Foundation June 2022 Paper 1 Q19
19
(a) Work out \(\dfrac{3^{12}}{3^7}\)
Give your answer as a whole number. [2 marks]
(b) Simplify \(8 \times 2^6 \times 2^4\)
Give your answer as a power of 2 [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| 243 | B2 | B1 \(3^{12-7}\) or \(3^5\) oe single index or \(3 \times 3 \times 3 \times 3 \times 3\) oe multiplication string or 531 441 seen as \(3^{12}\) or as a numerator or 2187 seen as \(3^7\) or as a denominator or \(3^n\) correctly evaluated, where \(n\) is an integer \(\geqslant 4\) |
Additional guidance
| Condone \(3^5\) and 243 on the answer line, in either order | B2 |
| \(3^5\) only on the answer line | B1 |
| Do not allow a misread | |
| \(12 - 7\) is insufficient for B1 unless \(3^{12-7}\) or \(3^5\) is also seen | |
| Do not award B1 for a correct evaluation of \(3^n\) not ascribed to a particular value of \(n\) eg a list 3, 9, 27, 81 … does not score the mark unless 81 is identified as \(3^4\) |
| Answer | Mark | Comments |
|---|---|---|
| \(2^{13}\) | B2 | B1 \(2^{3+6+4}\) or (\(8 =\)) \(2 \times 2 \times 2\) or \(2^3\) or (\(2^6 \times 2^4 =\)) \(2^{6+4}\) or (\(2^6 \times 2^4 =\)) \(2^{10}\) or \(2^9\) (\(\times\, 2^4\)) or \(2^7\) (\(\times\, 2^6\)) or 8192 |
Additional guidance
| 8192 and \(2^{13}\) on answer line, in either order | B2 |
| 8192 only on the answer line | B1 |
| Correctly combined powers can be implied eg \(8 = 2^4\) with answer \(2^{14}\) implies \(2^6 \times 2^4 = 2^{10}\) | B1 |
| Evaluations other than 8192 do not score eg \(8 \times 1024\) without seeing \(8 \times 2^{10}\) eg \(8 \times 64 \times 16\) | B0 B0 |
| Do not award B1 for 8192 if it is in a list of powers of 2 unless it is indicated or it is the highest power evaluated | |
| Changing terms to numbers with a base of 8 scores zero unless converted to a number with a base of 2 |