Sin30
1/2
Sin45
(Root 2)/2
Sin 60
(Root 3)/2
Sin90
1
Cos30
(Root 3)/2
Cos45
(Root 2)/2
Cos60
1/2
Cos90
0
Tan30
(Root 3)/3
Tan45
1
Tan60
Root 3
What to look for if given a long sequence?
Terms that cancel or simplify very easily
How is DOTS useful for multiplication of numbers around 50?
If they are equidistant from 50 then it can be used
e.g 48 x 52
(50 + 2)(50 - 2)
2500 - 4
2496
Trick for multiplying by 25
x 100/4
e.g 48 x 25
(48 x 100)/4
4800/4
1200
Trick for squaring near 100
Use (a + b)^2 = a^2 + 2ab + b^2
e.g 97^2
(100 - 3)^2
100^2 - 2(100x3) + 3^2
10,000 - 600 + 9
9409
Useful percentage shortcuts
1/6 = 16.7%
1/8 = 12.5%
Trick for multiplying numbers that are close together
Same as for 50 but general, use DOTS
e.g 21 x 19
(20 - 1)(20 + 1)
400 - 1
399
How to use estimation to eliminate answers
Estimate a rounded answer to wipe out a few. On average 3 answers are not reasonable.
Trick for when calculating new means
Total added = (New mean x new size) - (Old mean x old size)
Then you can divide by the number of new members
