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Formulae: Writing and Substitution
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Foundational skills
Identify the subject of a formula
\[ A = lw \rightarrow \text{subject is } A \]
Identify which variable is the subject.
Distinguish expressions, equations, and formulae
\[ P = 2l + 2w \text{ is a…?} \]
Expression, equation, or formula?
Writing formulae
Write a formula for perimeter
\[ P = 2l + 2w \]
Write perimeter formulae for shapes.
Write a formula for area
\[ A = \frac{1}{2}bh \]
Write area formulae for shapes.
Write a formula from real life
\[ C = 10 + 5h \]
Write formulae for practical scenarios.
Substitution with positive integers
Substitute with one operation
\[ A = 5n, \; n = 7 \]
Single operation formulae.
Substitute with two operations
\[ y = 3x + 5, \; x = 4 \]
Two-step formulae (BIDMAS).
Substitute with two variables
\[ A = bh, \; b = 6, \; h = 9 \]
Formulae with multiple variables.
Substitute with powers
\[ A = \pi r^2, \; r = 5 \]
Squared and cubed terms.
Substitute with brackets
\[ P = 2(l + w) \]
Brackets and order of operations.
Substitute with roots
\[ c = \sqrt{a^2 + b^2} \]
Square root formulae.
Substitution with negative numbers
Substitute negatives (basic)
\[ y = 2x + 10, \; x = -3 \]
Negative integers, basic operations.
Substitute negatives with squares
\[ y = x^2 – 5, \; x = -4 \]
Squaring negative numbers.
Substitute negatives with cubes
\[ y = x^3 + 10, \; x = -2 \]
Cubing negative numbers.
Substitution with decimals and fractions
Substitute decimals
\[ C = 5d + 2.5, \; d = 3.2 \]
Decimal substitution values.
Substitute fractions
\[ y = 4x + 3, \; x = \frac{1}{2} \]
Fractional substitution values.
Special cases
Substitute and interpret in context
\[ C = 30 + 0.2m \]
Real-world formulae with units.
Find an unknown input
\[ P = 4s, \; P = 36, \; s = \text{?} \]
Work backwards to find input.
Timer (Optional)
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