MATHEMATICS FORM 3- Amal Sufiah Akmal Shukri

- Tunku Kurshiah College - Form 2N (2014)

CONTENTS ... Chapter 1 - Lines and Angles II Chapter 2 - Polygons II Chapter 3 - Circles II Chapter 4 - Statistics II Chapter 5 - Indices Chapter 6 - Algebraic Expressions III Chapter 7 - Algebraic Formulae Chapter 8 - Solid Geometry III Chapter 9 - Scale Drawings Chapter 10 - Transformations II Chapter 11 - Linear Equations II Chapter 12 - Linear Inequalities Chapter 13 - Graphs of Functions Chapter 14 - Ratios, Rates and Proportions II Chapter 15 - Trigonometry

CHAPTER 1LINES AND ANGLES II

1.1 ANGLES ASSOCIATED WITH PARALLEL LINES

Angles are the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line.

Parallel lines are lines on the same plane that never meet, no matter how far they are extended.

In this topic, we will learn about transversal and the angles formed can be classified as corresponding angles, alternate angles or interior angles

Transversal A transversal is a

straight line that intersects two or more straight lines.

The figure on the right shows two parallel lines AC and DF intersected by the transversal MN.

Corresponding Angles

Corresponding angles are equal in size.

The figures on the right are the examples of corresponding angles.

To identify corresponding angles, look for angles formed by lines that resemble the letter 'F'.

Alternate angles are equal in size.

The figures on the right shows the examples of alternate angles.

To identify alternate angles, look for angles formed by lines that resemble the letter 'Z'.

Alternate Angles

Interior angles are angles between parallel lines on the same side of transversal.

The sum of two interior angles is 180 degrees.

The figures on the right are the examples of interior angles.

To identify interior angles, look for angles formed by lines that resemble the letter 'C'.

Interior Angles

EXAMPLE 1CORRESPONDING ANGLES

Find the value of x in the diagram above.

Solution: 2x = 130 degrees Hence,

EXAMPLE 2ALTERNATE ANGLES

In the following diagram, BCD and ACE are straight lines. Find the value of x.

Solution:

EXAMPLE 3INTERIOR ANGLES

Find the value of x in the diagram above.

Solution:

CHAPTER 2POLYGONS II

A polygon is a closed figure with at least three straight lines as its sides.

An irregular polygon is one with unequal sides or interior angles.

The axis of symmetry of a polygon is a line that divides the polygon into two identical parts.

Polygons

A regular polygon is a polygon in which all sides are of equal length and all interior angles are of equal size.

The number of axes of symmetry of a regular polygon is always the same as the number of its sides.

2.1 REGULAR POLYGONS

EXAMPLES OF REGULAR POLYGONS

Given that QPR is a straight line, then

u degrees is an interior angle formed between two adjacent sides PQ and PN.

v degrees is an exterior angle formed between the adjacent side PN and the extended side PR of the polygon.

2.2 ANGLES OF POLYGONS

The sum of the interior angle and the exterior angle is 180 degrees.

The sum of the exterior angles of a regular polygon with n sides is 360 degrees.

The sum of the interior angles of a regular polygon with n sides is (n - 2) x 180 degrees.

In a regular polygon with n sides,

a) the size of each interior angle

b) the size of each exterior angle

EXAMPLE 1

In the diagram below, AB, CD, EF and GF are straight lines.

Find the value of x.

Solution: The sum of exterior angle = 360 degrees

EXAMPLE 2

The diagram shows an irregular polygon.

Find the value of x.

Solution: Given a polygon with 6 sides, so n = 6. The sum of interior angles

Hence,

EXAMPLE 3The diagram below shows a part of a regular polygon.

Find the number of sides of the polygon.Method 1 Size of interior angle 144 degrees =

then,

Method 2 Exterior angle

Exterior angle

then,

CHAPTER 3CIRCLES II

A chord is a straight line connecting two points on the circumference of a circle.

The diameter of a circle is a chord that passes through the centre of a circle.

The diameter of a circle divides the circle into two equal parts.

Any diameter of a circle is an axis of symmetry.

If the chord KL intersects perpendicularly with radius PO, then KM = ML.

3.1 SYMMETRY OF CIRCLES

EXAMPLEThe diagram shows a circle with centre O. The straight line UOV is perpendicular to the chord PUQ. Given that PQ = 18cm and OV = 15cm.

Calculate the length of UV, in cm.

Solution:

Consider triangle OUQ,

Hence,

3.2 PROPERTIES OF ANGLES IN CIRCLES

The angle at the centre is twice the angle at the circumference.

The angles at the circumference subtended by the common arc are all equal.

The angle subtended at the circumference in a semicircle is a right angle.