4MA0 Foundation January 2016 Paper 1R Q17
17
(a) Express 600 as a product of powers of its prime factors.
Show your working clearly. (3)
Show your working clearly. (3)
(b) Simplify \(\dfrac{5^{12}}{5^2 \times 5}\)
Give your answer as a power of 5 (2)
Give your answer as a power of 5 (2)
| Scheme | Marks |
|---|---|
| Correct factor tree or repeated division to find factors 2, 2, 2, 3, 5, 5 (condone inclusion of 1’s) | M2 |
| \(2^3 \times 3 \times 5^2\) | A1 |
| (3) |
Notes
M2: for finding correct factors (condone the inclusion of 1)
M1 for finding a set of factors (with a product of 600) which includes at least 3 of the six prime factors. This may be a factor tree that is incomplete or only correct to this stage, for instance.
A1: dep on M2
Apart from Questions 5 and 17(a) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| \(\dfrac{5^{12}}{5^3}\) or \(\dfrac{5^{10}}{5}\) or \(\dfrac{5^{11}}{5^2}\) | M1 |
| \(5^9\) | A1 |
| (2) | |
| Total 5 marks |
Notes
M1: For a correct application of an index law.