Please Help me solve these SAT Maths II questions

Test Preparation SAT Subject Test Preparation
1

<p>I found these on SparkNotes.</p>

<ol>
<li> S and T are the centers of their respective circles. The two circles are mutually tangent at point U. If segment RS = d, what is the radius of the smaller circle in terms of d and ?
(A) cos
(B) d sin
(C) d(cos – sin )
(D) d(sin – cos )
(E) d(sin + cos )</li>
</ol>

<p>This question seems soo vague. Like, I don't know where is R. It is just so difficult to imagine the figure. Can this type of question appear on the real SAT Math II? I heard SparkNotes is very accurate so I'm worried.</p>

<p>Also, can you please explain how to solve this?</p>

<ol>
<li> In the triangle pictured below, what is Angle "A" ?
<a href="http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0055/question11.1.gif"&gt;http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0055/question11.1.gif&lt;/a&gt;&lt;/li>
</ol>

<p>(A) 25.7º
(B) 31.2º
(C) 37.7º
(D) 39.5º
(E) 68.3º</p>

<p>I got 41.13 when I tried to solve.</p>

<p>Excerpt from SparkNote's explaination of the above question:
5. E<br>
Since you have the measures of two sides and the angle between them, you can start with the law of cosines to find c. Plug the given values into the law of cosines formula: *c2 = 52 + 72 + 2(5)(7) cos 110º. *</p>

<p>The formula is c^2=a^2+b^2-2ab cos(C)
So, I solved it like this:
c^2= 49+25-70 cos(110)</p>

<p>How come they got the bolded formula? How did they get there?</p>

<p>Another one:</p>

<p>Go here: <a href="http://www.sparknotes.com/testprep/books/sat2/math2c/chapter9section11.rhtml"&gt;http://www.sparknotes.com/testprep/books/sat2/math2c/chapter9section11.rhtml&lt;/a>
Look at question no. 8.
When solved, I got 1/4 as an answer. But it's not a choice.
Here is what the explaination says:
8. A<br>
Without knowing the double-angle identity for sine, you could have found the arcsine of 1 /2, divided that angle by 2, found the sine and cosine of that angle, and then squared their product, which gives a value of 1/16.</p>

<p>So, I got 1/4, but WHY square it? The question never asked the "square" of the product.</p>

2

<ol>
<li><p>Yeah - I don’t think this one is solvable without more info. The trig functions (sin/cos) are missing the argument; all we see is sin and cos (as opposed to sine of an angle).
Edit: theta. However there is no diagram and we have no idea what theta is or where R is.</p></li>
<li><p>The bolded formula is exactly the law of cosines. Note: Use ^ for exponents, i.e. c^2 = 5^2 + 7^2 - 2<em>5</em>7 cos 110º.</p></li>
<li><p>This is a badly typed question. I solved it interpreting it as sin 2x and cos 2x, and there are two possible answers: ±sqrt(3)/4. Then I read it as sin^2 x and cos^2 x, and the answer is 1/4 (not 1/16). Then after looking at the solution, I believe the question is supposed to be interpreted as:</p></li>
<li><p>If sin 2x = 1/2, what is (sin^2 x)(cos^2 x)?</p></li>
</ol>

<p>Only THEN the answer is 1/16. </p>

3

<p>Moral is: avoid using these questions as they are of poor quality. I’m sure I or many others on CC are capable of putting out a better quality test than the stuff out there.</p>

4

<p>@MITer94‌ Thanks for helping!</p>

<p>You said the bolded formula is the law of cosdines. But SparkNotes ADDED 2<em>5</em>7 when in reality it should be subtracted (look at the bolded formula once again). Am I misinterpreting something?</p>

5

<p>@ssgupta Ah nvm. I thought it might’ve been a typo or something since you used - underneath, how silly of me. The + should be replaced with a -. </p>

<p>However I looked a bit further in their solution; the value of c they get (approx. 7.08) is the solution to the INCORRECT equation c^2 = 5^2 + 7^2 + 2<em>5</em>7 cos 110. The correct value of c is roughly 9.90. That means the value of angle A is also incorrect. So they didn’t just typo at one spot; their solution is incorrect.</p>

<p>I got angle A ≈ 44.6 deg (let me know if this is incorrect). </p>