ALl those tests....

[nsguy1350]

Can somebody help me with those questions? I know there are a lot of questions, but I figured a couple out, making it a little easier.
I still need help on vector cross products, angles of rotation, how to find the area of polygons given the vertices, how to find the coordinates of the orthocenter, incenter, and circumcenter, and a few other things I mentioned in previous posts. Help please!

[chrishuff]

:(
Sorry there. I tried working out some of the questions I think I have a legitimate shot at solving, but I should have known that you don't ask easy questions. You score on average 200+ points higher than what I score..

[nsguy1350]

[chrishuff]

I haven't really put much into Math recently, just Number Sense.

I haven't had much luck getting past the #30 mark. I am terribly inefficient when it comes to problems such as 16 * (16/19). I can do the 16*16 part just fine, it's just the dividing part to turn it back into a mixed number that takes me the most time. I am also fairly weak when it comes to mentally solving arithmetic sequences such as 2 + 4 + 6 ... + 28 (Well this is a relatively easy one, because I can add 2+4+6 etc given enough time, but make the sequence a bit longer, then I start to really have a problem in keeping track)

I'm just trying to improve my speed for the first 30 questions. Assuming I am just going to solve correctly 30 problems, that's 20 seconds per question.

[michel470]

Posted on cross-products of vectors, hope it helps you out some

[nsguy1350]

chris man, we NSers aren't super human. If you think that a problem will take you forever to do, YOU'RE DOING IT WRONG. Those two problems you posted are easy tricks... make sure you don't do thing the hard way, and learn the trick!

16 x 16/19: square the difference between the numerator and denominator to get 9, and put that over the denominator. Subtract the difference from the original whole number to get your whole part. This gives: (16-3) (19-16)^3/19 = 13 9/19. Keep posting questions like these to figure these things out.

2 + 4 + 6 + ... + 28:
Sum of an arithmetic series with first term [unparseable or potentially dangerous latex formula], last term [unparseable or potentially dangerous latex formula], and number of terms n is [unparseable or potentially dangerous latex formula]. The first + last should be fairly easy, and cancel if you need to.
The first + last is given by: [unparseable or potentially dangerous latex formula], where d is the common difference (2 + 4 + 6 + ... ) has a common difference of two.
You get the sum is: [unparseable or potentially dangerous latex formula].
A second way is to recognize that the series is 2(1+2+3+...+14), which is 2 x the 14th triangular number, which is 2(14x15)/2 = 210. This doesn't always work, because the series is usually a different form, so use the other trick unless you recognize this instantly.

[chrishuff]

This was the most recent Number Sense test I had taken:

Tell me if I am not doing things the most efficient way possible:
These are the ways I would think in my mind to solve problems like these

*A very old random number sense test was chosen and taken with the 10 minute time limit*
If there is no answer at the bottom of each question, I skipped it and did not have time to get back to it.

1. 17 * 12
(12 * 12 = 144) (5 * 12 = 60)
144 + 60 = 204

2. 0.2 + 40% + (3/10) [Decimal]
0.9 [Super easy]

3. 256 / 1.6
2560 / 16
160 (Took me some time figuring out how many times 16 went into 96)

4. 3 * 6 - 4 * 7
18 - 28
-10 [Super easy]

5. 420 * 15

420 / 2 = 210
210 + 420 = 630
630 * 10 = 6300

6. Which is larger, (11/13) or (10/11)?
11*11 = 13 * 10
121 = 130
(10/11) is larger

7. 0.125 (fraction)
(1/8) [Super easy]

8. 3 + 5 / 4 * 2 - 5
3 + 1.25 * 2 - 5
3 + 2.5 - 5
5.5 - 5
0.5

9. 19^2

19 * 19

9 * 9 = 81 write 1 carry 8
9 * 1 = 9 + 19 = 28 + 8 = 36 write 6 carry 3
361

*10. 7 + 26 + 63 + 124 + 215

339 + 63 = 402 + 26 = 428

428 is close enough

11. 3 (3/5) - 2 (1/4) [Mixed Number]

(12/20) - (5/20) = (7/20)
1 (7/20)

12. 4(3) + 36(4) + 5(8)
12 + 36(4) + 40
52 + 36(4)
52 + 72 + 72
52 + 144
196

13. The GCD of 32, 48, and 72 is
First tested out 16, does not work with 72
Tested 8, works on all 3

14. (2/3) of 72 = (3/4) of _____
24 * 2 = 48
48 * (4/3) =
96 + 96
192 / 3
64

15. 16 * (16/19)
16. 2 + 4 + 6 + ... + 28

17. 11 * 214
Write down 4
4 + 1 = 5 write down 5
1 + 2 = 3 write down 3
write down 2
2354

18. 4 (2/5)% [Fraction]
0.044
44/1000
22/500
11/250

19. Find the cost of driving 127 miles at 25 cents per mile
127 * 0.25
127 / 4
31 reminder 3
(3 * 0.25)
$31. 75

20. 41259/39
(39 goes into 41 once, 39 does not fit into 22, guestimate 9 on next term)
1090

