Higher November 2023 Paper 2 Q5
5 Three shops sell the same type and size of lip balm stick.
Which shop is the best value for 8 sticks and what is the total cost in that shop?
Show working to support your answer. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: price of buying 8 from each shop | ||
| \(2.39 \times 8\) or 19.12 | M1 | oe shop A |
| \(3.08 \times 4 + 3.08 \div 2 \times 4\) or 18.48 | M1 | oe shop B |
| \(11.4 \div 6\) or 1.9(0) or \(11.4 \times 2 \div 6\) or 3.8(0) | M1 | oe shop C |
| \(11.4 \times 2 -\) their \(1.9(0) \times 2\) or \(11.4 \times 2 -\) their 3.8(0) or 19(.00) | M1dep | oe dep on previous mark \(11.4 \times \dfrac{5}{6} \times 2\) oe scores 3rd & 4th marks |
| B and 18.48 with 19.12 and 19(.00) seen | A1 | |
| Alternative method 2: compares price of individual sticks first | ||
| \(3.08 \times 1.5 \div 2\) or 2.31 | M1 | oe shop B |
| \((11.4 \div 4) \div 6\) or 0.47(5) or 0.48 | M1 | oe shop C |
| \(11.4 \div 4 -\) their 0.475 or 2.37(5) or 2.38 | M1dep | oe dep on previous mark \(11.4 \times \dfrac{5}{6} \div 4\) oe scores 2nd & 3rd marks |
| their \(2.31 \times 8\) or 18.48 with M3 awarded | M1dep | oe |
| B and 18.48 with 2.31 and 2.37(5) or 2.38 seen | A1 | |
| Alternative method 3: compares the price of 4 sticks first | ||
| \(2.39 \times 4\) or 9.56 and \(3.08 \times 1.5 \times 2\) or 9.24 | M1 | oe shops A and B |
| \(11.4 \div 6\) or 1.9(0) | M1 | oe shop C |
| \(11.4 -\) their 1.9(0) or 9.5(0) | M1dep | dep on previous mark \(11.4 \times \dfrac{5}{6}\) oe scores 2nd & 3rd marks |
| their \(9.24 \times 2\) or 18.48 with M3 awarded | M1dep | oe |
| B and 18.48 with 9.56 and 9.24 and 9.5(0) seen | A1 | |
| Alternative method 4: compares the price of 2 sticks first | ||
| \(2.39 \times 2\) or 4.78 and \(3.08 \times 1.5\) or 4.62 | M1 | oe shops A and B |
| \((11.4 \div 2) \div 6\) or 0.95 | M1 | oe shop C |
| \(11.4 \div 2 -\) their 0.95 or 4.75 | M1dep | dep on previous mark \(11.4 \times \dfrac{5}{6} \div 2\) oe scores 2nd & 3rd marks |
| their \(4.62 \times 4\) or 18.48 with M3 awarded | M1dep | oe |
| B and 18.48 with 4.78 and 4.62 and 4.75 seen | A1 | |
Additional guidance
Up to M4 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts
Use the scheme which gives the highest mark
NB The 4th mark in Alts 2, 3 and 4 does not imply any earlier marks
Either the method or values must have been seen and awarded for the first 3 marks in order to give this mark
However 18.48 always implies M1 by Alt 1
If students use different numbers of sticks for different shops do not combine marks from different schemes
but note that there are possible valid methods that compare eg 2 sticks from A and B and then 4 sticks from B and C (escalate if seen)
All schemes can be oe in pence and allow work in a mix of pounds or pence for up to M4
Allow \(\times\) 0.16(6…) or \(\times\) 16(.6…)% or \(\times\) 0.167 or \(\times\) 16.7% or \(\times\) 0.17 or \(\times\) 17% if seen for method for one sixth for shop C but must recover to given values for A mark
Allow \(\times\) 0.83(3…) or \(\times\) 83(.3…)% if seen for method for five sixths for shop C but must recover to given values for A mark
| Shop | Cost for 1 | Cost for 2 | Cost for 4 | Cost for 8 |
|---|---|---|---|---|
| A | 2.39 | 4.78 | 9.56 | 19.12 |
| B | 2.31 | 4.62 | 9.24 | 18.48 |
| C | 2.37(5) or 2.38 | 4.75 | 9.5(0) | 19(.00) |