Maths

Question 1

unique factorisation theorem

Answer 1

every integer greater than 1 can be written as a product of its prime factors

Question 2

product/pi notation

Answer 2

repeated multiplication
https://mathmaine.com/2018/03/04/pi-notation/

Question 3

product rule for counting

Answer 3

to find the total number of outcomes for 2 or more events, multiply the number of outcomes for each event together

Question 4

inequality notation to specify error intervals due to truncation or rounding

Answer 4

for truncation:
the # in question ≤ x < UB

for rounding:
LB ≤ x < UB

Question 5

sketch graphs of:
y α x^3
y α root x
y α 1/x
y α 1/x^2

Answer 5

see revision book

Question 6

how do you find approximate solutions to equations using iteration?

Answer 6

sub x0 into iteration formula they give (or rearrange to make x the subject)
keep going until results are the same to the required degree of accuracy

Question 7

what conditions do similar triangles satisfy?

Answer 7

all 3 pairs of angles are =
all 3 pairs of sides are in the same ratio
2 sides are in the same ratio & the angle in b/w is =

Question 8

properties of quadrilaterals (kite & rhombus mainly)

Answer 8

https://www.bbc.co.uk/bitesize/articles/z4gsb7h#zp4vcxs

Question 9

order of graph transformations

Answer 9

multiplication stuff first
inside brackets first

Question 10

exact values for sin

Answer 10

sin0 = 0
sin30 = 1/2
sin45 = root2 / 2
sin60 = root3 / 2
sin90 = 1

Question 11

exact values for cos

Answer 11

cos0 = 1
cos30 = root3 / 2
cos45 = root2 / 2
cos60 = 1/2
cos90 = 0

Question 12

exact values for tan

Answer 12

tan0 = 0
tan30 = root3 / 3
tan45 = 1
tan60 = root3

Question 13

SA of sphere

Answer 13

4πr^2

Question 14

curved SA of cone

Answer 14

πrl

Question 15

volume of cone

Answer 15

1/3πr^2h

Question 16

SUVAT equations

Answer 16

v = u + at
s = ut + 1/2at^2
v^2 = u^2 + 2as
s = vt -1/2at^2
s = 1/2(u+v)t

Question 17

how to add & subtract in standard form

Answer 17

1. make sure powers of 10 are the same
2. add/subtract the front numbers
3. ensure answer is in correct standard form

Question 18

how to multiply & divide in standard form

Answer 18

1. multiply/divide front numbers
2. add/subtract powers of 10

Question 19

nth term formula

Answer 19

nth term = a + (n-1)d

Question 20

sum to n terms formula

Answer 20

Sn = n/2(2a + (n-1)d)

Question 21

quadratic sequences

Answer 21

the difference b/w first difference is the same
coefficient of n^2 is half of this 2nd difference
to find nth term, sub into xn^2 then find operation that links this value to the term

Question 22

nth term for geometric sequence

Answer 22

an = a1.r^(n-1)

Question 23

independence formulae

Answer 23

P(A ∩ B) = P(A)P(B)
&
P(A ∩ B) = P(A) × P(B|A)
Y2 AL multiplication formula

Question 24

formulae for UQ & LQ

Answer 24

LQ- n+1/4
UQ- 3 x n+1/4

Question 25

nth term for triangle numbers

Answer 25

n(n+1) / 2