Mathematics Form 3 chapter 4:Linear Equations

Mathematics Form 3 chapter 4:Linear Equations

Chapter 4: Linear Equations (I)

4.1 Linear Equations In One Unknown

1. A linear term is a term with one unknow and the power of the unknown is one.
Example:
5m, 10n, ½p → Linear terms
8x², 3ab, 6y ³z → Non-linear terms
2. A linear algebraic expression is formed when two or more terms with the power of one are combined by addition or subtraction or both.
Example:
3x-4y → linear expression
4m+5n → linear expression
a²+3 → not a linear expression
3. A linear equation involves only expressions where the power of the unknowns is one
Example:
4m + 7n = 10 → linear equation
9a² + 3 = 8 → not a linear equation
4. A linear equation in one unknown is an equation which shows the relationship between numbers and a linear term with one unknown.
Example:
2k + 3 = 6 → linear equation in one unknown
4x + 5y = 8 → not a linear equation in one because it consists of two unknowns, x and y.

4.2 Solutions of Linear Equations in One Unknown

1. Solving linear equation is a process of finding the value of an unknown which satisfies the equation.
2. the solutions of the equations are also known as the roots of the equations.
3. A linear equation in one unknown has only one root.
4. We can determining the solution of a linear equation by trial and improvement method, but not all the equations can be easily solved by this method.
5. There are 4 methods to solve linear equations in one unknown, depending on the form of the equations.
Example:

(i) Using subtraction (ii) Using addition

x + 8 = 14

x + 8 -8 = 14 - 8

x = 6

(ii) Using addition

x - 3 = 7

x - 3 + 3 = 7 + 3

x = 10

(iii) Using division (iv) Using multiplication

5x = 15 x/5 = 6

5x ÷ 5 = 15 ÷ 5 x/5 x 5 = 6 x 5

x = 3 x = 30

(iv) Using multiplication

x/5 = 6

x/5 x 5 = 6 x 5

x = 30

Read More

[Mathematic Form 3] Common Factors

[Mathematic Form 3] Common Factors

An algebraic term is made up of a numerical co-efficient and a variable. A divisor of an algebraic term is called the factor of the term.

Eg: 8p (8 is the numerical co-efficient and p is the variable)

Factors of an algebraic term can be multiplied together to produce the original term.

Eg: The factors of 4b are 1, 2, 4, b, 2b and 4b.

The common factors of algebraic terms can be determined by listing all the factors of the algebraic terms and then choosing the factors that are the same.

Example:

The factors of
6xy = 1, 2, 3, 6, x, y, xy, 2x, 2y, 2xy, 3x, 3y, 3xy, 6x, 6y, 6xy
3y² = 1, 3, y, y², 3y, 3y²

The common factors are 1, 3, y and 3y.

The Highest Common Factor or HCF is 3y because it has the highest value among the common factors.

** The number '1' is a factor and common factor for all algebraic terms. All algebraic terms are also factors of themselves. 

Read More