Friday, March 24, 2023

## Grade 11: Exponents And Surds

#### 1.1. Revision

1.1. Revision
A number means something you can count, just like counting the number of coins one has or the number of students in a class. These are natural numbers which are normally used for counting and sometimes called counting numbers

1.1.1. Natural Numbers
Natural numbers start from 1 to infinity ∞. Natural numbers are numbers you will use when counting things. For instance if you have to count the number of Oranges, you will start from 1.
Natural Numbers (N)  1,2,3,4,5,6,7,8,9,10,11,…………
1.1.2. Whole Numbers
Whole numbers start from 0 to infinity ∞. Whole numbers are Natural Numbers together with a zero.
Whole Number ( N): 0,1,2,3,4,5,6,7,8,….
1.1.3. Integers
Integers are Whole Numbers plus negatives.
Integers (Z): …-4,-3,-2,-1,0,1,2,3,4,…
1.1.4. Rational Numbers
Rational Numbers are all numbers of the form a/b, where both a and b are integers. b cannot be zero. Rational numbers include fractions.

Fractions can be numbers which are smaller than 1, i.e 1/2 ; 1/4 and 4/7. These are called proper fractions. Fractions can also be  numbers bigger than 1 and they are called improper fractions), i.e. 4/2 ; 5/3 ; 7/2.

1.1.5. Irrational Numbers
Irrational Numbers cannot be expressed as ratio of integers. As decimals they never repeat or terminate.

1.1.6. The Real Numbers
The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.
1.1.7. Non Real Numbers ( Imaginary Numbers)
Not all numbers are real numbers. For instance all square roots of the negative numbers are imaginary numbers or non real numbers. For example √-2 , √-4, √-1 and √-22.

#### 1.2. Rational Exponents and Surds

The laws of exponents can also be extended to include the rational numbers. A rational
number is any number that can be written as a fraction with an integer in the numerator
and in the denominator. We also have the following deﬁnitions for working with
rational exponents.

#### Videos (English)

Exercise 1-2: Laws of Exponents

Exercise 1-3: Rational Exponents and Surds

Exercise 1-4: Simplification of Surds

Exercise 1-5: Rationalising the Denominator

Exercise 1-6: Solving Surd Equations

Exercise 1-8: End of the Chapter Exercises

#### Videos (Venda)

Exercise 1-2: Laws of Exponents

Exercise 1-3: Rational Exponents and Surds

Exercise 1-4: Simplification of Surds

Exercise 1-5: Rationalising the Denominator

Exercise 1-6: Solving Surd Equations

#### Videos (Sepedi)

Exercise 1-2: Laws of Exponents

Exercise 1-3: Rational Exponents and Surds

Exercise 1-4: Simplification of Surds

Exercise 1-5: Rationalising the Denominator

Exercise 1-6: Solving Surd Equations