Additional MYX notes

Question 1

Modulus questions

Answer 1

square both sides
solve
test for solutions

Question 2

Factor/remainder theorem questions

Answer 2

Use long division else use factor theorem (sub factor into equation) for zero

Question 3

Partial fractions

Answer 3

split into one form of partial fraction
lay out as A + B + C
lay out as solvable equation
solve
sub answers back into A + B + C form

Question 4

Integrating partial fractions

Answer 4

Break into individual integrals
solve each integral at a time
combine in final answer

Question 5

Rsin(x + a)

Answer 5

expand second side of equation
let x = 0 and solve
let x = 90 and solve
solve for R and a

draw graph and figure out where answers lie
cos = 360 - answer
tan = 180 + answer
sin = 180 - answer or 360 + answer

Question 6

Implicit differentiation

Answer 6

for combined xy terms
Rule of thumb:
1.the y gets taken out as its own term as is (with an x value if x remains when differentiated)
2. the second dy/dx term (implicit term) the x gets taken out as its own term as is (with a y value if y remains when differentiated)

for singular terms regular differentiation rules apply given y’ is followed by dy/dx

Question 7

Parametric equations

Answer 7

dy/dx = dy/dt . dt/dx

Question 8

Trapezium rule

Answer 8

find y values to given x values for bars of trapezium
work out h
sub into equation