4MA0 Foundation January 2013 Paper 2 Q11
11
(a) Write these numbers in order of size.
Start with the smallest number.
\[\frac{4}{7} \qquad \frac{5}{9} \qquad 0.58 \qquad 56\%\] (3)
Start with the smallest number.
\[\frac{4}{7} \qquad \frac{5}{9} \qquad 0.58 \qquad 56\%\] (3)
(b) Show that \(\dfrac{1}{6} \div \dfrac{1}{4} = \dfrac{2}{3}\) (2)
| Scheme | Marks |
|---|---|
eg 0.571… 0.555… 0.58 0.56 Answer: \(\dfrac{5}{9}\), 56%, \(\dfrac{4}{7}\), 0.58 | B3 |
| (3) |
Notes
B3: B2 for 3 numbers in correct order or for two of \(\dfrac{4}{7}\), \(\dfrac{5}{9}\), 56% correctly converted to decimals (at least 2 dp rounded or truncated)
B1 for one of \(\dfrac{4}{7}\), \(\dfrac{5}{9}\), 56% correctly converted to a decimal (at least 2 dp rounded or truncated)
SC B1 for 0.58 \(\dfrac{4}{7}\) 56% \(\dfrac{5}{9}\) if none of previous marks scored
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{6} \times \dfrac{4}{1}\) | M1 |
fraction equivalent to \(\dfrac{4}{6}\) (but not \(\dfrac{2}{3}\)) coming directly from M1 or \(\dfrac{4}{6}\) or \(\dfrac{2}{3}\) from cancelling fractions within multiplication sum Answer: \(\dfrac{4}{6}\) | A1 |
| (2) |
Notes
M1: or \(\dfrac{2a}{12a} \div \dfrac{3a}{12a}\) (\(a \gt 1\); denominators the same and a multiple of 12)
A1: dep. on M1
SC : B2 for \(\dfrac{2}{12} \div \dfrac{3}{12}\)