Foundation June 2017 Paper 3 Q5
5
(a) Simplify \(\qquad a \times a \times a + b + b\) [2 marks]
(b) Simplify \(\qquad 5(x + 3) - x + 2\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(a^3 + 2b\) | B2 | B1 for \(a^3\) (+) or (+) \(2b\) |
Additional guidance
| Do not accept \(2 \times b\) or \(b2\) for \(2b\) | |
| Do not accept \({}^3a\) for \(a^3\) | |
| Do not accept further working for B2 eg \(a^3 + 2b = a^32b\) | B1 |
| Do not accept further working for B1 eg \(3a + 2b = 5ab \quad\) or \(\quad a^3 \quad b^2 = a^3b^2\) | B0 |
| \(a^3 + b^2\) | B1 |
| \(3a + 2b\) | B1 |
| \(a^3 \quad 2b\) | B1 |
| \(a^3 \quad 2b = a^32b\) | B1 |
| \(a^3 \times 2b\) or \(a^32b\) without working for B1 | B0 |
| \(a^3 \times b^2\) or \(a^3b^2\) | B0 |
| \(3a \times 2b\) | B0 |
| \(3a - 2b\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(5x\) (+) 15 | B1 | Implied by correct answer |
| \(4x + 17\) | B2ft | B2ft their \(5x + 15\) in the form \(5x + b\) or \(ax + 15\), both their terms with correct ft in final answer B1ft \(4x\) or (+)17 B1ft their \(5x + 15\) in the form \(5x + b\) or \(ax + 15\), one of their terms with correct ft in final answer |
Additional guidance
| ft \(4x\) or (+)17 or must use \(5x + b - x + 2\) or \(ax + 15 - x + 2\) | |
| \(4x + 17\) with no expansion seen | B1B2 |
| Ignore further working with an attempt to solve after their \(4x + 17\) eg \(4x + 17 = 0\) followed by \(x = -4.25\) | B1B2 |
| Do not ignore further working with an attempt to simplify after their \(4x + 17\) eg \(4x + 17\) followed by \(21x\) | B1B1 |
| \(5x + 15 - x + 2\) followed by \(4x + 15 = -2\) | B1B1 |
| \(5x + 3\) followed by \(4x + 5\) also \(5x - 15\) followed by \(4x - 13\) | B0B2ft |
| Ignore further working after \(5x + 15\) for first B1 eg \(5x + 15\) followed by \(20x\) and \(20x - x + 2\) followed by \(19x + 2\) | B1B0 |
| \(5x \quad 15\) | B1 |
| \(4x + k,\ k \ne 17\), with no expansion seen | B0B1ft |
| \(kx + 17,\ k \ne 4\), with no expansion seen | B0B1ft |
| \(5x + 15 - 5x + 10\) followed by 25 | B1B0 |
| \(5x + 3\) followed by \(4x + 1\) | B0B1ft |
| \(5x^2 + 15\) followed by \(5x^2 - x + 17\) | B0B1ft |
| \(5x + 3\) followed by \(4x + 1\) followed by \(5x\) | B0B0ft |
| \(5x + 3\) followed by \(6x + 1\) | B0B0ft |
| \(5x^2 + 3\) followed by \(5x^2 - x + 5\) | B0B0ft |