1. The rules you want do not exist, Try to do things without thinking of rules, the best students are confident of what they write not because they are sticking to a prepared method, but rather they understand what they are doing.
2. Understand everything, it's not in the spirit of mathematics to use a result that you cannot prove and not knowing these proofs slows you, because there's often less to learn if your understand the concept.
3. Do your algebra, 80% of your difficulties come from inability to manipulate algebraic expressions
4. a^2 - b^2 = (a-b)(a+b)
5. a^3 - b^3 = (a-b)(a^2 +ab + b^2)
6. f'(x) = lim (h ->0) { [f(x+h) - f(x)]/h }
7. d/dx [x^n] = nx^(n-1) POWER RULE
8. (uv)' = u'v + uv' PRODUCT RULE
9. (u/v)' = (u'v - uv')/(v^2) QUOTIENT RULE
10. d/dx [ f(g(x) ] = f'(g(x)) * g'(x) CHAIN RULE or FUNCTION OF A FUNTION RULE, this is VERY IMPORTANT since it is the most common rule which you need to apply, failure to grasp this will severely damage your marks
11. d/dx Ln(x) = 1/x
12. d/dx e^x = e^x
13. S = n(a+l)/2 = [n(2a + (n-1)d)]/2 partial SUM OF A.S
14. S = a(1 - r^n)/(1-r) partial SUM OF G.S
15. area formulae
16. d = sqrt( (x0 - x1)^2 + (y0-y1)^2) DISTANCE FORMULA
17. m = (y0 - y1)/(x0 - x1) GRADIENT FORMULA
18. M = ( (x0+x1)/2 , (y0+y1)/2 ) MIDPOINT FORMULA
19. (x-x0)*m = y - y0 POINT SLOPE FORMULA OF A LINE
20. x = [-b + sqrt(b^2 -4ac)]/(2a) or [-b-+ sqrt(b^2 -4ac)]/(2a)
QUADRATIC FORMULA
21. The Method of completing the square
22. method of factorizing
23 put +C after indefinite integrals.
24. INTEGRAL {a->b} f(x) dx = F(b) - F(a) where F is the antiderivative of f. FUNDAMENTAL THEOREM OF CALCULUS.
25. V = Pi * INTEGRAL {a->b} [f(x)]^2 dx VOLUME OF SOLID OF REVOLUTION
26. A = INTEGRAL {a->b} f(x) dx AREA UNDER CURVE.
27. GO BACK TO RULE #1
will post more later when I recall them
Thanks!
