**2.1- Introduction**

Use and interpret algebraic manipulation, including:

• ab in place of a × b

• 3y in place of y + y + y and 3 × y

• a^{2} in place of a × a, a^{3} in place of a × a × a, a^{2} b in place of a × a × b

• \(\frac{a}{b}\) in place of a ÷ b

• coefficients written as fractions rather than as decimals.

• brackets

**2.2- Simplifying expressions**

Simplify and manipulate algebraic expressions (including those involving surds) by:

● collecting like terms

● multiplying a single term over a bracket

● taking out common factors

● expanding products of two binomials

● factorising quadratic expressions of the form x^{2} + bx + c, including the difference of two squares;

● simplifying expression

**2.3- Indices**

• Understand and use the rules of indices

– Simplify 2^{-3} x 2^{4}

3x^{-4} x \(\frac{2}{3} x^{\frac{1}{2}} \)

\(\frac{2}{5} x^{\frac{1}{2}} \)÷ \({2x^{-2}}\)

\(\frac{(2x^5}{3})^3\)

• Use and interpret positive, negative, fractional and zero indices

e.g \(5^{\frac{1}{2}}\)= \(\sqrt{5}\)

Evaluate 2^{5},4^{0},5^{2}, \(100^{frac{1}{2}\), \(8^{frac{-2}{3}\)

Solve 32^{x}= 2

**2.4- Expanding and factorising 1**

-Manipulate directed numbers

• use brackets and extract common factors

e.g factorise 9x^{2}+ 15 y

• expand products of algebraic expressions

e.g expand 3x(2x-4y) ; (x+4)(x-7)

• Factorise where possible expressions of the form:

ax + bx + kay + kby

a^{2} x^{2}– b^{2} y^{2}

a^{2}+ 2ab + b^{2}

ax^{2} + bx + c

• Manipulate algebraic fractions

e.g \(\frac{x}{3} + \frac{x-4}{2}\); \(\frac{2x}{3} - \frac{3(x-5)}{2}\);\(\frac{3a}{4} × \frac{9a}{10}\);\(\frac{3a}{4} ÷ \frac{9a}{10}\);\(\frac{1}{x-2} + \frac{2}{x-3}\)

• Factorise and simplify rational expressions

e.g \(\frac{x^2 -2x}{x^2 - 5x+6}\)

**2.5- Algebraic functions**

-Substitute numerical values into formulae and expressions, including scientific formulae

-Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

-Understand and use standard mathematical formulae; rearrange formulae to change the subject

-know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

-Where appropriate, interpret simple expressions as functions with inputs and outputs.

**2.6-Summary and Review**

BODMAS (/BIDMAS)

When simplifying an expression such as 3 + 4 × 5 – 4(3 + 2), remember to work it out in the following order: brackets, of (/indices), division, multiplication, addition, subtraction.

So do the thing in the brackets first, then any division, followed by multiplication and so on. The above is: 3 + 20 – 4 × 5 = 3 + 20 – 20 = 3 .

You mustn’t just work out the sum in the order that it is written down.

**2.7- Assessment 2**

Question 1 :

Calculate 9×5-2(7-4) ; (7-5)÷2+(93)×4 ?

Question 2 : Rearrange 2x = \(\frac{y}{w}\)to make **w** the subject