Numeracy Higher June 2025 Unit 2 Q7
7. Dyfan has two different 25 g bars of chocolate, a Chocodusk bar and a Luxury Dark bar.
The Chocodusk bar has a lower cocoa content than the Luxury Dark bar.
The nutritional information from these bars of chocolate is given below.
| Chocodusk bar: lower cocoa content | |
|---|---|
| Per 25 g bar | |
| Saturated fat | 6·6 g |
| Sugar | 7·1 g |
| Protein | 3·5 g |
| Salt | 0·01 g |
| Luxury Dark bar: higher cocoa content | |
|---|---|
| Per 25 g bar | |
| Saturated fat | 7·7 g |
| Sugar | 3·5 g |
| Protein | 2·9 g |
| Salt | 0·09 g |
Complete the following statement. [1]
‘The amount of salt in the Luxury Dark bar is …………… % of the amount of salt in the Chocodusk bar.’
Dyfan eats 20 g of the Luxury Dark bar.
Calculate the percentage of the Chocodusk bar that gives Dyfan the same amount of saturated fat.
You must show all your working. [3]
The diagram below shows the symmetrical uniform cross-section of one of the chocolate bars.
Diagram not drawn to scale
The label on this chocolate bar states,
‘The thickness of this chocolate bar is 6 mm, correct to the nearest millimetre.’
Use the measurements given on the diagram to decide whether this statement is true or false.
True ☐ False ☐
You must show all your working. [5]
| Scheme | Mark | Comments |
|---|---|---|
| (i) 900 (%) | B1 | |
| (ii) \(\dfrac{20}{25}\) × 7.7 ÷ 6.6 (× 100) or equivalent | M2 | May be seen in stages Accept equivalents to \(\dfrac{20}{25}\), e.g. \(\dfrac{4}{5}\), 0.8 or \(\dfrac{80}{100}\) M1 for appropriate sight of any one of the following, or equivalent, may be embedded in further working:
|
| (% of the Chocodusk bar is) 93(.333... %) | A1 | Allow an answer that rounds to 93(%) provided not from incorrect working FT from M1 to award A1 for the mass of the bar eaten (20 × 7.7 ÷ 6.6 =) 23(.33...g) If no marks, award SC1 for an answer of 68.57(..%) 68.6(%) or 69(%) (from 100 × \(\dfrac{20}{25}\) × 6.6 ÷ 7.7), i.e. starting with the incorrect bar |
Corrected by Westie's Workshop
- The board's mark scheme printed “(% of the 70% cocoa bar is)”. Changed to “(% of the Chocodusk bar is)” because the question never mentions a 70% cocoa bar; the percentage asked for is of the Chocodusk bar. The answer 93(.333…%) is unchanged.
Original: see the board's mark scheme PDF (link above).
| Scheme | Mark | Comments |
|---|---|---|
| (Side of right-angled triangle (68 – 60) ÷ 2 =) 4 (mm) | B1 | Accept seen on the diagram or implied in further working |
| \(4^2\) + thickness\(^2\) = \(7^2\) or (thickness\(^2\) =) \(7^2 - 4^2\) | M1 | FT ‘their 4’ provided < 7 |
| thickness\(^2\) = 33 or (thickness =) \(\sqrt{33}\) | A1 | |
| (Thickness =) 5.7(4...mm) AND indicates ‘True’ | A2 | Allow appropriate sight of 5.7(4…) = 6 as implication of ‘True’’ provided not contradicted in the answer box Ignore additional spurious statements A1 for 5.7(4...mm) FT from M1 for the correctly evaluated square root of ‘their 33’ provided ‘their answer’ < 7 (mm) for: either A2 (with appropriate conclusion true or false) or A1 (if no conclusion) If M0 A0 A0, award: either SC2 for 3.6(0555 mm) (from \(\sqrt{(7^2 - 6^2)} = \sqrt{13}\) ) or SC1 for \(x^2 = 7^2 - 6^2\) or (\(x\) =) \(\sqrt{(7^2 - 6^2)}\) OR either SC2 for 7.2(11.. mm) (from \(\sqrt{(4^2 + 6^2)} = \sqrt{52}\) ) or SC1 for \(x^2 = 4^2 + 6^2\) or (\(x\) =) \(\sqrt{(4^2 + 6^2)}\) |
Alternative
Alternative method (Use of bounds)
| Scheme | Mark | Comments |
|---|---|---|
| (Side of right-angled triangle (68 – 60) ÷ 2 =) 4 (mm) | B1 | Allow use of 6.499(… mm) for 6.5(mm) |
| \(x^2 = 7^2 - 6.5^2\) or (\(x\) =) \(\sqrt{(7^2 - 6.5^2)}\) AND \(x^2 = 7^2 - 5.5^2\) or (\(x\) =) \(\sqrt{(7^2 - 5.5^2)}\) | M2 | M1 for \(x^2 = 7^2 - 6.5^2\) or (\(x\) =) \(\sqrt{(7^2 - 6.5^2)}\) OR \(x^2 = 7^2 - 5.5^2\) or (\(x\) =) \(\sqrt{(7^2 - 5.5^2)}\) |
| 4.3(30… mm) AND 2.59(8… mm) or 2.6(mm) AND indicates ‘True’ OR similar using 4(mm) with 5.5(mm) and 6.5(mm) working towards 7(mm) | A2 | A1 for 4.3(30… mm) OR 2.59(8… mm) or 2.6(mm) |