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29. The correct answer is (B). First find the value of k
2
in terms of i:
k
2
= (2 + i)
2
= (2 + i)(2 + i) = 4 + 2i + 2i + i
2
= 4 + 4i + i
2
Since i
2
= –1:
4 + 4i + i
2
= 4 + 4i + (–1) = 3 + 4i
30. The correct answer is (A). One way to attack this problem is to try to find the values for the general
equation y = mx + b, where m is the slope of the line and b the y–intercept. Since the line contains the
points (–2,1) and (4,4), the value of m is:
Now, to find b, use one of the sets of points already known:
The equation of the line is:
The line crosses the x–axis where the value of y is 0:

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Alternatively, you can quickly sketch the line:
Now look at the choices. There is only one choice available that could be the value for x when y = 0.
And that is (A).
31. The correct answer is (B). Before we do any math on this problem, use common sense to eliminate
some choices. The question asks for the ratio of the area of the larger figure to the area of the smaller
figure. That means that the numerator of the fraction must be larger than the denominator of the
fraction. What about (D) and (E)? They must be wrong. Now for the math. Since r is the radius of the
circle, the larger square has a side of length 2r.
So the larger square has an area of 4r
2
. The diameter of the circle, which is also the diagonal of the
smaller square, is 2r. So the smaller square has sides of r 
:
And the area of the smaller square is 2r
2
. So the ratio asked for is:

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