Actual Formula Test #1 Test #2 Formula

(a + b)(a2

– ab + b2) a

3+ b

3=

(a – b)(a2

+ ab + b2) a

3– b

3=

x = – b ± b2

– 4ac 2a

Quadratic Formula

f(x) = f( – x) Test for even functions

f( – x) = – f(x) Test for odd

functions

(x – h)2

+ (y – k)2

= r2

General equation of a circle

y = r2

– x2

Equation of a semi-circle

0 limx → ∞

1x =

1

2 sin

π

4 =

1

2 cos

π

4 =

1 tan π

4 =

32

sin π

3 =

12 sin

π

6 =

12 cos

π

3 =

32

cos π

6 =

3 tan π

3 =

13

tan π

6 =

sinθcosθ

tanθ =

cosθsinθ

cotθ =

1 sin2θ + cos

2θ =

1 + cot2θ = cosec

2θ Other trig identity

tan2θ + 1 = sec

2θ Other trig identity

sinAa

= sinBb

Sine rule

a2

= b2

+ c2

– 2bccosA Cosine rule for side

cosA = b

2+ c

2– a

2

2bc Cosine rule for an

angle

A = 12 ab sinC

Area of a triangle

using trig

cosx cosy + sinx siny cos(x – y) =

cosx cosy – sinx siny cos(x + y) =

sinx cosy + cosx siny sin(x + y) =

sinx cosy – cosx siny sin(x – y) =

tanx + tany1 – tanx tany

tan(x + y) =

tanx – tany

1 + tanx tany tan(x – y) =

2sinx cosx sin 2x =

cos2x – sin

2x

1 – 2sin2x

2cos2x – 1

cos 2x =

2tanx

1 – tan2x

tan 2x =

tan

θ2

Ratios:

2t

1 – t2

tanθ =

1 – t

2

1 + t2

cosθ =

2t

1 + t2

sinθ =

rsin(θ + α) asinθ + bcosθ =

rsin(θ – α) asinθ – bcosθ =

rcos(θ – α) acosθ + bsinθ =

rcos(θ + α) acosθ – bsinθ =

r = a2

+ b2

tan α = b

a

Where r = and α =

θ = π × n + (-1)n α General solution

for sine

θ = 2π × n ± α General solution for cosine

θ = π × n + α General solution for tan

Graphs

d = (x2 – x1)2 + (y2 – y1)

2 Distance formula

P = x1 + x2

2 , y1 + y2

2

Midpoint Formula

m = y2 – y1

x2 – x1 Gradient Formula

m = tanθ Gradient using trig

y – y1 = m(x – x1) Point-gradient formula

y – y1

x – x1 = y2 – y1

x2 – x1 Two-point formula

m1 = m2 Parallel lines proof

m1m2 = -1 Perpendicular lines proof

d = |ax1 + by1 + c|

a2

+ b2

Perpendicular distance formula

tanθ = m1 – m2

1 + m1m2

Angle between two lines

x = mx2 + nx1

m + n

y = my2 + ny1

m + n

Dividing interval in ratio m:n

dydx

= limh → 0

f(x + h) – f(x)h

First principle differentiation

n xn – 1

ddx

xn

f'(x)n [ f(x)]n – 1

ddx

[ f(x)]n

=

vu' + uv' ddx

uv

vu' – uv'

v2

d

dx u

v

x = – b

2a Axis of symmetry

in quadratic

∆ = b2

– 4ac The discriminant

– b

a Sum of roots

ca

Sum of roots two at a time

– da

Sum of roots three at a time

ea

Sum of roots four at a time

x2

= 4ay

(0, a)(0, 0)

Equation of basic parabola.

Focus Vertex

(x – h2) = 4a(y – k)

(h, k)(h, k + a)

General equation of parabola.

