GCSE Maths
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what can dif be used for
 to find the gradient of a curve at a given coordinate
 motion of a particle
 turning points
 rate of change
 work out maximum and minimum problems

to find the gradient of a curve at a given coordinate
 dif
 put x value into dy/dx equation

to find turning points of an equation
 dif
 dy/dx = 0
 solve to find x
 put x value into original equation to find y

to find out whether maximum or minimum
 dif dif
 put x value into dif dif
 if this > 0 minimum , < 0 maximum

find the maximum/minimum in problems
 dif
 dy/dx = 0 to find letter
 may need to put letter value back into the original equation to find area for eaxmple

square root of a positive number
can be positive or negative

motion of a particle
 original equation = displacement or s in metres (M)
 dif = velocity in m/s
 dif dif = acceleration in m/s2



double dash ones
 mean
 less than or equal to for double dash <
 more than or equal to for double dash>

with inequalities whenever you multiply or divide by a negative number
flip the inequality sign


open circle means
not included in the solution

shaded circle means
included in the solution

graphical inequalities method
 convert each inequality into an equation
 draw the graph for each equation (if the inequality is
 work out which side of each line you want by putting x = 0 into the inequality if it gives a false answer the origin is on the wrong side of the line
 shade the region this gives u