CALEBPROF

Topic Review  The question \( 48 \div 2(9+3) \) has been a war on the internet for years now. I will like you to follow my prove with a pen and note in your hand Maths Is The Study Of Balance You will probably think what does this guy mean my maths is the study of balance. Let take a look at weighing scale Weighing scale Weighing scale is a good example of left-hand side {LHS} and right-hand side {RHS} in our day to day mathematics. it also explains the value at the LHS is equal to the value at the RHS to make it stay balanced. we have \( x^a \times x^b =  x^{ab} \) example \( 2^2 \times 2^3 = 2^{2+3} = 2^5 = 32 \) to bring our answer back to the first step we need to use this \( x^{ab} = x^a \times x^b \) example \( 32 = 2^5 = 2^{2+3} = 2^2 \times 2^3 \) which tells you ether you use the reverse way \( x^a \times x^b =  x^{ab} \) or \( x^{ab} = x^a \times x^b \) you are still use the rule of indices only in the reverse way Word Example I will take you back to y

Error in mathematics Today I will show you Common mistake made in Algebraic. and ways to go about them Error     Correct/Justification/Example $$ \frac{2}{0} \neq 0 \text{ and } \frac{2}{0} \neq 2 $$ Division by zero is undefined \begin{align}  -3^2 & \neq  9 \\ \text{But} \\ (-3)^2 & = 9 \\ \text{ and} \\ -3^2 & = -9 \end{align} Watch parenthesis! \begin{align} (x^2)^3 & \neq  x^5 \quad \text{but} \\ (x^2)^3 & = x^2x^2x^2 \\ & = x^6 \end{align} \begin{align} \frac{a}{b+c} \neq & \frac{a}{b} + \frac{a}{c} \\ _ \text{Clear Example below} \\ \rightarrow\ \frac{1}{2} & = \frac{1}{1+1} \\ \text{but} \quad \frac{1}{1+1} & \neq \frac{1}{1} + \frac{1}{1} \\ \frac{1}{1} + \frac{1}{1} & = 2 \end{align} $$ \frac{1}{x^2+x^3} \neq x^{-2} + x^{-3} $$ A more complex of the previous error $$ -a(x-1) \neq -ax-a \quad \text{but} \\ {-a(x-1) = -ax+a } $$ Make sure you distribute the "-"! \begin{align} (x+a)^2 & \neq x^2+a^2 \quad \text{bu

Topic Overview The index of a number says how many times to use in a multiplication. it is written as a small number to the right and above the base number The plural of index is indices (other names for index are exponent or power) Positive Exponents Positive Exponents is nothing but the power of a number is to be positive. Example: 5 2 = 5*5*5 = 125 2 4 = 2*2*2*2 = 16 you can multiply any number by itself, as many as you want using exponents. [exponent] make it easier to write 8 4 is easier to write and to read than 8*8*8*8 In General a n tells you to multiply a by itself so there are n of those a ’s: Negative Exponents A Negative Exponent  is nothing but the power of a number is to be , what could the opposite of multiply?      Dividing. A Negative exponent means how many times to divide one by the number Example 4 -1 =1 ÷4 = 0.25 you can have many divides 5 -3 = 1 ÷5÷5÷5 =0.008 5 -3 could also be calculated like 5 -3 = 1

Topic Overview When solving an equation, you are trying to find a  solution  which will make a particular mathematical equation  true  or  correct . For example: x - 3 = 2 If you put 5 in place of x; 5 - 3 = 2 This solution is true, therefore x = 5 is a solution of this equation. In the example above, there is only one solution for x. However, during your  maths working, you will be asked to solve various equations which have multiple solutions. For example: (x-4)(x-3)= 0 If x is 4, the solution to the equation is: (4-4)(4-3)=0 = 0 x 1= 0 When x is 3, the solution to the equation is: (3-4)(3-3)=0 = -1 x 0 = 0 Both of these solutions make the results of the equation true, therefore the solutions to this equation are  x = 4  or  3 Key Concepts In your working, you will be required to solve various mathematical equations. but as a rule you will be required to: Recognise the different symbols within algebraic equations Manipulate and solve alge