Some Math Question Help.

Test Preparation
1

<li>For how many different positive integer values of k does (kx - 6)^2 = 0 have integer solutions?</li>
</ol>

<p>a. 0
b. 1
c. 2
d. 4
e. 6</p>

<li>The first two numbers of a sequence are 1 and 3, respectively. The third number is 4, and, in general, every number after the second is the sum of the two numbers immediately preceding it. How many of the first 1,000 numbers in this sequence are odd?</li>
</ol>

<p>a. 333
b. 500
c. 665
d. 666
e. 667</p>

<li>Circle C has radius squareroot(2). Squares with sides of length 1 are to be drawn so that, for each square, one vertex is on circle C and the rest of the square is inside circle C. What is the greatest number of such squares that can be drawn if the squares do not have overlapping areas?</li>
</ol>

<p>a. 0
b. 1
c. 2
d. 3
e. 4</p>

<p>I hate this. hahaha. I hate how I’m in Calc BC as a Junior, but can’t figure out some simple algebra problems. Please explain how you got the answers. </p>

<p>Thanks.</p>

2

<p>1.d - 1,2,3,6 factors of 6
2.e - it repeats in a pattern of odd odd even so you have 999 and the last term is odd
3.e - sqrt(2) is the length of the diagonal of the square. in order to maximize the the number of squares, place them in diagonals and you find you can fit 4 inside</p>

3

<p>x=2,3,6,1 so its four because its the factors of six</p>

<p>2)
odd, odd, even, odd,odd, even........odd 1000th is an odd because 999th is an even
so (2/3)(999)=666+1=667</p>

<p>3) a square is inscribed into a circle with side 2, so four squares of side 1 can fit in a square with side 2.</p>