Higher June 2024 Paper 1 Q19
19 \(A\), \(B\) and \(C\) are numbers.
Here is some information about \(B\) and \(C\).
| \(B\) | \(\dfrac{7}{4}\) of \(A\) |
|---|---|
| \(C\) | \(A\) increased by 150% |
Work out \(C\) as a fraction of \(B\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: expressing \(C\) in terms of \(A\) | ||
| \((C =)\ \dfrac{5}{2}A\) | M1 | oe eg \((C =)\ A + 1.5A\) or \((C =)\ 2.5A\) |
| \(\left(\dfrac{C}{B} =\right)\) \(\dfrac{\frac{5}{2}A}{\frac{7}{4}A}\) | M1dep | oe fraction with \(A\) on numerator and denominator eg \(\left(\dfrac{C}{B} =\right)\) \(\dfrac{2.5A}{1.75A}\) or \(\dfrac{5}{2}A \div \dfrac{7}{4}A\) |
| \(\left(\dfrac{C}{B} =\right)\) \(\dfrac{\frac{5}{2}}{\frac{7}{4}}\) or \(14C = 20B\) | M1dep | oe fraction with \(A\) eliminated eg \(\left(\dfrac{C}{B} =\right)\) \(\dfrac{2.5}{1.75}\) oe method to eliminate \(A\) |
| \(\dfrac{10}{7}\) or \(1\dfrac{3}{7}\) | A1 | oe fraction SC3 \(\dfrac{7}{10}\) oe fraction with \(A\) eliminated SC2 \(\dfrac{6}{7}\) oe fraction with \(A\) eliminated |
| Alternative method 2: using a value for \(A\) | ||
| Chooses a value for \(A\) works out the correct value of \(B\) or \(C\) | M1 | eg \(A = 100\) and \(B = 175\) or \(A = 20\) and \(C = 50\) |
| Chooses a value for \(A\) and works out correct values for \(B\) and \(C\) | M1dep | eg \(A = 10\) and \(B = 17.5\) and \(C = 25\) |
| Puts the correct values for \(B\) and \(C\) into fraction form (may have non-integer values) | M1dep | oe eg \(\dfrac{25}{17.5}\) |
| \(\dfrac{10}{7}\) or \(1\dfrac{3}{7}\) | A1 | oe fraction eg \(\dfrac{250}{175}\) SC3 \(\dfrac{7}{10}\) oe fraction with \(A\) eliminated SC2 \(\dfrac{6}{7}\) oe fraction with \(A\) eliminated |
Additional guidance
| Ignore an incorrect conversion of \(\dfrac{10}{7}\) to a mixed number | |
| \(\dfrac{6}{7}\) is from taking \(C\) as \(1.5A\) | SC2 |
| Condone the inclusion of \(B\) in the fraction eg \((C =)\ \dfrac{10}{7}(\times)\ B\) or \((C =)\ \dfrac{10B}{7}\) | M3A1 |
| Alt 2 The chosen value of \(A\) does not need to be explicitly stated if method is shown and working is unambiguous or values are in correct proportion |