Higher November 2022 Paper 6 Q14
14
(a) The time taken to paint a wall is inversely proportional to the number of people painting.
It takes 40 minutes for 3 people to paint the wall if nobody stops painting.
It takes 40 minutes for 3 people to paint the wall if nobody stops painting.
Layla, Mia and Nina start painting the wall.
After 10 minutes Layla stops painting.
She leaves Mia and Nina to finish painting the wall.
Assume that Layla, Mia and Nina paint at the same rate.
Work out the total time taken to paint the wall, in minutes. [3]
(b) \(y\) is inversely proportional to \(x^3\).
\(y = 16\) when \(x = 2\).
\(y = 16\) when \(x = 2\).
Find the value of \(y\) when \(x = 8\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 55 nfww | 3 | M2 for [(40 × 3) – (10 × 3)] ÷ 2 oe implied by 45 or for [(40 × 3) – 10] ÷ 2 oe or M1 for 40 × 3 implied by 120 Alternative method: M2 for 40 + (40 — 10) ÷ 2 or M1 for (40 — 10) ÷ 2 | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].25 oe | 3 | B1 for \(y = \frac{k}{x^3}\) oe soi by \(16 = \frac{k}{2^3}\) or \(k\) = 128 M1 for \(y = \frac{their\ k}{8^3}\) OR M2 for \(2^3 \times 16 = 8^3 \times y\) or \(16 \div \left(\frac{8}{2}\right)^3\) | |