<p>I've started studying for the PSAT, and I've been SAT practice tests. I have a few math questions I'm not sure how to go about solving, so hopefully someone will help me out. Also, what is the best way to look up how to solve certain types of problems so that I don't have to post somewhere when I get stuck?</p>
<ol>
<li><p>If x = 5^y and y = z + 1, what is (x/5) in terms of z?
A. z
B. z + 1
C. 5^z
D. 5^z + 1
E. 5^(z+1)</p></li>
<li><p>The sum of the positive odd integers less than 100 is subtracted from the sum of positive even integers less than or equal to 100. What is the resulting difference?</p></li>
<li><p>f(x) = kg(x) + 2
The function f above is defined in terms of another function g for all values of x, where k is a constant. If t is a number for which f(t) = 30 and g(t) = 8, what does k equal?</p></li>
<li><p>A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the large cube?</p></li>
</ol>
<p>x = 5^y, y = z+1 plug in y
x = 5 ^(z+1) = 5^z * 5^1
x/5 = 5^z</p>
<ol>
<li>The sum of the positive odd integers less than 100 is subtracted from the sum of positive even integers less than or equal to 100. What is the resulting difference?</li>
</ol>
<p>these problems look very difficult, but when you write out the numbers, and you’ll find a pattern that simplifies the entire equation, try it. Let me know if you’re still stuck.</p>
<ol>
<li>f(x) = kg(x) + 2
The function f above is defined in terms of another function g for all values of x, where k is a constant. If t is a number for which f(t) = 30 and g(t) = 8, what does k equal?</li>
</ol>
<p>dont get confused by the variable t here, it’s just an input to the function instead of x. f(t)= 8 = kg(t)+2 , and g(t)=8, solve, k = 28/8 or 13/4.</p>
<ol>
<li>A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the large cube? </li>
</ol>
<p>The outer layer is painted, so the inside cube(without red paints) are made up of 27 smaller cubes, so its a 3x3x3. My intuition or what i pictured in my mind tells me the entire thing is 4x4x4 since there’s 1 red cube on each outer layer. But its always safer to draw out the actual picture, lets start with the rubiks cube, its 3x3x3, and there’s 1 or 1x1x1 in the middle that’s not colored. Now put draw another outer layer around the rubiks cube, it turns out to be 5x5x5.
So 125 smaller cubes</p>