L2 Calculus

Louise Addison
Mind Map by Louise Addison, updated more than 1 year ago
Louise Addison
Created by Louise Addison over 6 years ago
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NCEA Level 2 Mathematics Mind Map on L2 Calculus, created by Louise Addison on 10/23/2013.
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L2 Calculus
1 Differentiation
1.1 Finding the gradient or rate of change at a point (Differentiate, substitute in the x value)
1.1.1 Find the equation of a tangent (Use y-y1=m(x-x1)
1.1.1.1 Find the equation of a normal (Use m1xm2=-1 and y-y1=m(x-x1)
1.1.2 Find velocity given distance
1.1.3 Find acceleration given velocity or distance
1.2 Find the point with a certain gradient (Differentiate, set equal to gradient given, solve for x, substitute to find y / f(x)
1.2.1 Find where increasing / decreasing (Differentiate, solve f'(x)>0 or f'(x) <0)
1.2.2 Finding turning points (Differentiate, solve f'(x)=0)
1.2.2.1 Finding maximums and minimums (Find equation to maximise or minimise, differentiate, solve f'(x)=0 to find where max/min occurs, substitute into f(x) to find max or min
1.2.2.1.1 Prove a point is max or min (Find f''(x), if f''(x)>0 then a min, if f''(x)<0 then a max, if f''(x)=0 we cannot tell
1.2.2.1.2 Find max or min distance (where v=0)
1.2.2.1.3 Find max or min velocity (where a=0)
2 Anti-differentiation
2.1 Finding the function from the gradient function and a point (Anti-differentiate, substitute in point to find c)
2.1.1 Find a point on the orginal cuve or function (Find original function, substitute or solve to find point
2.1.2 Find velocity given acceleration
2.1.3 Find distance given velocity or acceleration
3 Sketching functions
3.1 Sketch function from gradient function (x-intercepts become turning points, above y-axis is increasing, below y-axis is decreasing
3.1.1 Sketch velocity function from acceleration function
3.1.2 Sketch distance function from velocity function
3.2 Sketch gradient function from function (Turning points becomes x-intercepts, Increasing is above y-axis, decreasing is below y-axis
3.2.1 Sketch acceleration function from velocity function
3.2.2 Sketch velocity function from distance function
4 Kinematics
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