mathematics form 3 (4)
DESCRIPTION
Mathematics Syllabus Form 3, MalaysiaTRANSCRIPT
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A variable is a quantity that changes in value.
A variable is usually represented by an alphabet, for example x, y.
EXAMPLES
The number of participants in a competition can be represented by n.
The output of eggs at a poultry can be represented by x.
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A constant is a quantity of a fixed value.EXAMPLES
1 m = 100 cm
1 kg = 1000 g
The values of a variable can be expressed in the form of integers, fractions and decimals.EXAMPLES
31 km
50.75 g
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7.2 FORMULAE A formula is an equation that relates a few variables.
The value of a variable in a formula can be determined if the values of other variables are given.
Subject of a formula is a variable to be expressed in term of other variables.
EXAMPLE
a is the subject of the formula in terms of t, u and v.
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Expressing a certain variable as the subject of the formula is a process of rewriting a formula so that one of the variables becomes the subject of the formula.
This often involves
- the operations of addition, subtraction, multiplication and division.
- the operations of indices.
If a variable occurs at both sides of an equation, the variable is NOT a subject.EXAMPLE
Then, a is not the subject.
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EXAMPLESExpress x as the subject of the formula for each formula below.
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CHAPTER 8SOLID GEOMETRY III
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8.1 RIGHT PRISM AND RIGHT CIRCULAR CYLINDER
A prism is a solid which has two or more parallel and congruent polygons as faces.
A right prism is a prism where the two end-faces are polygons that are at right angles to the other rectangular surface.
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A cylinder is a solid with two circular ends and uniform cross section of circular shape.
A right circular cylinder with its axis perpendicular to both its ends.
Axis of a cylinder is the line connecting the centre of both of its ends.
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Volume of a right prism.
Volume of a right circular cylinder.
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A pyramid is a solid with its base in the form of a polygon and other surfaces in the form of triangles with a common vertex.
A right pyramid is a pyramid with its vertex situated vertically above the centre of the base.
8.2 RIGHT PYRAMID AND RIGHT CIRCULAR CONE
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A right circular cone is a solid in the form of a right pyramid, but its base is in the form of a circle and has only one curved surface.
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Volume of a right pyramid.
Volume of a right circular cone.
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8.3 SPHERE
A sphere is a solid where all the points on its surface are the same distance from a fixed point.
The fixed point is known as the centre of the sphere.
Hemisphere
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Volume of a sphere.
Volume of a hemisphere.
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8.4 COMPOSITE SOLID
Volume of a composite solid can be calculated by identifying each solid and finding their volumes separately.
Then, total up the volumes of all parts.
EXAMPLE
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CHAPTER 9SCALE DRAWINGS
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9.1 SCALE DRAWINGS
A scale drawing is a drawing that represents a real object with its size reduced or enlarged according to a given ratio.
Scale of a drawing
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A scale is a ratio that compares a length on a drawing in relation to its actual length.
(i) The scale is normally in the form of 1 : n where n = 1, 2, 3, 4 and so on.
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(ii) For a scale of 1 : n,(a) If n = 1, the size of the drawing is the same as
the size of the actual object.
(b) If n > 1, the size of the drawing is smaller than the size of the actual object.
(c) If n < 1, the size of the drawing is bigger than the size of the actual object.
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EXAMPLE 1
In the diagram below, CD is the scale drawing of AB.
Find the scale used. Solution:
Scale = 4cm : 12 cm = 4 : 12 = 1 : 4
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EXAMPLE 2
In the diagram, draw trapezium P, using the scale of 1 : 2.
Solution:
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EXAMPLE 3 Draw the above shape to the scale of 1 : 5.
Solution:
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CHAPTER 10TRANSFORMATIONS II
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10.1 SIMILARITY
The word similar implies a comparison between objects which have the same properties in common.
Similar figures have the same shape but the sizes may be different.
Two shapes are similar if the
- corresponding angles are the same.
- pair of corresponding sides are in a constant ratio.