Core 2

Question 0

Remainder Theorem

Answer 0

When a polynomial f(x) is divided by (ax - b) the remainder is given by f(b/a)

Question 1

Factor Theorem

Answer 1

If (x-a) is a factor of f(x) then:
> f(a) = 0
> x=a is a root/solution to the equation f(x) = 0

Question 2

Sine Rule

Answer 2

a/sinA = b/sinB = c/sinC
OR
sinA/a = sinB/b = sinC/c

Question 3

Cosine Rule

Answer 3

a² = b² + c² - 2bc cosA
OR
cosA = (b²+c²-a²) / (2bc)

Question 4

Area of a Triangle

Answer 4

1/2ab*sinC

Question 5

The Ambiguous Case

Answer 5

When the angle you are finding is bigger than the angle you are given there are two possible results as two triangles can be drawn with the given information ( two sides, one angle)

In general:
sin(180-x) = sinx

Question 6

Logs

Answer 6

x = loga n
x equals log base a of n
Means
a^x = n
a to the power x equals n

Question 7

Logs

Multiplication Law

Answer 7

loga x + loga y = loga xy

Log base a of x plus log base a of y equals log base a of xy

Question 8

Logs

The Division Law

Answer 8

loga x - loga y = loga (x/y)

log a of x minus log a of y equals log a of x/y

Question 9

Logs

Changing Bases

Answer 9

loga x = (logb x) / (logb a)

Log base a of x equals log b base of x divided by log base b of a

Question 10

Logs
Changing Bases - Special Case
loga b

Answer 10

loga b = (logb b) / (logb a) = 1 / (logb b)

log base a of b equals 1 divisions sed by log base b of b

Question 11

Midpoint of a Line

Answer 11

Line (x1,y1) -> (x2,y2)

Midpoint = (x1+x2 / 2, y1+y2 / 2)

Question 12

Distance Between Two Points On A Line

Answer 12

√[(x1-x2)² + (y1-y2)²]

Question 13

Equation of a Circle

Answer 13

(x-a)² + (y-b)² = r²

Question 14

Equation of a Circle

Centre

Answer 14

(a,b)

Question 15

Equation of a Circle

Radius

Answer 15

r

Question 16

360° In Radians

Answer 16

2π radians

Question 17

180° In Radians

Answer 17

π radians

Question 18

Converting from Radians to Degrees

Answer 18

multiply by 180/π

Question 19

Converting from Degrees to Radians

Answer 19

Divide by 180/π

Question 20

Length of an Arc When Angle is in Radians

Answer 20

l = rθ

l = length of arc
r = radius of circle
θ = angle in radians

Question 21

Geometric Series

General Term

Answer 21

a r^n-1

a= first term 
r = common ratio
n = term number

Question 22

Sum of a Geometric Series

Answer 22

Sn = a(1-r^n) / r-1

Sn = sum
a = first term
r = common ratio
n = number of terms

Question 23

Geometric Series

Definition

Answer 23

To get from one number to the next, multiply by the same number each time, the common ratio

Question 24

Sum to Infinity of a Geometric Sequence

Answer 24

If -1< r >1 the series is convergent and the sum to infinity exists
This means that r^n tends to 0 as n tends towards infinity
In this case: SumToInfinity = a / 1-r

Otherwise the series is divergent and the sum to infinity does not exist

Question 25

Circle Triangle

sinθ

Answer 25

sinθ = y/r

Question 26

Circle Triangle

cosθ

Answer 26

cosθ = x/r

Question 27

Circle Triangle

tanθ

Answer 27

tanθ = y/x

Question 28

Types of Stationary Point

Answer 28

Maximum Point
Minimum Point
Point of Inflection

Question 29

d²y/dx²

Minimum Point

Answer 29

d²y/dx² > 0

Question 30

d²y/dx²

Maximum Point

Answer 30

d²y/dx² < 0

Question 31

d²y/dx²

Point of Inflection

Answer 31

d²y/dx² = 0

Question 32

Stationary Points

Gradient

Answer 32

f’(x) = 0

Question 33

Trigonometrical Identities

Answer 33

tanθ = sinθ / cosθ

sin²θ + cos²θ = 1

Question 34

sin 30

Answer 34

1 / 2

Question 35

cos 30

Answer 35

√3 / 2

Question 36

tan 30

Answer 36

√3 / 3

Question 37

sin 60

Answer 37

√3 / 2

Question 38

cos 60

Answer 38

1 / 2

Question 39

tan 60

Answer 39

√3

Question 40

sin 45

Answer 40

√2 / 2

Question 41

cos 45

Answer 41

√2 / 2

Question 42

tan 45

Answer 42

1

Question 43

Trapezium Rule

Answer 43

Area Under Line

≈ 1/2 h [ y0 + 2( y1 + y2 + … + yn-1) + yn]