Foundation January 2023 Paper 1 Q12
12
(a) Show that \(\dfrac{7}{8} - \dfrac{5}{12} = \dfrac{11}{24}\) (2)
(b) Find the highest common factor (HCF) of 130 and 208
Show your working clearly. (2)
Show your working clearly. (2)
| Scheme | Marks |
|---|---|
e.g. \(\dfrac{21}{24} - \dfrac{10}{24}\) or \(\dfrac{84}{96} - \dfrac{40}{96}\) or \(\dfrac{21n}{24n} - \dfrac{10n}{24n}\) | M1 |
e.g. \(\dfrac{21}{24} - \dfrac{10}{24} = \dfrac{11}{24}\) \(\dfrac{84}{96} - \dfrac{40}{96} = \dfrac{44}{96} = \dfrac{11}{24}\) or \(\dfrac{21n}{24n} - \dfrac{10n}{24n} = \dfrac{11n}{24n} = \dfrac{11}{24}\) Answer: Shown | A1 |
| (2) |
Notes
M1: for finding a common denominator of 24 or a multiple of 24 with at least one fraction correct
A1: dep on M1, for a complete method leading to \(\dfrac{11}{24}\)
| Scheme | Marks |
|---|---|
| 2, 5, 10, 13, 26, 65 and 2, 4, 8, 16, 26, 52, 104 or 2, 5, 13 and 2, 2, 2, 2, 13 oe  | M1 |
| Working required Answer: 26 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for starting to list at least two factors of each number excluding 1 and \(n\)
(Two factors may be written as, for e.g, 130 ÷ 26 = 5 and 208 ÷ 26 = 8 oe or 130 ÷ 13 = 10 and 208 ÷ 13 = 16 etc)
or
2, 5, 13 and 2, 2, 2, 2, 13 seen
(may be in a factor tree or a ladder diagram and ignore 1)
or a fully correct Venn diagram oe
or other clear method, e.g, table
A1: dep on M1