Algebraax2+bx+c | sum roots: -b/a | Δ =b2-4ac | product roots: c/a |
Ratiosq1 : q2 = q2-final : q1-final | 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: a-10 + b-20 + c-15 = 11k + 18k + 24k so 1105-45=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 propertiesremainder 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 -> 23*51*31-> (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 2n+2m = 23m-1 then n+2m = 3m-1) | AP Sum of arithmetic progression = (1st + Last / 2) * nb of terms | AP nth term → an = a1 + (n-1) * d (common divisor) | AP sum of the n first terms : n/2 [2a1 + (n-1)d] | GP sum of first n terms = a(rn-1) / r-1where 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 |
SetsP(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 AverageStandard deviation = mean -> (number-mean)2 -> mean -> square root(mean) |
From videoWork and Rate | R=J/T | machines identiques: nR=J/T |
| | Geometry / Coordinate Geometryair triangle = 1/2 * products of sides * sin (inside angle) | sin 150° = 1/2 | sum of interior angles of polygon = (n-2)*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) * semi-perimeter triangle | equation of a circle center (a,b): (x-a)2 + (y-b)2 = r2 | 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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