Algebra
ax^{2}+bx+c 
sum roots: b/a 
Δ =b^{2}4ac 
product roots: c/a 
Ratios
q1 : q2 = q2final : q1final 
num<denum so fraction<1 so (x+1)/(y+1) > x/y 
num>denum so fraction>1 so (x+1)/(y+1) < x/y 
from exercise: a10 + b20 + c15 = 11k + 18k + 24k so 110545=53k (ratios gains) 
efficacy=1/t (inverse proportionnality) 1/t1 : 1/t2 : 1/t3 take LCM = k so you have k/t1 : k/t2 : k/t3 compute to get x : y : z form then do x + y + z and cross product 
Rate of interest = interestperyear/principalinvested * 100 
When compared, use compared amount as the base so you have Δ / base * 100 
Use quantity as unit of q, the percentage change is Δ = increased or decrease quantity Δ/1(original amount) * 100 
To make a profit, take initial price and add the desired profit so that: new price per unit = initial (1+profit) 
Always find a 100 that makes the calculation easy = if it's not marked price it's cost price etc. 
On Y1, simple and compound interests are the same Find interest rate w/ difference and interest on interest 
Interest = principal * rate * time 
discount of marked price = discount / marked price * 100 
Usually, these questions include: 1. ratios of shared amounts, 2. time to perform a task,
3. investments and interests 4. price increases or decreases => FOR PROFITS


Number properties
remainder of sum = sum of remainders 
remainder of product = product of remainders 
nb of trailing zeros = at least nb of 5s 
number of factors = product of each power + 1 [ex: 120 > 2^{3}*5^{1}*3^{1}> (1+1)*(1+1)*(3+1) = 16] 
from exercise: If remainder of product to find, can work by pairs 
If two expressions are equal, the exponents must be equal (if 2^{n+2m} = 2^{3m1} then n+2m = 3m1) 
AP Sum of arithmetic progression = (1st + Last / 2) * nb of terms 
AP nth term → an = a1 + (n1) * d (common divisor) 
AP sum of the n first terms : n/2 [2a1 + (n1)d] 
GP sum of first n terms = a(r^{n}1) / r1where r is common ratio 
Number of ways of selecting two distinct integers from the set of first 100 positive integers = 100C2 ways. i.e., 100C2 = 100 × 992 
Sets
P(AUB) = P(A) + P(B)  P(A∩B) 
P(AUBUC) = P(A) + P(B) + P(C) + P(A∩B∩C)  [P(A∩B) + P(A∩C) + P(B∩C)] 
Statistics and Average
Standard deviation = mean > (numbermean)^{2} > mean > square root(mean) 
From video
Work and Rate 
R=J/T 
machines identiques: nR=J/T 


Geometry / Coordinate Geometry
air triangle = 1/2 * products of sides * sin (inside angle) 
sin 150° = 1/2 
sum of interior angles of polygon = (n2)*180 
Pythagorean triplets (c is odd, at least 2 prime numbers, 1 even number): (3,4,5) / (5,12,13) / (7,24,25) / (8,15,17) / (9,40,41) / (11,60,61) / (12,35,37) 
area triangle = r (inserted circle) * semiperimeter triangle 
equation of a circle center (a,b): (xa)^{2} + (yb)^{2} = r^{2} 
equation of a line that crosses two intercepts: x/value x + y/value y = 1 so (value x)y + (value y)x = (value x)(value y) 

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