Foundation November 2022 Paper 3 Q24

24 A solid statue has volume 512 cm\(^3\)

The statue has mass 3.6 kilograms.

density of iron = 7.87 grams per cubic centimetre

Is the statue made of iron?

You must show your working. [3 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
\(3.6 \times 1000\) or 3600	M1
\(\dfrac{\text{their } 3600}{512}\) or 7(.0…) or \(\dfrac{\text{their } 3600}{7.87}\) or 457(.4…)	M1dep	oe
7(.0…) and No or 457(.4…) and No	A1
Alternative method 2
\(3.6 \times 1000\) or 3600	M1
\(7.87 \times 512\) or 4029(.4…)	M1	oe
4029(.4…) and 3600 and No	A1
Alternative method 3
\(\dfrac{3.6}{512}\) or 0.007(0…) or \(\dfrac{3.6}{7.87}\) or 0.457(4…)	M1	oe eg \(7(.0\ldots) \times 10^{-3}\)
their \(0.007(0\ldots) \times 1000\) or 7(.0…) or \(0.457(4\ldots) \times 1000\) or 457(.4…)	M1dep	oe
7(.0…) and No or 457(.4…) and No	A1
Alternative method 4
\(7.87 \div 1000\) or 0.00787 or \(7.87 \times 512\) or 4029(.4…)	M1
their \(0.00787 \times 512\) or their \(4029(.4\ldots) \div 1000\) or 4(.0…) or \(\dfrac{3.6}{\text{their } 0.00787}\) or 457(.4…)	M1dep	oe
4(.0…) and No or 457(.4…) and No	A1
Alternative method 5
\(\dfrac{3.6}{512}\) or 0.007(0…)	M1	oe eg \(7(.0\ldots) \times 10^{-3}\)
\(7.87 \div 1000\) or 0.00787	M1	oe
0.007(0…) and 0.00787 and No	A1

Up to M2 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts
In Alt 2 and Alt 5 the 2nd mark is not dependent In Alt 1, Alt 3 and Alt 4 the 2nd mark is dependent
\(7.87 \times 512 = 1\,056\,293\,519\)	M1
\(7.87 \times 512^3\) or \(3.6 \div 512^3\) unless recovered	M0