Alternative Solutions to the Official Practice Tests

MITer94
Thu, 10 Mar 2016 01:04:38 +0000

@pckeller
Test 2, Sec. 4 #30: I recommend simply adding the formula for the area of an equilateral triangle of side length s (A = s^2 sqrt(3)/4) to our list of formulas. We could derive it by drawing an altitude, but why do that every time?

Test 3, Sec. 3 #9 You can avoid a lot of algebra by noticing that the second equation is represented by x+y = 3. So without determining a,b, we know that a+b = 3.

Test 3, Sec. 3 #13 I just did 16/2 = 8 because determining the sum of the roots of a polynomial is fairly easy (for a quadratic ax^2 + bx + c, the sum of the roots is -b/a). The only caveat is that you have to check that 4 is not a double root.

Test 4, Sec. 3 #16: You can just shortcut and say that the height of the bottle is 3/6 (or 1/2) of 18 in, since the ratio of the height to the edge lengths (x, 2x, 3x) is constant.