Focus Vertex

x = 2at

y = at2

Parametric form of: x

2= 4ay

Tn = a + (n – 1)d Term of an arithmetic series

Sn = n2

(a + l)

Sn = n

2 [2a + (n – 1)d]

Sum of an arithmetic series

S = (n – 2) × 180° Sum of interior angles of an n-sided polygon

A = lb Area of rectangle

A = x2

Area of a square

A = 12 bh

Area of a triangle

A = bh Area of a parallelogram

12 xy

Area of rhombus

A = 12 h(a + b)

Area of trapezium

A = π r2

Area of circle

S = 2(lb + bh + lh) Surface area of a rectangular prism

V = lbh Volume of a rectangular prism

S = 6x2

Surface area of a

cube

V = x3

Volume of a cube

S = 2π r2 + 2π r h

Surface area of a cylinder

V = π r2h Volume of a

cylinder

S = 4π r2

Surface area of a sphere

V = 43 π r

3

Volume of a

sphere

S = π r2 + π rl Surface area of a

cone

V = 13 π r

2h

Volume of a cone

xn + 1

n + 1 + c

⌡⌠ x

n dx

h2 [ (y0 + yn) + 2(y1 + y2 + ... + yn – 1)]

where h = b – a

n

Trapezoidal rule

h3

[ (y0 + yn) + 4(y1 + y3) + 2(y2 + y4)]

where h = b – a

n

Simpson’s Rule

(ax + b)n + 1

a(n + 1) + c

⌡⌠ (ax + b)

n dx

V = π ⌡⌠ y

2 dx

Volume about the x-axis

V = π ⌡⌠ x

2 dy

Volume about the

y-axis

ex d

dx e

x

f'(x) ef(x)

ddx

e f(x)

ex + c

⌡⌠ e

x dx

1a

eax + b

+ c

⌡⌠ e

ax + b dx

loga x + loga y loga (xy)

loga x – loga y loga xy

n loga x loga xn

loga x = loge xloge a

Change of base rule

1x

ddx

loge x

f'(x)f(x)

ddx

loge f(x)

loge x + c ⌡⌠ 1

x dx

loge f(x) + c ⌡⌠ f'(x)

f(x) dx

180° π radians =

C = 2πr Circumference of a circle

l = rθ Length of an arc

A = 12 r

2θ

Area of a sector

A = 12 r

2(θ – sinθ)

Area of a minor

segment sinx ≈ x tanx ≈ x cosx ≈ 1

Small Angles

f'(x) cos [ f(x)] ddx

sin [ f(x)]

– f'(x) sin [ f(x)] ddx

cos [ f(x)]

f'(x) sec2f(x) d

dx tan f(x)

1a

sin(ax + b) + c

⌡⌠ cos(ax + b) dx

– 1a

cos(ax + b) + c

⌡⌠ sin(ax + b) dx

1a

tan(ax + b) + c

⌡⌠ sec

2(ax + b) dx

12 x + 1

4a sin 2ax + c

⌡⌠ cos

2ax dx

12 x – 1

4a sin 2ax + c

⌡⌠ sin

2ax dx

Exponential

Growth & Decay

kQ dQdt

=

Q = Aekt

Quantity

dNdt

= k(N – P)

N = P + Ae

kt

Complex growth and decay

a = ddx

1

2 v

2

Special result for

acceleration

x = a cos(nt + ∈) Displacement for

SHM

..x = – n

2x Acceleration for

SHM

a Amplitude of SHM

2πn

Period of SHM

v2 = n

2(a

2– x

2) Velocity of SHM

.x = Vcosθ.y = Vsinθ

Initial Velocity of projectile

.x = 0.y = – g

Acceleration of a projectile

x = Vt cosθ Horizontal

displacement

y = Vt sinθ – gt2

2 Vertical

displacement

y = – gx2

2V2 (1 + tan

2θ) + xtanθ

Cartesian equation of motion

t = 2V sinθg

Time of flight

x = V2sin 2θg

Range

x = V2

g Max Range

h = V2sin

2θ

2g Greatest height

f-1

[ f(x)] = f[ f-1

(x)] = x Proof for mutually inverse functions

– sin-1

x sin-1

( – x) =

π – cos-1

x cos-1

( – x) =

– tan-1

x tan-1

( – x) =

π2

sin-1

x + cos-1

x =

r = T2

T1 Common ratio in

geometric series

Tn = arn – 1

Term of a geometric series

Sn = a(r

n– 1)

r – 1 for |r| > 1

Sn = a(1 – rn)

1 – r for |r| < 1

Sum of a geometric series

S∞ = a1 – r

Sum to infinity of a geometric series

A = P 1 + r

100 n

Compound interest

formula

If f a + b

2 = 0

Halving the interval

method

a1 = a – f(a)f'(a)

Newton’s method of approximation

n – k + 1k

× ba

TK + 1

TK =

n!(n – r)!

nPr =

n!s! t! ...

Arrangements

where some are alike

(n – 1)! Arrangements in a circle