Pure Maths - errors/mistakes/pointers

any errors made or stuff i want to highlight to remember for the future

question 1b - failing to factorise to find solutions

i only got the 3/2 solutions and not the 0 because i didn’t factorise

so make sure you factorise to not loose solutions

+ analyse the second derivative before and after each solution when you’ve solved f’’(x) = 0

problem-solving/manipulation (algebraic expression)

yeah so just be smart use difference of two squares a² -b² = (a+b)(a-b)

missing a solution

deduce that 0 is also a solution

something squared is always greater than or equal to zero

errors in factorising correctly

incorrectly completed the square (factorising skill issue)

recognising f(x-5) is a translation of f(x) to the right by 5 :D

recognising (x-1) is a factor from part a and using polynomial division and the quadratic formula (no relying on the calcs)

multiply by (x-3)²

2020 paper 1 Q7
using vertex form of an equation

The vertex form of a parabola is

y=a(x−h)2+ky equals a open paren x minus h close paren squared plus k

𝑦=𝑎(𝑥−ℎ)2+𝑘

, where

(h,k)open paren h comma k close paren

(ℎ,𝑘)

is the vertex.

vertex = min/max point?

recognizing it’s 2x not x

don’t ask me either

look at the number of marks…

deducing that x<0 is also a solution…

if they intersect at x=1/2

you can deduce that (2x-1) is a factor

area of a parallelogram without height
is ABSintheta

bearing: trig ratios

just some notes to refer to from spec

area of a segment

formulas for surface area and volume good for calculus problems

concavity checking

determining the nature of a stationary point

standard differentials

standard integrals (you dont need allat for the mocks tho)

laws of logs

model wording for iterations/cobweb/staircase etc numerical methods

specifically a

trig identities

double and half identities
(you don’t need to know half tan identity but maybe double)

in these questions just deducing 0/+- 180
just ponder where sin/cos/tan is 0 so just to get that extra mark