Formulae Flashcards
ax^2 + bx + c = 0 has roots
-b + or - √(b^2 — 4ac)
over
2a
a^xa^y
a^(x + y)
a^x divided by a^y
a^(x — y)
(a^x)^y
a^xy
x = a^n ⟺
n = log x for a > 0 & x > 0
a
log x + log y
a a
log (xy)
a
log x — log y
a a
log (x/y)
a
k log x
a
log (x^k)
a
A straight line graph with gradient m passing through (x1, y1) has equation
y — y1 = m(x — x1)
Straight lines with gradients m1 and m2 are perpendicular when…
m1m2 = -1
General term of an arithmetic progression
Un = a + (n — 1) d
General term of a geometric progression
Un = ar^(n — 1)
In the triangle ABC, the sine rule:
a b c
— = — = —
sinA sin B sinC
In triangle ABC, cosine rule:
a^2 = b^2 + c^2 — 2bccosA
In triangle ABC, area =
1/2 absinC
cos^2 A + sin^2 A =
1
sec^2 A =
1 + tan^2 A
cosec^2 A =
1 + cot^2 A
sin2A =
2 sinAcosA
cos 2A=
cos ^2 A — sin^2 A
tan 2A =
2 tan A
over
1 — tan^2 A
Circumference
2π r = π d
Area of a circle
π r^2
Pythagoras’s theorem, where c is the hypotenuse
c^2= a^2 + b^2
Area of a trapezium where a & b are side lengths and h is their perpendicular separation
1/2(a+b)h
Volume of a prism
Area of the cross-section x length
For a circle of radius r, where an angle at the centre of θ radians subtends an arc of length s and encloses an associated sector of area A:
s= r θ Area = 1/2 r^2 θ
Derivative of x^n
nx^(n — 1)
Derivative of sin kx
k cos kx
Derivative of cos kx
—k sin kx
Derivative of e^kx
ke^kx
Derivative of ln x
1/ x
Derivative of f(g) + g(x)
f’(x) + g’(x)
Derivative of f(x)g(x)
f’(x)g(x) + f(x)g’(x)
Derivative of f(g(x))
f’(g(x))g’(x)
Integral of x^n
1
— x^(n + 1) + c, n != —1
n + 1
Integral of cos kx
1 over k times by (sin kx) + c
Integral of sink kx
— 1/k times by cos kx + c
Integral of e^kx
1/k times by e^kx + c
Integral of 1/x
ln|x| + c, x != 0
Integral of f’(x) + g’(x)
f(x) + g(x) + c
Integral of f’(g(x))g’(x)
f(g(x)) + c
Area under a curve
b
∫ y dx (y >= 0)
a
|xi + yj|
= √(x^2 + y^2)
|xi + yj + zk|
= √(x^2 + y^2 + z^2)
Friction
F <= μR
Newtons 2nd law
F = ma
For motion in a straight line with variable acceleration: v =
v = dr/ dt
For motion in a straight line with variable acceleration: a=
dv/dt = d^2r/ dt^2
For motion in a straight line with variable acceleration: r =
∫v dt
For motion in a straight line with variable acceleration: v = (using integration)
∫a dt
For motion in a straight line with variable acceleration: v= (using s)
v = ds/ dt
For motion in a straight line with variable acceleration: a= (using s)
a= dv/dt = d^2s/dt^2
The mean of a set of data
-
X = Σx / n = Σ fx / Σf
The standard Normal variable
Z = X — μ where X ~ N(μ, σ^2)
over
σ
