pure

find value of k in y= k(x-2)(x-4)

-substitute in values of x and y from graph

derivative of 2^x

(ln2)(2^x)

find quadratic equation lonking H with x

H= a(x+b)(x+c)

proof by contradiction

a rational number is a number in the form a/b where a and b are integers with no common factors (a/b is in its simplest form)

arithmetic equations

Un = a + (n-1)d

sum: n/2(2a+ (n-1)d)

n/2(a+L)

proving arithmatic sequence sum….

a + (a+d) + (a+2d)…a+(n-1)d

reverse: a+ (n-1)d + a+(2d) + a+d +a

2sum :ADD TOGETHER: 2a + (n-1)d

sum:

geometric sequene equation

un= a x r^n-1

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

proving sum of geometric sequence

Sn: a + ar + ar²…+ar^n-1

multiply by r: ar + ar²

subtract both equation: a-ar^n

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

convergent geometric series equation (sum to infinity)

a/1-r

convergent if r<1

inequality set notation

{x:x<5}U{x:x>10}

area of segment

1/2r²x - r²sinx

x is angle

area of sector

1/2r² x angle

only applies when angle is in radians, not degrees

arc sector length

angle x radius

sine rule

a/sin(A) = b/sin(B) = c/sin(C)

cosine rule

a²=b²+c² -2bcsin(a)

cast diagrams

cos all sin tan

Area of a rhombus

Cross section x cross section /2

Prove using vectors that a shape is a trapezium

Has 2 parallel lines so vectors will be factors of each other

3D vectors: find angle that vector a=2i-3j-k makes with +ve x axis

cosX = x/ magnitude of a

magnitude of a is hypotenuse