

<p>Answer: A</p>

<p>So if anyone can explain how to arrive to the answer step by step, I would really appreciate it.</p>

2

<ol>
<li>f(x) can’t be negative because squaring eliminates that possibility. Since it can’t be negative and the equation specifies an addition of 2, it can’t be either 0 or 1. Thus, the minimum value for this equation is 2 - when x=0. When x=1 or -1, f(x) would be 3 and you get a parabola opening upwards with its vertex at (0,2).</li>
</ol>

3

<ol>
<li><p>x^2 ≥ 0, so x^2 + 2 ≥ 2 (for real x). The only possible answer is E) 2.</p></li>
<li><p>Angle QPT = 90-a, angle SPU = 90-b (where T and U are the points between {Q,R} and {R,S}).</p></li>
</ol>

<p>Therefore,</p>

<p>(90-a) + (90-b) + x = 90</p>

<p>180 + x = 90 + a + b</p>

<p>a + b = 90 + x, choice A.</p>