Math (C)

Question 1

Splitting the work

Answer 1

AB / (A+B) = T || 1/A + 1/B = 1/T
ABC / (AB + AC + BC) = T || 1/A + 1/B + 1/C = 1/T

Where T is the time taken when they work together, A is time taken for A, B is time taken for B, C is time taken for C

Question 2

Special Triangle Ratios

Answer 2

For an isosceles right-angled triangle, if the legs have length x, the hypotenuse is x√2

For a 30-60-90 triangle, the side lengths are x, x√3 and 2x

Question 3

Sines of Common Angles

Answer 3

0: 0
30: 1/2
45: √2/2
60: √3/2
90: 1

Question 4

Cosines of Common Angles

Answer 4

0: 1
30: √3/2
45: √2/2
60: 1/2
90: 0

Question 5

Divisibility rules

Answer 5

2: Last digit divisible by 2
3: Sum of digits is a multiple of 3
4: Last two digits make a number divisible by 4
5: Last digit is 0 or 5
6: Divisible by 2 and 3
8: Last three digits make a number divisible by 8
9: Sum of digits is a multiple of 9

Question 6

Special numbers for variables and inequality questions

Answer 6

FROZEN

Fractions, repeated numbers, one, zero, extreme values, negatives

Question 7

Remainder consideration

Answer 7

Zero quotient w/ remainder of divisor

Question 8

Super Pythagoras

Answer 8

3D Diagonal of a box:

d^2 = a^2+b^2+c^2

Question 9

Primes Under 20

Answer 9

2, 3, 5, 7, 11, 13, 17, 19

WRITE AT START OF MATH SECTION

Question 10

Standard Deviation Formula

Answer 10

square root of (sum of (squares of differences between mean and individual observation), divided by number of observation)