Page 105 - Knowledge Organiser Yr8 24-25

Knowledge Base: Mathematics TOPIC 24: Rearranging Equations Year 8 | Summer Term 2nd
By the end of this topic you should be able to:
• Simplify expressions
• Solve multi-step equations
• Solve simple inequalities
• Recognise identities
• Work with formulae
• Rearrange formulae
• Change the subject of a formula
Language
Meaning
Example
Expression
Made from numbers, letters and operations, but not including an equals sign
2a + 3b
Equation
An algebraic statement which has particular solutions
4x – 7 = 5 has only one solution x = 3
Inequality
An inequality is where one side is greater than the other
7 < 8 is the same as 8 > 7
Identity
An algebraic statement which is true for all solutions
2(x+4) = 2x + 8 For every possible value of x
Formula
An algebraic statement that connects things (plural formulae)
Area of a circle 𝐴 = 𝜋𝑟2
Substitute
Replace variables with numerical values
Substitute a = 4 in a2 - 2a gives 16 – 8 = 8
Solve
To solve an equation means to find the value of the unknown
Solve 2x – 5 = 13 2x = 18
x= 9
Change the Subject
Rearrange a formula so that a different ‘variable’ is on its own
𝑣 = 𝑏2 rearranged to make 𝑏 the subject gives 𝑏 = √𝑣𝑘 𝑘
Important things to remember:
Whatever you do to one side of the equation you do to the other!
The inverse of + is –
The inverse of × is ÷
The inverse of 2 (square) is √ (square root)
Worked examples
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