C2

Question 1

Dividing polynomials by (x±p)

Answer 1

Put in order of powers

1) divide highest power of x by x
2) put the answer in the column that’s up and along to the right
3) multiplly by (x±p) then subtract
4) bring the next term down

Repeat for all terms

Question 2

Factor theorem

Answer 2

If f(x) is a polynomial and f(p)=0

Then (x-p) is a factor of f(x)

Question 3

Sine rule to find a length

Answer 3

a/sinA = b/sinB

Question 4

Sine rule to find an angle

Answer 4

sinB/b = sinC/c

Question 5

Cosine rule to find a side

Answer 5

a²=b²+c²-2bcCosA

Question 6

Cosine rule to find an angle

Answer 6

cosA= b²+c²-a²/2bc

Question 7

Area of a triangle

Answer 7

½absinC

½acsinB

½bcsinA

Question 8

Pythagoras rules

Answer 8

SOHCAHTOA

sin= opp/hyp

Cos= adj/hyp

Tan= opp/adj

a²+b²=c²

Question 9

Form of a logarithm

Answer 9

Logₐn=x

ₐ= number

n = answer

x = power

a^x=n

Question 10

Logs - multiplication law

Answer 10

logₐxy=logₐx+logₐy

Question 11

Logs - division law

Answer 11

logₐ(x/y)=logₐx-logₐy

Question 12

Logs - power law

Answer 12

logₐ(x)^k=Klogₐx

Question 13

logs - negative power law

Answer 13

Logₐ(1/x)= -logₐx

Question 14

How to solve a^x=b with logs

Answer 14

Take log to base 10 of each side and solve

Question 15

Change of base rule for logs

Answer 15

logₐx= logₔx/logₔa

ₔ=b

Question 16

Midpoint of (x₁,y₁) and (x₂,y₂)

Answer 16

x₁+x₂/2, y₁+y₂/2

Question 17

equation of a circle centre (a,b) and radius r

Answer 17

(X-a)²+(y-b)²=r²

Question 18

Angles in a semi circle =

Answer 18

90 degrees

Question 19

Angle between a tangent and a radius=

Answer 19

90 degrees

Question 20

Conversions for degrees & radians

Answer 20

Degrees –> radians x π/180

Radians –> degrees x 180/π

Question 21

If a circe has an arc and radius ‘r’ then how big will the angle and the centre be

Answer 21

1 radian

Question 22

Arc length in radians

Answer 22

L = rθ

Radius x angle at centre

Question 23

Area of a sector in radians

Answer 23

½r ²θ

½ x radius x radius x angle at centre

Question 24

Area of a segment in radians

Answer 24

½r ²(θ - sinθ)

0.5 x radius x radius x (angle at centre - SIN angle at centre)

Question 25

What is common ratio

Answer 25

What you divide/multiply by to get the next term of a geometric series

Question 26

Nth term of geometric series

Answer 26

arⁿ-¹

First term x (common ratio)ⁿ-¹

Question 27

Sum to n terms of geometric series

Answer 27

Sn = a(1-rⁿ)/1-r

Question 28

Sum to infinity of geometric series

Answer 28

S∞= a/1-r

Question 29

Quadrants that trigonometrical functions are positive

Answer 29

SACT

1st - sin
2nd - sin, cos, tan
3rd - cos
4th - tan

Question 30

How to solve

Sinθ= 0.3 For 0

Answer 30

1- check if the interval is degrees or radians
2- find the acute angle with sin-¹ to 1.d.p.
3- draw cast diagram with acute angles in for when it will be positive
4- calculate the angles from y=0