mathematics form 3 (5)
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Mathematics Syllabus Form 3, MalaysiaTRANSCRIPT
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EXAMPLE 1In the diagram above, which two figures are similar?
Solution: If all the corresponding angles of the two figures are the same and all their corresponding sides are similar in the same ratio, then the two figures are similar. Therefore, figure B is similar to figure C.
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EXAMPLE 2 Find the value of x. Solution:
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10.2 ENLARGEMENT
Enlargement is a transformation with a fixed point known as the centre of enlargement.
All the other points on the plane will move from the fixed point following a constant ratio.
The ratio is known as scale factor.
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Properties of enlargement
- the object is similar to the image.
- C'B' is the image of CB under an enlargement at centre O and scale factor of k.
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EXAMPLE
Draw the image of triangle PQR under an enlargement at centre O with scale factor 3.
Solution:
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Area of image:
Where k is the scale factor.
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CHAPTER 11LINEAR EQUATIONS II
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11.1 LINEAR EQUATIONS IN TWO VARIABLES
Linear equation in two variables is an equation involving numbers and linear terms in two variables.
Example : x + 2y
Linear equation in two variables can be formed based on given information.
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The value of a variable can be determined when the value of the other variable is given.
EXAMPLE
Given that x + 2y = 5, find the value of x if y = 1.
Solution:
Substitute y = 1 in the equation, x + 2 (1) = 5 x = 5 - 2 x = 3
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EXAMPLES
Determine whether 2x + 3 = 9 is a linear equations in two variables.
Solution:
No, because it is a linear equation in one variable.
Form a linear equation in two variables based on the given information. Siti bought a few postcards, some postcards cost RM1.20 and some cost 80 sen each. The total amount Siti paid is RM4.00.
Solution:
Let the number of postcards costs RM1.20 be x and the number of postcards costs RM0.80 be y.
Therefore, 1.2x + 0.8y = 4 Multiply by 2.5, 3x + 2y = 10
Given that 7x - y = 3, find the value of y, if x = 1.
Solution:
7(1) - y = 3 y = 7 - 3 y = 4
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11.2 SIMULTANEOUS LINEAR EQUATIONS IN TWO VARIABLES
Simultaneous linear equation in two variables are two linear equations in two variables having a common solution.
Both equations must have two common variables.
Simultaneous linear equations in two variables can be solved by substitution method and elimination method.
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EXAMPLE 1Solve the following simultaneous equations.
2x + 5y = 3 x - y = 5
Method 1: Substitution
2x + 5y = 3 ...! x - y = 5 ..."
From ", x = 5 + y Substitute x into !,
2 (5 + y) + 5y = 3 10 + 2y + 5y =3 2y + 5y = 3 - 10 7y = -7 y = -1
From ", x = 5 + (-1) = 5 - 1 = 4
Therefore, x = 4, y = -1
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Method 2: Elimination
2x + 5y = 3 ...! x - y = 5 ..."
! 2x + 5y = 3 " x 5 = 5x - 5y = 25 Form an equation which is # ... (2x + 5y) + (5x - 5y) = 3 + 25 2x + 5y + 5x - 5y = 28 7x = 28 x = 4
From ", 4 - y = 5 -y = 5 - 4 y = -1
Therefore, x = 4, y = -1
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CHAPTER 12LINEAR INEQUALITIES
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12.1 INEQUALITIES
An inequality is a relationship between two unequal quantities.
Symbol Definition
Greater than
Less than
Greater than or equal to
Less than or equal to
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12.2 LINEAR INEQUALITIES
Linear inequalities can be represented on number lines.
Symbols on the number line:
Symbol Definition
Include
Not included
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12.3 OPERATIONS INVOLVING LINEAR INEQUALITIES
The condition of inequality is unchanged when both sides are;
(a) added or subtracted from a number (b) multiplied or divided by a positive number.
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EXAMPLES (a) 15 > 7 15 + 4 > 7 + 4 19 > 11
(b) x > 10 x - 4 > 10 - 4 x - 4 > 6
(c) 21 < 27 21 x 3 < 27 x 3 63 < 81
State the new inequalities when a number is added to or subtracted from both sides of the following inequalities.
(a) 15 > 7 (add 4) (b) x > 10 (subtract 4) (c) 21 < 27 (multiplied by 3)
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When an inequality is multiplied or divided by a negative number on both sides, the inequality symbol is reversed.EXAMPLESState a new inequality when both sides of the following inequalities are multiplied or divided by a negative number.
(a) 4 > -3, multiplied by -2
(b) x < -18, divided by -6
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12.4 SOLVING LINEAR INEQUALITIES IN ONE VARIABLE
The solution for a linear inequality in one variable is the equivalent inequality in its simplest form.
EXAMPLE
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12.5 SIMULTANEOUS LINEAR INEQUALITIES IN ONE VARIABLE
Solutions for two simultaneous linear inequalities in one unknown are the common values that satisfy both inequalities.
EXAMPLESSolve the following linear inequalities.
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CHAPTER 13GRAPHS OF FUNCTIONS
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13.1 FUNCTIONS
A function expresses the relationship of a variable in term of another variable.
For a coordinate (x,y), x is called the independent variable and y is called the dependent variable.
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EXAMPLES