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Flashcards · Maths · Ratio and Proportion

Direct and Inverse Proportion

17 cards

  1. What does direct proportion mean?

    As one quantity increases, the other increases at the same rate, so doubling one doubles the other.

  2. What is the unitary method?

    Find the value of one unit, then multiply to find the value of the amount you need.

  3. 5 pens cost \(\pounds 3.50\). What do 8 pens cost?

    One pen costs 70p, so 8 pens cost \(\pounds 5.60\).

  4. What does a direct proportion graph look like?

    A straight line through the origin.

  5. How do you decide the better value between two packs?

    Compare the price of the same amount of each, or the amount per penny, and write a conclusion.

  6. Which is better value: 500 g for \(\pounds 1.20\), or 750 g for \(\pounds 1.65\)?

    750 g, at 22p per 100 g compared with 24p per 100 g.

  7. How do you use an exchange rate of \(\pounds 1 = \$1.25\)?

    Multiply by 1.25 to change pounds to dollars, and divide by 1.25 to change dollars to pounds.

  8. What does inverse proportion mean?

    As one quantity increases, the other decreases, and the product of the two stays the same.

  9. How do you solve an inverse proportion problem?

    Find the total (such as workers times days), then divide by the new quantity.

  10. 3 painters take 8 days. How long do 6 take?

    The total is 24 painter-days, so 6 painters take 4 days.

  11. What does an inverse proportion graph look like?

    A curve that falls and flattens and never touches the axes.

  12. How can you test whether a table shows direct proportion?

    Divide \(y\) by \(x\) for each pair. If the answer is always the same, it is direct proportion.

  13. Is a taxi fare of \(\pounds 3\) plus \(\pounds 2\) a mile in direct proportion to distance?

    No, because the fixed charge means the graph does not pass through the origin.

  14. What does \(y \propto x\) mean (Higher tier)?

    \(y\) is directly proportional to \(x\), which can be written \(y = kx\) for a constant \(k\).

  15. What does \(y \propto \dfrac{1}{x}\) mean (Higher tier)?

    \(y\) is inversely proportional to \(x\), which can be written \(y = \dfrac{k}{x}\).

  16. How do you find \(k\) (Higher tier)?

    Substitute a known pair of values into the equation, such as \(15 = k \times 3\) giving \(k = 5\).

  17. If \(y = kx^2\) and \(y = 20\) when \(x = 2\), what is \(y\) when \(x = 3\) (Higher tier)?

    \(k = 5\), so \(y = 5 \times 9 = 45\).