Question 3 - A-Level Maths

AQA Paper 2 2020 June — Question 3 3 marks

Exam Board	AQA
Module	Paper 2 (Paper 2)
Year	2020
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Binomial Theorem (positive integer n)
Type	Binomial with negative or fractional powers of x
Difficulty	Moderate -0.3 This is a straightforward application of the binomial theorem requiring identification of the correct term where powers of x sum to x^2, then calculation using binomial coefficients. It's slightly easier than average as it's a standard 3-mark technique question with no conceptual difficulty, though students must be careful with the algebra and negative powers.
Spec	1.04a Binomial expansion: (a+b)^n for positive integer n

Find the coefficient of \(x^2\) in the binomial expansion of \(\left(2x - \frac{3}{x}\right)^8\) [3 marks]

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Question 3:

Answer	Marks
3	(2x)5

Uses the product of and

3  3

 ±  terms condone sign error

 x

and/or omission of nC term

r

Or

Obtains any two correct terms

Answer	Marks	Guidance
(unsimplified) term	3.1a	M1

 3

8C ( 2x )5×  −  =56×32×−27x2

3  x

∴ coefficient is −48384

3  3

Multiplies their (2x)5 and −  by

 x

8C or 8C or 56 OE

3 5

condone(2x)3

For this mark and

5  3

−

 

Answer	Marks	Guidance
 x	1.1a	M1

Obtains correct coefficient of x2

−48384

Answer	Marks	Guidance
condone inclusion x2	1.1b	A1
Total	3
Q	Marking instructions	AO

Question 3:
3 | (2x)5
Uses the product of and
3
 3
 ±  terms condone sign error
 x
and/or omission of nC term
r
Or
Obtains any two correct terms
(unsimplified) term | 3.1a | M1 | 3
 3
8C ( 2x )5×  −  =56×32×−27x2
3  x
∴ coefficient is −48384
3
 3
Multiplies their (2x)5 and −  by
 x
8C or 8C or 56 OE
3 5
condone(2x)3
For this mark and
5
 3
−
 
 x | 1.1a | M1
Obtains correct coefficient of x2
−48384
condone inclusion x2 | 1.1b | A1
Total | 3
Q | Marking instructions | AO | Marks | Typical solution

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Find the coefficient of $x^2$ in the binomial expansion of $\left(2x - \frac{3}{x}\right)^8$

[3 marks]

\hfill \mbox{\textit{AQA Paper 2 2020 Q3 [3]}}

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