• Index expressions raised to a power can be simplified by

a) repeated multiplication

b) multiplication of indices

5.4 RAISING THE POWER OF INDEX NOTATIONS

• Computations involving raising the power of index notations.

EXAMPLES

• Combined operations involving index notations.

EXAMPLE

5.5 NEGATIVE INDICES

EXAMPLES

5.6 FRACTIONAL INDICES

EXAMPLES

5.7 COMPUTATIONS INVOLVING LAWS OF INDICES

• Combined operations involving numbers

EXAMPLES

• Combined operations involving numbers and algebra.

EXAMPLE

CHAPTER 6ALGEBRAIC EXPRESSIONS III

• Expanding algebraic expressions involving a pair of bracket.

6.1 EXPANSION OF ALGEBRAIC EXPRESSIONS

EXAMPLES

• Expanding algebraic expressions involving two pairs of brackets.

EXAMPLES

6.2 FACTORIZATION

• Factorization is a process of writing an expression as a product of two or more factors.

Process I is called expansion while process II is called factorization.

• Factors of algebraic terms.

EXAMPLES

• Common factors and HCF.

EXAMPLES

• Factorizing algebraic expressions.

EXAMPLES

• Factorizing algebraic fractions.

EXAMPLES

6.3 ADDING AND SUBTRACTING ALGEBRAIC FRACTIONS

• Algebraic fractions with the same denominator.EXAMPLES

• Algebraic fractions with one denominator as a multiple of the other.

EXAMPLES

• Algebraic fractions having denominators with or without common factors.

EXAMPLES

6.4 MULTIPLYING AND DIVIDING ALGEBRAIC FRACTIONS

• Multiplying algebraic fractions.EXAMPLES

• Dividing algebraic fractions.

EXAMPLES

CHAPTER 7ALGEBRAIC FORMULAE

• To determine wether a quantity is a variable or constant, we must find out if its value varies or remains unchanged.

7.1 VARIABLES AND CONSTANTS

EXAMPLEDetermine if the following quantities are variables or constants. (a) The number of days in a week. (b) The number of schooldays in each month.

Solution:

(a) There are 7 days in a week. Therefore, the number of days in a week is a constant.

(b) The number of schooldays differs from month to month. Therefore, the number of schooldays in each month is a variable.

Months Number of schooldays

January 22

February 16

March 21