IB Math SL- Things to Memorize 2023

IB Math SL- Things to Memorize 2023 Vector lines - ANS-If perpendicular: costheta will be 0 when u do the angle formula If parallel: If theta when we do costheta formula is 180 Coincident lines: They are the same line, they share a point & their direction vectors are scalar multiples If the question is talking about movement, then the direction vector tells you the velocity and its magnitude is the speed If you have a question asking for the equation of the tangent line at x = 1, for example... - ANS--Plug in 1 into original equation. The value u get is the 'y' in the y = ax +b! -Plug in 1 into first derivative equation. The value u get is the exact slope! -Don't forget to attach an x to this slope value once u put it into the y = ax + b format! -Solve for 'b' by plugging in your 'y' value from the first step and your slope (plug in slope into 'a' and your given x value into the 'x'). -After getting 'b', write the equation in the format y = ax+b! Questions in which they ask you for the x to the power of four term in a sequence... - ANS-Put it in the binomial theorem format. 'N' is the exponent on the sequence and 'R' is what value of the term they want (in this case the fourth term)! If there's an x multiplying on the outside of the expansion, then consider it as well! In this case, for the 'a' term, you should think of your 'R' and 'N' subtracting to give a power that will also multiply by the outside term....This ensures you get x^4 when you multiply by the outside at the end For limit questions where you have to use the "h -- 0" equations...I need to plug in (x+h) wherever I see 'x' on the given equation only, right? - ANS-Yes! But, don't forget to subtract by f(x) after you're done doing that (this is part of the formula) and dividing by 'h'! For limit questions where you have to use the "h -- 0" equations, I always factor out all the 'h's so that I can cancel it out with the 'h' on the denominator, right? - ANS-Yes! After that, don't forget to plug in '0' wherever you see any 'h' as part of the 'h -- 0" thing. Your answer should be the only number or term left after you finishing plugging it. How do I do factorials without calculator? - ANS-The formula is in the data booklet. You multiply backwards to 1 on the numerator. On the denominator, you subtract the 'n' and the 'r' in the factorial from each other and do the factorial of this number * the factorial of the 'r' term. You'll see that some of the top multiplications should cancel out from the bottom multiplications. :) If I have to solve for smth that cannot be negative, I do... - ANS-The absolute value on the calculator by going on 'Math' then 'Num' To get rid of a fractional exponent when solving an equation.... - ANS-Do the reciprocal of the power on both sides Concavity is up when... - ANS-F´´(x) 0 Concavity is down when... - ANS-F´´(x) 0 Inflection point/Graph of f(x) changing direction when... - ANS-F´´(x) = 0 "Particle is at rest" - ANS-Velocity is 0 Order of operations - ANS-BEMDAS! Rules everything bro "Find the maximum..." - ANS-Find first derivative, equal it to 0, do sign diagram to see which x-intercept is max and which is min... OR Plug in equation into Y = on your calculator, if it's a paper 2 question, and 2nd-tracemaximum that shit Amplitude - ANS-Max - min /2 Vertical shift - ANS-Max+min/2 Integral of e - ANS-Still e Derivative of ln - ANS-1/x Period - ANS-2 pi/b Phase shift - ANS-See how far it is on the x axis from where the graph should have started... Typical cosine graph... - ANS-Starts at max or min Typical sine graph... - ANS-Starts at origin If they say a point is 'tangent' to a circle at Point P... - ANS-It's perpendicular to the circle at Point P Quadrants - ANS-From left to right: I, II, IV, III. If I have a question where I am to solve a trig function's zeroes, I should attempt... - ANS-Rewriting it as a regular quadratic equation and equaling it to 0, then bringing back the sin or cos to solve what the x (or angle) would be for that specific value. Before you do this, make sure it's in a format like: sin^2x + sinx + constant, and vice versa for cosine. But it cannot be sin^2x+cosx+constant...Try using trig identity to get it all sin or all cos... Area Integration - ANS-Top function - bottom function AND Top thing on curly bracket - bottom thing on curly bracket... Continues...