Moderate -0.5 This is a straightforward binomial expansion question requiring students to expand (√3 + √2)^4, identify which terms contain odd powers of the surds (making them irrational), and subtract them. While it requires careful algebraic manipulation and understanding of when terms are rational vs irrational, it's a standard AS-level technique with no novel insight needed—slightly easier than average due to the small power and clear structure.
Question 4:
4 | Expands with correct binomial
coefficients for at least the two
terms required. Accept 4C etc. PI
2 | 1.1a | M1
(√3)4 + 4(√3)3√2 + 6(√3)2(√2)2 +
4√3(√2)3 + (√2)4
4 × 3√3 × √2 – 4 × √3 × 2√2
= 12√6 - 8√6
= 4√6
Correctly simplifies or evaluates at
least one of the irrational terms PI
by 20√6 | 1.1b | B1
Obtains ± correct answer
Accept AWRT 9.8 | 1.1b | A1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
In the binomial expansion of $(\sqrt{3} + \sqrt{2})^4$ there are two irrational terms.
Find the difference between these two terms. [3 marks]
\hfill \mbox{\textit{AQA AS Paper 1 2020 Q4 [3]}}