FDPR Mixed Context: WJEC GCSE Numeracy Intermediate June 2019 Unit 2 Q7

Numeracy Intermediate June 2019 Unit 2 Q7

WJECIntermediateCurrent spec8 marksFDPR Mixed Context Similar Shapes Volume & Surface Area

(a)

(i)

The internal measurements of a tin of baked beans are:

radius 3·6 cm,
height 9·3 cm.

Calculate the internal volume of the tin. [2]

(ii)

Every 1 cm³ of baked beans in a tin has a mass of 1 g.
A portion of baked beans is \(\frac{1}{2}\) a tin.
What is the mass of a portion of baked beans? [1]

A portion of baked beans has a mass of …………… g

(b)

A mathematically similar tin of baked beans has a radius of 4·2 cm.

A smaller tin and a larger tin of baked beans

Diagram not drawn to scale

Calculate the height of the larger tin of beans. [2]

(c)

In a portion of baked beans there is:

1·85 g of salt,
11·7 g of sugar.

For women, the recommended daily allowance of:

salt is 6 g,
sugar is 90 g.

Consider a portion of baked beans.
Is it salt or sugar that provides the greater proportion of the recommended daily allowance for women?
You must show all your working. [3]

Mark scheme (a)

Scheme	Marks	Comments
(i) (Volume) π × 3.6² × 9.3	M1
Answer in the range 378.4 (cm³) to 378.7 (cm³) 378 (cm³) or 379 (cm³)	A1	Mark final answer
(ii) 189 (g) or an answer in the range 189.2 (g) to 189.5 (g)	B1	Allow rounding or truncation to whole number or a number of decimal places FT, for a similar range, ‘their 379’ accurately divided by 2

Mark scheme (b)

Scheme	Marks	Comments
(Height is) 9.3 × 4.2 ÷ 3.6 or 1.16666... × 9.3 or 9.3 ÷ (3.6 ÷ 4.2) or equivalent	M1	Allow M1 for 1.16 × 9.3 or 1.17 × 9.3 or 9.3 ÷ 0.85(7...)
10.85 (cm)	A1	Allow answers in the inclusive range 10.78 (cm) to 10.95 (cm)

Mark scheme (c)

Scheme	Marks	Comments
Comparison of salt and sugar, e.g. (Salt) \(\dfrac{6}{1.85}\) AND (Sugar) \(\dfrac{90}{11.7}\) (Salt)(100×) \(\dfrac{1.85}{6}\) AND (Sugar)(100×) \(\dfrac{11.7}{90}\) (Recommend) 1 : 15 AND (Beans)1 : 11.7÷1.85	B1	Or equivalent Ignore any units given
Conclusion SALT and an accurate calculation of comparison, e.g. 3(.24...) AND 7(.69...), 0.3(083...) AND 0.13, 30(.83....%) AND 13(%), 31(%) AND 13(%), 0.31 AND 0.13 1 : 15 AND 1 : 6(.32...)	B2	Ignore any units given and any additional statements if SALT unambiguously concluded with appropriate calculations evaluated correctly Accept rounded or truncated answers Ignoring units, B1 for an accurate calculation of comparison, e.g. 3(.24...) AND 7(.69...), 0.3(083...) AND 0.13, 30(.83....%) AND 13(%), 31(%) AND 13(%) 1 : 15 AND 1 : 6(.32...) OR B1 for SALT with one of the two comparative values correct (i.e. as above with ‘OR’)

Alternative

7(c) Alternative method 1:

Scheme	Marks	Comments
Conclusion SALT with evidence of a full method looking at the same number of portions, including ratio methods, e.g. 1.85 × 3 (portions) ≈ 6 (g) AND 11.7 × 8 (portions) ≈ 90 (g)	B3	Allow approximately or similar words for ‘≈’ B2 for evidence of, e.g. 1.85 × 3(portions) ≈ 6(g) and 11.7 × 8(portions) ≈ 90(g) OR B1 for conclusion SALT with evidence of, e.g. 1.85 × 3 (portions) ≈ 6 (g) or 11.7 × 8 (portions) ≈ 90 (g)

Alternative

7(c) Alternative method 2:

Scheme	Marks	Comments
Full method with one calculated proportion, compared with same proportion of the other ingredient, e.g. 31% salt with 0.31 × 90 13% sugar with 0.13 × 6	B1
Conclusion SALT and an accurate calculation of comparison, e.g. 27.9 (g) (sugar which is > 11.7 g in a portion) 0.78 (g) (salt which is < 1.85 g in a portion)	B2	Ignore any units given and any additional statements if SALT unambiguously concluded with appropriate calculations evaluated correctly B1 for appropriate calculations evaluated correctly, with no or incorrect conclusion