AQA AS Paper 1 2023 June — Question 3 3 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
Year2023
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle coefficient given directly
DifficultyModerate -0.3 This is a straightforward binomial expansion question requiring recall of the binomial coefficient formula and solving a simple quadratic equation. While it involves two steps (finding the coefficient expression and solving for a), both are routine procedures that students practice extensively, making it slightly easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

The coefficient of \(x^2\) in the binomial expansion of \((1 + ax)^6\) is \(\frac{20}{3}\) Find the two possible values of \(a\) [3 marks]

Question 3:
AnswerMarks
3Obtains 15 as the binomial
coefficient of the ( a x ) 2 term.
AnswerMarks Guidance
Can be unsimplified.1.1b B1
2 0
= 15a2
3
2
a = ±
3
Forms an equation in a2 for the
AnswerMarks Guidance
coefficient of x2 using their ‘15’1.1a M1
Obtains their correct ± pair of
values for a
FT their ‘15’
AnswerMarks Guidance
ACF1.1b A1F
Question 3 Total3
QMarking instructions AO
Question 3:
3 | Obtains 15 as the binomial
coefficient of the ( a x ) 2 term.
Can be unsimplified. | 1.1b | B1 | 15
2 0
= 15a2
3
2
a = ±
3
Forms an equation in a2 for the
coefficient of x2 using their ‘15’ | 1.1a | M1
Obtains their correct ± pair of
values for a
FT their ‘15’
ACF | 1.1b | A1F
Question 3 Total | 3
Q | Marking instructions | AO | Marks | Typical solution
The coefficient of $x^2$ in the binomial expansion of $(1 + ax)^6$ is $\frac{20}{3}$

Find the two possible values of $a$
[3 marks]

\hfill \mbox{\textit{AQA AS Paper 1 2023 Q3 [3]}}