I was destroyed by this test: 152. What makes me sooo mad about it was that I wasted waaaay too much time on stuff that I eventually ended up getting wrong anyway... And that kept me from completing the easier last section of the test... But I can't stand skipping problems... It always messes with my mindset. If I feel that I am raping a test inside out as I progress through a test, I will usually act accordingly. If I feel disorieted by the first few problems... Then I am utterly screwed for the rest of the test. I get the same anxiety in NS as well. Anyways...
A few problem areas:
9) Sec(3pi/2 +theta) equals:
Correct answer choice is -csc(pi + theta). I thought these trig problems were supposed to simplify the problem. It pissed me off, because I got the problem down to -csc(x), but it wasnt an answer choice, and I lost a lot of time in the process. How do y'all do these?
14) Let f(x) = x^5 - 5x^4 + 5x^3 + 20. Find the sum of the critical points in the interval (-3,3)
I used my graphing calculator, and still couldnt get the right answer. Apparently, there were more critical points than I thought there were. How do you do this without being calculator dependant, or rather, correctly? (Correct answer: 4)
16) How many 9 letter words, real or imagenary can be made by using the letters: STATEMEET?
I thought it was 9!/(3!3!), but that wasnt an answer choice. (Correct answer: 10,080)
31) Find the digit in the thousandth place of the series: 1 + x + x^2/2! +x^3/3!....
I know the one with even powers is cos, and odd is sin, but what is this one?
36) If it takes x builders to build z houses in y days, how many days would it take q builders to build r houses?
Please explain. (ca: xyr/(qz))
56) Suppose Y varies inversely with the cube of X and X varies directly with the square of Z and inversely with W. Which is true?
Too many words. Why is Y = kw^3/z^6 correct?
57) A ladder, 20 feet long, is leaned up a vertical wall and the base of the ladder is 12 feet from the wall on level ground. The ladder slides down on the wall to a point where the angle formed at the base of the ladder and the ground is now one half of its original value. If the base of the ladder is now asqrt(b) feet from the wall where a>b and a and b are positive integers, find b.
I've done this problem 8 times, and I'm still getting (2)sqrt(10). Which is wrong because of the a must be bigger that b noise. Damn calculator... only gives decimal answer.
Those are the only 7 that I really had any trouble with.
14) Let f(x) = x^5 - 5x^4 + 5x^3 + 20. Find the sum of the critical points in the interval (-3,3)
critical points are where the first derivative is zero so
f ' (x) = 5x^4 - 20x^3 + 15x^2 = 5x^2(x^2-4x+3) = 5x^2(x-3)(x-1) zeroes are 0,3,1 0+3+1 = 4 technically i wouldn't count 3 because (-3,3) is the interval from -3 to 3 but not including -3 and 3. [-3,3] would be the interval from -3 to 3 including -3 and 3.
56) Suppose Y varies inversely with the cube of X and X varies directly with the square of Z and inversely with W. Which is true? Y = kw^3/z^6
go through it statement by statement. first "Y varies inversely with the cube of X" means y = k/x^3 X varies directly with the square of Z and inversely with W means x = kz^2/w now combine the two expressions: y = k/(z^2/w)^3 = k(w^3)/(z^6) we can ignore the second k (constant) because it will combine w/ the first to make a new one
36. By given, 1 guy in 1 day can build z/(xy) house, q builders in 1 day (qz)/(xy) houses, and since there're r houses to be built, so r / (qz)/(xy) = (xyr)/(qz)
