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Section 2.2 · Algebra

Using expressions and formulae

Substitute numbers into expressions, and write and use formulae.

6 teaching slides 56 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

formulaA mathematical rule showing the relationship between two or more quantities, such as A = l × w.
formulaeThe plural of formula.
substituteTo replace a letter with a number.
deriveTo write your own formula from a situation.
variableA quantity in a formula that can change.

3 · Summary of the sectionrevise from this

  • A formula is a rule connecting quantities. It always has an equals sign.
  • To substitute, replace each letter with its number and then calculate.
  • Keep the order of operations: brackets and indices before × ÷, and those before + −.
  • Be careful with negatives: when x = −4, 3x² means 3 × (−4)² = 3 × 16 = 48.
  • You can derive your own formula. Choose letters that suggest what they stand for, and always say what each one means.
  • You can work backwards from a formula: if T = 25h + 40 and T = 190, then h = 6.
PDFPrintable worksheet All 56 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons4 videos

Substitution into Expressions

British Corbettmaths

The British-curriculum method for substituting values, including negatives.

Intro to Evaluating Algebraic Expressions

American Math with Mr. J

What substitution is and why you replace the letter before calculating. (“Evaluate” is the American word for it.)

Evaluating Expressions with One Variable

American Math with Mr. J

A step-by-step guide with several worked examples.

Evaluating Expressions with Two Variables

American stretchMath with Mr. J

Extends the method to formulae with two or more letters.

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4 · Practice56 questions, easiest first

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2.1 Constructing expressions
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2.3 Collecting like terms