1.3 Variations

• Direct and inverse variation
• Joint and combined variation
• Graphs of variation
• Applications of variations in real life

• identify direct and inverse variations of different quantities
• determine direct and inverse variations of different quantities
• determine joint and combined variations in different situations
• apply direct, inverse, joint and combined variations to real life situations
• appreciate the use of direct and indirect variations in day to day life

“How are variations applied in real life?”

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1. Quantities that vary together
   40 min · 1 practice tasks · quiz
   Tell the difference between quantities that rise together and quantities where one falls as the other rises.
2. Direct variation and the constant
   40 min · 1 practice tasks · quiz
   Write direct variation as y = kx and find the constant of variation k.
3. Direct variation from a table
   40 min · 1 practice tasks · quiz
   Use a table of values to find k and write the rule of a direct variation.
4. Direct variation: finding unknowns
   40 min · 1 practice tasks · quiz
   Use one known pair of values to find k and then answer other questions.
5. Direct variation with a power
   40 min · 1 practice tasks · quiz
   Work out direct variation when one quantity varies as the square of another.
6. Graphs of direct variation
   40 min · 1 practice tasks · quiz
   Read a direct variation from its graph and use the slope as the constant.
7. Wages and hours worked
   40 min · 1 practice tasks · quiz
   Apply direct variation to wages paid at a fixed hourly rate.
8. The cost of similar items
   40 min · 1 practice tasks · quiz
   Apply direct variation to the cost of buying many similar items.
9. Fuel and distance
   40 min · 1 practice tasks · quiz
   Relate the distance travelled to the fuel used when consumption is steady.
10. Mass and length of a rod
    40 min · 1 practice tasks · quiz
    Relate the mass of uniform rods to their length.
11. Inverse variation and the constant
    40 min · 1 practice tasks · quiz
    Write inverse variation as y = k ÷ x and find the constant from the product.
12. Inverse variation from a table
    40 min · 1 practice tasks · quiz
    Use the constant product in a table to write the rule of an inverse variation.
13. Inverse variation: finding unknowns
    40 min · 1 practice tasks · quiz
    Use one known pair to find k and then answer other questions in an inverse variation.
14. Inverse variation with a power
    40 min · 1 practice tasks · quiz
    Work out inverse variation when one quantity varies as 1 over the square of another.
15. Graphs of inverse variation
    40 min · 1 practice tasks · quiz
    Read an inverse variation from its curve and its constant product.
16. Workers and time
    40 min · 1 practice tasks · quiz
    Relate the number of workers to the time taken to finish a fixed job.
17. Speed and time for a journey
    40 min · 1 practice tasks · quiz
    Relate the speed of a vehicle to the time taken for a fixed distance.
18. Pressure and volume of a gas
    40 min · 1 practice tasks · quiz
    Relate the pressure and volume of a fixed mass of gas at steady temperature.
19. Joint variation
    40 min · 1 practice tasks · quiz
    Write and use joint variation when a quantity varies as the product of two others.
20. Volume of a cylinder
    40 min · 1 practice tasks · quiz
    Apply joint variation to the volume of a cylinder, which depends on r squared and h.
21. Combined variation
    40 min · 1 practice tasks · quiz
    Write combined variation when a quantity is directly proportional to one and inversely proportional to another.
22. Combined variation: a worked example
    40 min · 1 practice tasks · quiz
    Work through a full combined variation, finding the constant and a new value.
23. Comparing graphs of variation
    40 min · 1 practice tasks · quiz
    Use the shape of a graph to tell direct variation from inverse variation.
24. Current, voltage and resistance
    40 min · 1 practice tasks · quiz
    Apply combined variation to the current in a circuit.
25. Variations around us
    40 min · 1 practice tasks · quiz
    Sort real life situations into direct, inverse, joint and combined variations.
26. Variations: mixed review
    40 min · 1 practice tasks · quiz
    Bring together direct, inverse, joint and combined variation in one review.