Formulae

Question 1

ax^2 + bx + c = 0 has roots

Answer 1

-b + or - √(b^2 — 4ac)
over
2a

Question 2

a^xa^y

Answer 2

a^(x + y)

Question 3

a^x divided by a^y

Answer 3

a^(x — y)

Question 4

(a^x)^y

Answer 4

a^xy

Question 5

x = a^n ⟺

Answer 5

n = log x for a > 0 & x > 0
a

Question 6

log x + log y
a a

Answer 6

log (xy)
a

Question 7

log x — log y
a a

Answer 7

log (x/y)
a

Question 8

k log x
a

Answer 8

log (x^k)
a

Question 9

A straight line graph with gradient m passing through (x1, y1) has equation

Answer 9

y — y1 = m(x — x1)

Question 10

Straight lines with gradients m1 and m2 are perpendicular when…

Answer 10

m1m2 = -1

Question 11

General term of an arithmetic progression

Answer 11

Un = a + (n — 1) d

Question 12

General term of a geometric progression

Answer 12

Un = ar^(n — 1)

Question 13

In the triangle ABC, the sine rule:

Answer 13

a b c
— = — = —
sinA sin B sinC

Question 14

In triangle ABC, cosine rule:

Answer 14

a^2 = b^2 + c^2 — 2bccosA

Question 15

In triangle ABC, area =

Answer 15

1/2 absinC

Question 16

cos^2 A + sin^2 A =

Answer 16

1

Question 17

sec^2 A =

Answer 17

1 + tan^2 A

Question 18

cosec^2 A =

Answer 18

1 + cot^2 A

Question 19

sin2A =

Answer 19

2 sinAcosA

Question 20

cos 2A=

Answer 20

cos ^2 A — sin^2 A

Question 21

tan 2A =

Answer 21

2 tan A
over
1 — tan^2 A

Question 22

Circumference

Answer 22

2π r = π d

Question 23

Area of a circle

Answer 23

π r^2

Question 24

Pythagoras’s theorem, where c is the hypotenuse

Answer 24

c^2= a^2 + b^2

Question 25

Area of a trapezium where a & b are side lengths and h is their perpendicular separation

Answer 25

1/2(a+b)h

Question 26

Volume of a prism

Answer 26

Area of the cross-section x length

Question 27

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:

Answer 27

s= r θ Area = 1/2 r^2 θ

Question 28

Derivative of x^n

Answer 28

nx^(n — 1)

Question 29

Derivative of sin kx

Answer 29

k cos kx

Question 30

Derivative of cos kx

Answer 30

—k sin kx

Question 31

Derivative of e^kx

Answer 31

ke^kx

Question 32

Derivative of ln x

Answer 32

1/ x

Question 33

Derivative of f(g) + g(x)

Answer 33

f’(x) + g’(x)

Question 34

Derivative of f(x)g(x)

Answer 34

f’(x)g(x) + f(x)g’(x)

Question 35

Derivative of f(g(x))

Answer 35

f’(g(x))g’(x)

Question 36

Integral of x^n

Answer 36

1 — x^(n + 1) + c, n != —1 n + 1

Question 37

Integral of cos kx

Answer 37

1 over k times by (sin kx) + c

Question 38

Integral of sink kx

Answer 38

— 1/k times by cos kx + c

Question 39

Integral of e^kx

Answer 39

1/k times by e^kx + c

Question 40

Integral of 1/x

Answer 40

ln|x| + c, x != 0

Question 41

Integral of f’(x) + g’(x)

Answer 41

f(x) + g(x) + c

Question 42

Integral of f’(g(x))g’(x)

Answer 42

f(g(x)) + c

Question 43

Area under a curve

Answer 43

b ∫ y dx (y >= 0) a

Question 44

|x**i** + y**j**|

Answer 44

= √(x^2 + y^2)

Question 45

|x**i** + y**j** + z**k**|

Answer 45

= √(x^2 + y^2 + z^2)

Question 46

Friction

Answer 46

F <= μR

Question 47

Newtons 2nd law

Answer 47

F = ma

Question 48

For motion in a straight line with variable acceleration: v =

Answer 48

v = dr/ dt

Question 49

For motion in a straight line with variable acceleration: a=

Answer 49

dv/dt = d^2r/ dt^2

Question 50

For motion in a straight line with variable acceleration: r =

Answer 50

∫v dt

Question 51

For motion in a straight line with variable acceleration: v = (using integration)

Answer 51

∫a dt

Question 52

For motion in a straight line with variable acceleration: v= (using s)

Answer 52

v = ds/ dt

Question 53

For motion in a straight line with variable acceleration: a= (using s)

Answer 53

a= dv/dt = d^2s/dt^2

Question 54

The mean of a set of data

Answer 54

- X = Σx / n = Σ fx / Σf

Question 55

The standard Normal variable

Answer 55

Z = X — μ where X ~ N(μ, σ^2) over σ