Pure math 2

Question 1

mod(a-b) < x

Answer 1

a-b < x and a-b > -x

Question 2

mod(a-b) > x

Answer 2

a-b > x and a-b < -x

Question 3

How to sketch graphs of the form mod(ax+b) + c

Answer 3

First sketch the mod(ax+b), with the x-intercept being the turning point, and then add c to the y-coordinates

Question 4

How to draw quartic functions

Answer 4

Find x-intercepts by polynomial division. Find the midpoint of each pair of intercepts when arrange in ascending order. The midpoints are the turning points, and use these to find the stationary values

Question 5

How do I implicitly differentiate

Answer 5

https://qr.ae/pGSls4

Question 6

How to sketch parametric graphs

Answer 6

Choose a diverse set of values for the parameter, and find the corresponding x and y values. Almost always, if forms some kind of ellipse

Question 7

How do you integrate cos^2 (x) and sin^2 (x)

Answer 7

Use double angles

Question 8

How does the trapezium rule work?

Answer 8

It is used in finding the area under curves that cannot be integrated. Formula is h/2 * (y0 + y4 + 2(y1+y2+y3)) where h = b-a/n