Foundation June 2023 Paper 3 Q10
10
(a) Write 18 : 42 as a ratio in its simplest form. [2]
(b) In a bag of sweets \(\dfrac{1}{5}\) of the sweets are green.
The rest of the sweets are red.
The ratio of the number of green sweets to the number of red sweets can be written in the form 1 : \(n\).
Find the value of \(n\). [2]
(c) A factory has a large order for copper pipe.
The factory has many machines that make the copper pipe.
The factory has many machines that make the copper pipe.
Each machine makes the same length of copper pipe in a day.
3 machines can make the copper pipe for this order in 25 days.
Find the number of machines needed to make this order in 15 days. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3 : 7 | 2 | B1 for 9 : 21 or 6 : 14 or seen or for answer 1 : 2.3[3...] or 0.42 to 0.43 : 1 | Ignore incorrect cancelling once a correct, partially simplified ratio seen |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 4 | 2 | M1 for \(\dfrac{1}{5} \times 5\) or \(1 \div \dfrac{1}{5}\) or \(\dfrac{4}{5}\) oe seen or B1 for equivalent ratio to 1 : 4 oe seen | 0.8 or 80% e.g. 2 : 8, \(\dfrac{1}{4}\) : 1, 0.25 : 1 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5 nfww | 3 | M2 for \((3 \times 25) \div 15\) or M1 for \((3 \times 25)\) implied by 75 or \(\dfrac{25}{15}\) implied by 1.6 to 1.7 OR M2 for \(3 \times 5 \div 3\) | NB The following are wrong methods and score M0 \(25 \div 3 = 8.33\)... and then \(15 \div 8.33... = 1.8\) rounded to 2 So 3 + 2 = 5 Also \(15 \div 3 = 5\) and also \(25 \div 5 = 5\) From using the inverse of 25 days \(\div 5 \times 3\) to get 15 days |