You know that feeling you get when you think youre on top of the world, and then an easy test comes around that for some reason or another that markedly easy test beats your face in with some sort of embarrassing instrument like a wiffle bat or a spork?
Well... I decided to retake, yes RETAKE invitational A, along with all the other tests from last year, and my timer goes off at problem 44. I think to myself, wow... I must really suck. Then I start grading the test... 5 wrong! Well.... (stretches arms*) that brings me to a grand total of a 175.... YAK! To augment to my gloomy state, the next two problems on the sheet seem pretty sheety if you ask me.
(SAC questions)
#47 6P2 = _________
I think I know how to do this, but I am not exactly sure. Does it work in this manner: 6!/((6 - 2)! 2!) which would simplify to 1*2*3*4*5*6/1*2*3*4*1*2 which simplifies to 5*6/*2 which should be 15, but ze answer says 30. I feel dumb for some reason.
#59 5C2 = __________
I dont know what the C means...
#61 4/7 - 35/64 = ___________
um... I tried power arithematic, but no. 4/7 - 5*7/4^3 = (4^4 - 5(7^2))/7(4^3) = 256-245/448 = 11/448. Too much thinking for my blood. Help.
#64 2 sin120 cos30 = ____________
Question mark. 2 * sqrt(3)/2 * sqrt(3)/2. So the answer is 3/2? Faster way?
#73 sin(arccos 1) = __________
arccos... I am guessing that it is the opposite of cos? Which would mean that it would be asking opp/hyp(hyp/adj 1) which would mean that the hypotenuse would have to equal the adj, meaning that the opp would have to be zero, because the hyp and adj are on the same line. Am I right? I havent had trig and I am shooting in the dark here.
#75 the remainder when x^3 - 3x + 3 is divided by x + 3 is ______________
I forgot how to do synthetic division! help!
#77 (2, pi/3) are the polar coordiantes for (x,y) x = __________
47. mPn is "start from m, count down n numbers and find their product." 6P2=6*5=30
59. mCn is "mPn divided by the product of numbers starting from n counted down to 1." 5C2 = (5*4)/(2*1)=10
61. m/n - (km-1)/(kn+1) = (m+n)/(n(kn+1));
64. None that I know of.
73. Arccos is cos^-1, when cos=1, sin=0; similarly, cos(arcsin 4/5): when sin=4/5, cos=3/5(consider the pythagorean right triangle); Try this tan(arcsin 20/29)
75. Let P(x) be the polynomial and R(k) be the remainder when P(x) is divided by (x-k), R(k)=P(k); id est, when dividing by x+3, plug evalueate the f(-3), you should get -15.
77. The polar coordinate (2, pi/3) means: the point is 2 units from the origin with an angle of pi/3 counterclockwise from the positive x-axis. It's (1, Sqrt(3)) in rectangular(Cartesian plane) coordinate. Polar(r, theta) is Rect(rcos theta, rsin theta.)
52. For one degree binomial (ax+by), its nth power has n+1 terms.
54. When you multiplied by i, you forgot that i*i=-1 not 1.
57. 466 2/3 is 1400/3, so 12% of it would be like 4% of 1400, which is 56.
58. See 61 above.
63. You should start at 5/7, not 5.
64. No matter how complex the trig function looks like, the amplitude is the coefficient of cos or sin, thus the b in f(x)=a+bsin(x-k);
You need to read the PreCal book if you haven't taken it; if you have, I wonder how you could pass...(joking behind the semicolon)
I tried doing it the way sam did for district and regionals, but right before state, I saw that there was such an easy way of doing these that i kicked myself for not seeing it earlier (I would've won at regionals).
Think of it this way
Rewrite it as 12/100 * 466 2/3
notice that 466 2/3 is the same as (4 2/3) * 100
so, we rewrite it again as 12/100 * (4 2/3) * 100
100's cancel out
12 * 4 2/3
now it's easy
48 + 8
56
basically, what I'm saying is...
multiply the percent number by the number that's not repeated, then multiply it by the fraction and add it together. So much easier!
try these...
18 % of 533 1/3 is...
42 % of 916 2/3 is... (this is tricky, be careful)(HINT: The fraction isn't 2/3)
15 % of 233 1/3 is...
35 % of 414 2/7 is... (another tricky one... but a fun one)
In 2005, Dr. White stuck to a66 2/3 and a33 1/3... hopefully he won't do that next year... it would be much more fun
I guess its blaringly obvious that I have not had precal yet... I wish that they would've allowed me to test out of Geometry, but then again, there is nothing beyond calc 1 offered at my school.
