1.5 Formulae and Variations

• Changing the subject of a formula, including powers, roots and a subject that appears twice
• Direct and inverse variation; the constant of proportionality
• Joint, combined and partial variation
• Graphs of direct and inverse variation; applications such as planning activities and events

• rewrite a formula to change the subject in different situations
• solve direct and inverse variations from real life situations
• solve combined, joint and partial variations in different situations
• draw graphs of direct and inverse variations
• apply variations to real life situations
• appreciate the use of variations in day-to-day life

“How is formula and variations applied in real life situations?”

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1. Changing the subject
   40 min · 1 practice tasks · quiz
   Rearrange a linear formula so that a chosen letter stands alone, and check the new formula with a known pair of values.
2. A power or a root in the formula
   40 min · 1 practice tasks · quiz
   Make the subject a letter that is squared or under a square root, and keep the positive root when the letter is a length.
3. The subject appears twice
   40 min · 1 practice tasks · quiz
   Collect every term that contains the new subject, factor it, and divide, including the thin-lens formula.
4. Direct variation
   40 min · 1 practice tasks · quiz
   Find the constant when one quantity varies directly as another, or as its square, and use the equation to find a missing value.
5. Inverse variation
   40 min · 1 practice tasks · quiz
   Find the constant product when one quantity varies inversely as another, and use it for shared work and a fixed journey.
6. Joint and combined variation
   40 min · 1 practice tasks · quiz
   Separate a joint law, y = k x z, from a combined law, y = k x / z, and find the missing value in each.
7. Partial variation
   40 min · 1 practice tasks · quiz
   Model a quantity that is partly constant and partly varying, or partly one variable and partly another, using two known pairs.
8. Graphs of direct and inverse variation
   40 min · 1 practice tasks · quiz
   Plot y = 2x as a straight line through the origin, and y = 12/x as a curve whose coordinates multiply to 12.
9. Planning with variation
   40 min · 1 practice tasks · quiz
   Use direct, inverse and partial laws to cost learners, share a painting job, and price a tent for an event.