Non-logic/proof notes

Question 1

Change of base law

Answer 1

Question 2

Order of graph transformations

Answer 2

See functions cards in A2 deck

Question 3

Square root of (-5)^2

Answer 3

It’s 5, not -5

Question 4

When does trapezium rule give over/under-estimate

Answer 4

Question 5

Maybe know proper formula for trapezium rule

Answer 5

https://www.savemyexams.com/a-level/maths_pure/edexcel/18/revision-notes/10-numerical-methods/10-1-solving-equations/10-1-5-trapezium-rule-numerical-integration/

Question 6

Quadrilaterial family tree

Answer 6

Using the chart below we can answer such questions as:
- Is a Square a type of Rectangle? (Yes)
- Is a Rectangle a type of Kite? (No)

Question 7

What is the key to finding the point of intersection of these graphs?

Answer 7

Recognising that the point of intersection is where the gradients are the same (as the graphs ‘touch’ // meet tangentally)

Question 8

Neat trick

Answer 8

Multinomial expansion

Question 9

Relate cos and sin

Answer 9

Question 10

Use trapezium rule formula to do

Answer 10

Question 11

Know first 4 pythagorean triples

Answer 11

Question 12

Prime numbers under 110

Answer 12

+ 101, 103, 107, 109

Question 13

Square numbers up to 20^2

Answer 13

Question 14

Square root approximations up to root 10

Answer 14

Question 15

1 over root 2 // root 2 over 2

Answer 15

Question 16

root 3 over 2

Answer 16

Question 17

1 over root 3 // root 3 over 3

Answer 17

Question 18

e and e^2

Answer 18

Question 19

pi and pi^2

Answer 19

Question 20

pi/2 and pi/3

Answer 20

Question 21

Swapping limits of integration

Answer 21