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31 cardsGCE O/L Mathematics (Sri Lanka)

GCE O/L Mathematics: Indices, Logarithms and Geometry Facts

Flashcards on laws of indices, logarithms, surds, standard form, sets, statistics and circle and angle theorems for GCE Ordinary Level Mathematics in Sri Lanka. Original study material.

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Law of indices: multiplication

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Law of indices: multiplication

a^{m} \times a^{n} = a^{m + n}

Law of indices: division

a^{m} \div a^{n} = a^{m - n}

Law of indices: power of a power

(a^{m})^{n} = a^{mn}

Zero index

a^{0} = 1

for

a \neq = 0

Negative index

a^{- n} = \frac{1}{a ^{n}}

Fractional index

a^{\frac{m}{n}} = (n a)^{m}

Definition of a logarithm

lo g_{a} b = c

means

a^{c} = b

Log of a product

lo g_{a} (x y) = lo g_{a} x + lo g_{a} y

Log of a quotient

lo g_{a} \frac{x}{y} = lo g_{a} x - lo g_{a} y

Log of a power

lo g_{a} x^{n} = n lo g_{a} x

ab

a \times b

(a)^{2}

a

Standard form

A number written as

a \times 1 0^{n}

with

1 \leq a < 10

and

n

an integer.

HCF

The largest number that divides each of the given numbers exactly.

LCM

The smallest number that is a multiple of each of the given numbers.

Prime number

A number greater than

1

whose only factors are

1

and itself.

Mean, median and mode

The average value, the middle value when ordered, and the most frequent value.

Range

The largest value minus the smallest value.

Complement of a set

A

The elements of the universal set that are not in

A

, written

A^{'}

Intersection of sets

A \cap B

contains the elements that belong to both

A

and

B

Exterior angle of a triangle

Equals the sum of the two opposite interior angles.

Angle at the centre of a circle

Twice the angle at the circumference standing on the same arc.

Angles in the same segment

Angles standing on the same arc in the same segment are equal.

Opposite angles of a cyclic quadrilateral

They add up to

18 0^{\circ}

Tangent and radius

A tangent to a circle is perpendicular to the radius at the point of contact.

Tangents from an external point

The two tangents have equal length.

Angle in a semicircle

It is a right angle.

Alternate angles

Equal when two parallel lines are cut by a transversal.

Corresponding angles

Equal when two parallel lines are cut by a transversal.

Co-interior angles

Add up to

18 0^{\circ}

when the lines are parallel.

Rates (Sri Lanka local authorities)

A yearly tax charged as a percentage of the assessed annual value of a property, often paid in quarterly instalments.

GCE O/L Mathematics (Sri Lanka) in Sri Lanka

In Sri Lanka, GCE O/L Mathematics (Sri Lanka) is part of: National exams in Sri Lanka.

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