4MA0 Foundation June 2012 Paper 2 Q20
20
(a) Show that \(\dfrac{4}{5} \div \dfrac{7}{15} = 1\dfrac{5}{7}\) (2)
(b) Show that \(5\dfrac{1}{4} - 1\dfrac{2}{3} = 3\dfrac{7}{12}\) (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{4}{5} \times \dfrac{15}{7}\) | M1 |
| \(\dfrac{12}{7}\) oe | A1 |
| (2) |
Notes
M1: or \(\dfrac{12a}{15a} \div \dfrac{7a}{15a}\) (denominators the same and a multiple of 15)
A1: dep on M1. Improper fraction equivalent to \(1\dfrac{5}{7}\) required produced directly from M1
| Scheme | Marks |
|---|---|
| \(\dfrac{21}{4} - \dfrac{5}{3}\) | M1 |
| \(\dfrac{63a}{12a} - \dfrac{20a}{12a}\) | M1 |
| \(\dfrac{43}{12}\) oe | A1 |
| (3) | |
| (Total 5 marks) |
Notes
M1: Correct improper fractions
M1: Correct fractions with a common denominator a multiple of 12
A1: dep on M2 Improper fraction required.
Alt method
| Scheme | Marks |
|---|---|
| \((5)\,\dfrac{3}{12} - (1)\,\dfrac{8}{12}\) (i.e. can ignore integer parts) | M1 |
| \(-\dfrac{5}{12}\) | M1 |
| A1 |
Notes
A1: Improper fraction required or \(4 - \dfrac{5}{12}\). Ans dep on M2.
Alt method
| Scheme | Marks |
|---|---|
| \((4)\,\dfrac{5}{4} - (1)\,\dfrac{2}{3}\) (i.e. can ignore integer parts) | M1 |
| \((4)\,\dfrac{15}{12} - (1)\,\dfrac{8}{12}\) (i.e. can ignore integer parts) | M1 |
| \((3\,+)\,\dfrac{7}{12}\) or improper fraction | A1 |
Notes
A1: Ans dep on M2
NB: Follow one strand that gives most marks.