June 2023 Paper 2 Q14
14 Simplify fully \(\qquad \dfrac{15a^2}{a^2 + 6a - 16} \times \dfrac{8 - 4a}{3a}\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Simplifies \(15a^2\) and \(3a\) to \(5a\) or \(\dfrac{120a^2 - 60a^3}{3a^3 + 18a^2 - 48a}\) | M1 | eg seen as cancelling or single fraction with numerator and denominator expanded may be implied |
| Correct numerator with factor \((a - 2)\) or \((2 - a)\) | M1 | eg \((8 - 4a =)\; 4(2 - a)\) or \(-4(a - 2)\) or \((40a - 20a^2 =)\; 20a(2 - a)\) or \((120a^2 - 60a^3 =)\; 60a^2(2 - a)\) or \((40a^2 - 20a^3 =)\; 20a^2(2 - a)\) or \((120a - 60a^2 =)\; -60a(a - 2)\) |
| Correct denominator with factor \((a - 2)\) or \((2 - a)\) | M1 | eg \((a^2 + 6a - 16 =)\; (a + 8)(a - 2)\) or \((-a - 8)(2 - a)\) or \((a^3 + 6a^2 - 16a =)\; a(a + 8)(a - 2)\) or \(a(-a - 8)(2 - a)\) or \((3a^3 + 18a^2 - 48a =)\; 3a(a + 8)(a - 2)\) or \((3a^2 + 24a)(a - 2)\) or \((3a^2 + 18a - 48 =)\; 3(a + 8)(a - 2)\) or \((3a + 24)(a - 2)\) |
| \(-\dfrac{20a}{a + 8}\) | A1 | oe simplest form eg \(\dfrac{-20a}{a + 8}\) or \(\dfrac{20a}{-a - 8}\) |
Additional guidance
| Up to M3 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| NOTE ‘crossed out’ work may be the student ‘cancelling’ | |
| 2nd M1 denominator may be incorrect or missing | |
| 3rd M1 numerator may be incorrect or missing | |
| 2nd M1 and 3rd M1 may not necessarily be seen in a fraction | |
| Correct answer followed by further incorrect work | M3A0 |
Notes
(corrected from the printed mark scheme: a stray “#” is printed inside the bracket “(a – 2 # )” in the 2nd M1 answer)