Foundation June 2023 Paper 2 Q5
5
(a) A shop sells bottles of orange juice.
Each bottle costs 75p
Work out the greatest number of bottles that can be bought with £5 [2 marks]
(b) Two shops sell bottles of apple juice.
| Shop X pack of 4 bottles Was £2.50 Now 10% off | Shop Z pack of 12 bottles £7 |
At which shop is it cheaper to buy 24 bottles?
Show working to support your answer. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(5 \div 0.75\) or \(500 \div 75\) or 6.6(…) or 6.7 or \(75 \times 6\) or 450 or \(0.75 \times 6\) or 4.5 or \(75 \times 7\) or 525 or \(0.75 \times 7\) or 5.25 | M1 | oe eg build up or build down |
| 6 | A1 |
Additional guidance
| Incorrect work seen is A0 eg \(75 \times 6 = 450\) and \(75 \times 7 = 575\) Answer 6 | M1A0 |
| Do not allow \(5 \div 75\) or \(500 \div 0.75\) unless recovered | |
| Build up must be fully correct method, no errors, 75, 150, 225, 300, 375, 450, (525) | |
| Build down must be fully correct method, no errors, 425, 350, 275, 200, 125, 50 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 Comparing the cost of 24 bottles | ||
| \(2.5 \times 0.1\) or 0.25 or \(1 - 0.1\) or 0.9 | M1 | oe eg \(2.5 \div 10\) discount or multiplier for shop X implied by \(2.5 \times 6 \times 0.1\) or 1.5 or 2.25 |
| \((2.5 -\) their \(0.25) \times 6\) or \(2.5 \times\) their \(0.9 \times 6\) or \(2.25 \times 6\) or 13.5 | M1dep | oe eg \(15 \times 0.9\) or \(15 - 1.5\) shop X |
| \(7 \times 2\) or 14 | M1 | oe shop Z |
| X with 13.5 and 14 seen | A1 | oe |
| Alternative method 2 Comparing the cost of 1 bottle | ||
| \(2.5 \times 0.1\) or 0.25 or \(1 - 0.1\) or 0.9 | M1 | oe eg \(2.5 \div 10\) discount or multiplier for shop X implied by \(2.5 \div 4 \times 0.1\) or 0.06(25) or 2.25 |
| \((2.5 -\) their \(0.25) \div 4\) or \(2.5 \times\) their \(0.9 \div 4\) or \(2.25 \div 4\) or 0.56(25) or 0.563 | M1dep | oe eg \(0.62(5) \times 0.9\) or \(0.62(5) - 0.06(25)\) shop X |
| \(7 \div 12\) or 0.58(3…) | M1 | oe shop Z |
| X with 0.56(25) or 0.563 and 0.58(3…) seen | A1 | oe |
| Alternative method 3 Comparing the cost of 12 bottles | ||
| \(2.5 \times 0.1\) or 0.25 or \(1 - 0.1\) or 0.9 | M1 | oe eg \(2.5 \div 10\) discount or multiplier for shop X implied by \(2.5 \times 3 \times 0.1\) or 0.75 or 2.25 |
| \((2.5 -\) their \(0.25) \times 3\) or \(2.5 \times\) their \(0.9 \times 3\) or \(2.25 \times 3\) | M1dep | oe eg \(7.5 \times\) their 0.9 or \(7.5 - 0.75\) shop X |
| X with 6.75 (and 7) seen | A2 | A1 6.75 oe |
Additional guidance
| Up to 3 marks may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | ||||||||||||||||
| Use the scheme that favours the student eg 0.56 and 0.58 followed by 13.44 and 13.92 and X (mark by Alt 2) | M3A1 | |||||||||||||||
| Ignore incorrect money notation eg 13.5 or 14.0 | ||||||||||||||||
| All schemes can be oe in pence and allow work in a mix of pounds or pence for up to 3 marks | ||||||||||||||||
| Condone eg answer 13.5 with 14 seen | M3A1 | |||||||||||||||
| For \(0.1 \times 2.5\), accept \(10\% \times 2.5\) but do not accept 10% of 2.5 unless recovered | ||||||||||||||||
| Allow variations eg Shop X £15, Shop Z £14, Shop X is £1 more but the discount is £1.50 Shop X cheaper | M1 M1M1 A1 | |||||||||||||||
Where the student compares eg 2, 3, 4, 6, 48 or 96 bottles apply the principles of Alt 2 – some relevant figures given below (after offer)
|