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30 cardsGCE O/L Mathematics (Sri Lanka)

GCE O/L Mathematics: Key Formulae

Flashcards on the area, volume, angle, interest, speed, algebra and probability formulae needed for GCE Ordinary Level Mathematics in Sri Lanka. Original study material.

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Area of a circle and circumference

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Area of a circle and circumference

A = π r^{2}

and

C = 2 π r

; in Sri Lankan O/L papers

π = \frac{22}{7}

is often used.

Area of a trapezium

\frac{1}{2} (a + b) h

, where

a

and

b

are the parallel sides.

Area of a triangle

\frac{1}{2} \times base \times height

Volume of a cylinder

π r^{2} h

Volume of a cone

\frac{1}{3} π r^{2} h

Volume of a sphere

\frac{4}{3} π r^{3}

Curved surface area of a cone

π r l

, where

l

is the slant height

r^{2} + h^{2}

Surface area of a sphere

4 π r^{2}

Pythagoras' theorem

In a right-angled triangle,

c^{2} = a^{2} + b^{2}

where

c

is the hypotenuse.

Sum of the interior angles of an

n

-sided polygon

(n - 2) \times 18 0^{\circ}

Each exterior angle of a regular

n

-sided polygon

\frac{36 0 ^{\circ}}{n}

Arc length and sector area (angle

θ

)

\frac{θ}{360} \times 2 π r

and

\frac{θ}{360} \times π r^{2}

Sine, cosine and tangent in a right-angled triangle

sin θ = \frac{opp}{hyp}

cos θ = \frac{adj}{hyp}

tan θ = \frac{opp}{adj}

Simple interest

I = \frac{P R T}{100}

Compound amount after

n

years

A = P (1 + \frac{r}{100})^{n}

Percentage increase

\frac{increase}{original} \times 100

Speed, distance and time

speed = \frac{distance}{time}

Average speed for a whole journey

\frac{total distance}{total time}

Difference of two squares

a^{2} - b^{2} = (a - b) (a + b)

Square of a binomial

(a + b)^{2} = a^{2} + 2 ab + b^{2}

Gradient of a line through

(x_{1}, y_{1})

and

(x_{2}, y_{2})

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Equation of a straight line

y = m x + c

, with gradient

m

and

y

-intercept

c

n

th term and sum of an arithmetic progression

T_{n} = a + (n - 1) d

and

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

Union of two sets

n (A \cup B) = n (A) + n (B) - n (A \cap B)

Number of subsets of an

n

-element set

2^{n}

Probability of an event

P (E) = \frac{favourable outcomes}{all equally likely outcomes}

Mean of a frequency table

\frac{\sum f x}{\sum f}

Ratio of areas of similar figures

The square of the ratio of corresponding lengths.

Back bearing

Add

18 0^{\circ}

if the bearing is less than

18 0^{\circ}

, otherwise subtract

18 0^{\circ}

Litres and cubic centimetres

1 litre = 1000 cm^{3}

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