21. The average of -34, 29, and 62 is
62 + 29 = 91
91 - 34 = 57
57 / 3 = 19

22. 15 * 3367
Uhh, skipped for the meantime


23. If today is July 21, 1999, then 27 days ago was June _____ 1990
June 24th (30 days in June, so 27 * 21 yields 6, and 30 - 6 = 24)

24. 1643/ 7 has a remainder of ____
16 / 7
24 / 7
33 / 7
5

25. If 30 bananas cost $4.20 then 5 bananas cost _____
30 / 4.20
0.14 cents each

0.28 + 0.28 + 0.14 = 0.56 + 0.14 = 0.7

26. 12^2 + 36^2
144 (memorized) + uhhhh

27. The number 48 has ___ positive integral divisors
1,2,3,4,6,8,12,16,24,48
10

28. If A = 2, B = 4, and C=3, then ABC^2 = _____
2*4*9
8*9
72

29. 314 base 7 = ____ base 10

30. 18 * 39 * 69 = __________________
40 * 18 = 720
720 * 70
50400

*TIME UP*

[chrishuff]

24 right, 6 wrong
120 - 24 = 96

I made a 96 and would of probably got a 114 if I knew those two tricks you explained to me earlier.

[nick3194]

I've seen a lot of combination problems that include repetition (pizza slices, coins, etc.). It is not simply nCr. This website explains better than I can.

http://www.mathsisfun.com/combinatorics ... tions.html.

I can NEVER get geometry problems right. I tend to score between 200-230, but I may answer one geometry question throughout the entire test.

[nsguy1350]

Nice post chris. Here are a few things:

1 = LOIF.
3. 256 = 16^2. Notice the shifted over decimal point and you get 10 x 16. Easy 2 second trick.
5 - you could LOIF 42 and 15 and then add the extra zero, or use a different technique. I say for now, even though I wouldn't do it (I think tehre is a faster way that might save a second or two), LOIF and add the zero.
6. - nice, that's the way to do it.
9 - memorize squares to 40, cubes to 20, then maybe higher if necessary later. This eliminates all that hassle.
10. 215 + 124 ~ 350, 7 + 26 + 63 ~ 100, 450? That's a bit high, maybe subtract a few, but should be fine.
11. (3-2)+(3/5-1/4) = 1 7/20. Mixed number is addition so just break it up to make it easier.
13. Look up Euclid's method if you like, but yeah, this is easy, just recognition is fine for this one.
14. 2/3 of 72 = 48, 4/3 x 48 = 64.
15. said earlier
16. said earlier
17. Great! That 11 trick is very useful! Keep reading math-magic!
18. Convert to improper fraction percent, multiply denom by 100 to get rid of percent sign.
22/5 --> 22/500 --> 11/250
19. good, use the 25 trick :D
20. fine, estimation I hope :D
22. 3 x 3367 = 10101, so 15 x 3367 = 5 x 3 x 3367 = 50505
23. yea
24. I know what you did, yes
25. you could just divide by 6, dollar/cent problems require 2 decimal places btw, .7 is wrong, .70 is correct
26. [unparseable or potentially dangerous latex formula] Or, you could use the nice trick and do: [unparseable or potentially dangerous latex formula]. Use the trick! Whenever two numbers are squared, you're adding them, and one is 3x the other, just multiply the smaller one by 10.
27. Find the prime factorization, add 1 to each exponent, multiply. [unparseable or potentially dangerous latex formula].
29. 3 x 49 + 1 x 7 + 4, learn your bases! :D = 158
30. great, maybe take a little off to compenstate for rounding up, but should be fine.

Time up? :'( --- haha nah you're improving, and you'll start consistently breaking 100, then higher and higher as you learn and become familiar with the tricks. We're counting on you to make State Chris!! :D Haha, if I had told you that 2 weeks ago, you would've wondered which mental hospital I belonged to.

One last note: 96 is definitely good progress, considering you couldn't break 50 not too long ago. This is a very weird NS test, (not to mention easy), so try to work on the more recent ones. Go to the downloads and maybe do the SACs, Invitationals, and TMSCAs from 2005 and on or so. That should give you enough tests for a while. Make sure you learn all of the tricks, and memorize! Good luck!

[chrishuff]

Heh heh 96 was counting .7 correct, so it would be 87, but thanks for the heads up. I've learned that putting a leading zero is considered incorrect, and now I know that you have to put a zero in money problems when needed.

[chrishuff]

I'll see what I can do the next week in taking some more recent NS tests. Not feeling 100% right now (Probably because of the cold weather) and that probably says that I need to bundle up, and rest for the upcoming school week.

[chrishuff]

Random question: Can you always split it apart like you did in #6?

[nsguy1350]

#6? Just the butterfly trick or whatever people call it.

[chrishuff]

SORRY HAHA I meant #26

[nsguy1350]

The Laws of algebra say yes! Don't do the algebra in your head, but instantly recognize the trick, knowing the 3x the lesser square means 10x is the answer.