Mathematics Form 3 1x867
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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 1 LINES 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 •
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'.
Interior 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'.
EXAMPLE 1
CORRESPONDING ANGLES
Find the value of x in the diagram above. Solution: 2x = 130 degrees Hence,
In the following diagram, BCD and ACE are straight lines. Find the value of x.
EXAMPLE 2
ALTERNATE ANGLES
Solution:
EXAMPLE 3
INTERIOR ANGLES
Find the value of x in the diagram above. Solution:
CHAPTER 2 POLYGONS II
Polygons •
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.
2.1 REGULAR 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.
EXAMPLES OF REGULAR POLYGONS
2.2 ANGLES OF 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.
•
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
In the diagram below, AB, CD, EF and GF are straight lines.
EXAMPLE 1
Find the value of x. Solution: The sum of exterior angle = 360 degrees
The diagram shows an irregular polygon.
Find the value of x.
EXAMPLE 2
Solution: Given a polygon with 6 sides, so n = 6. The sum of interior angles
Hence,
EXAMPLE 3 The diagram below shows a part of a regular polygon.
Find the number of sides of the polygon. Method 1 Method 2 Size of interior angle Exterior angle 144 degrees = Exterior angle then, then,
CHAPTER 3 CIRCLES II
3.1 SYMMETRY OF CIRCLES •
A chord is a straight line connecting two points on the circumference of a circle.
•
The diameter of a circle is a chord that es 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.
EXAMPLE The diagram shows a circle with centre O. The straight line UOV is perpendicular to the chord PUQ. Given that PQ = 18cm and OV = 15cm.
Solution:
Calculate the length of UV, in cm. 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.
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 1 LINES 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 •
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'.
Interior 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'.
EXAMPLE 1
CORRESPONDING ANGLES
Find the value of x in the diagram above. Solution: 2x = 130 degrees Hence,
In the following diagram, BCD and ACE are straight lines. Find the value of x.
EXAMPLE 2
ALTERNATE ANGLES
Solution:
EXAMPLE 3
INTERIOR ANGLES
Find the value of x in the diagram above. Solution:
CHAPTER 2 POLYGONS II
Polygons •
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.
2.1 REGULAR 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.
EXAMPLES OF REGULAR POLYGONS
2.2 ANGLES OF 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.
•
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
In the diagram below, AB, CD, EF and GF are straight lines.
EXAMPLE 1
Find the value of x. Solution: The sum of exterior angle = 360 degrees
The diagram shows an irregular polygon.
Find the value of x.
EXAMPLE 2
Solution: Given a polygon with 6 sides, so n = 6. The sum of interior angles
Hence,
EXAMPLE 3 The diagram below shows a part of a regular polygon.
Find the number of sides of the polygon. Method 1 Method 2 Size of interior angle Exterior angle 144 degrees = Exterior angle then, then,
CHAPTER 3 CIRCLES II
3.1 SYMMETRY OF CIRCLES •
A chord is a straight line connecting two points on the circumference of a circle.
•
The diameter of a circle is a chord that es 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.
EXAMPLE The diagram shows a circle with centre O. The straight line UOV is perpendicular to the chord PUQ. Given that PQ = 18cm and OV = 15cm.
Solution:
Calculate the length of UV, in cm. 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.
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