AQA Paper 3 2023 June — Question 4 5 marks

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2023
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeRewrite with fractional indices
DifficultyEasy -1.2 This is a straightforward index law manipulation question requiring only the application of basic rules: rewriting the cube root as x^(1/3) and using the division rule to get x^(1/3-2) = x^(-5/3). With only 2 marks and no problem-solving element, this is easier than average—purely procedural recall of index laws.
Spec1.02a Indices: laws of indices for rational exponents

Express $$5 - \frac{\sqrt[3]{x}}{x^2}$$ in the form $$5x^p - x^q$$ where \(p\) and \(q\) are constants. [2 marks]

Question 4:
AnswerMarks
41
− 2
Obtains 5x −2 or x3
5
PI by p = –2 or q = −
AnswerMarks Guidance
31.1a M1
5x −2 −x 3
5
Obtains 5x −2 −x 3
5
PI by p = –2 and q = − OE
3
5
Allow −1.67 or better for −
3
AnswerMarks Guidance
Do not ISW incorrect algebra1.1b A1
Question 4 Total2
QMarking instructions AO
Question 4:
4 | 1
− 2
Obtains 5x −2 or x3
5
PI by p = –2 or q = −
3 | 1.1a | M1 | 5
−
5x −2 −x 3
5
−
Obtains 5x −2 −x 3
5
PI by p = –2 and q = − OE
3
5
Allow −1.67 or better for −
3
Do not ISW incorrect algebra | 1.1b | A1
Question 4 Total | 2
Q | Marking instructions | AO | Marks | Typical solution
Express
$$5 - \frac{\sqrt[3]{x}}{x^2}$$

in the form
$$5x^p - x^q$$

where $p$ and $q$ are constants.

[2 marks]

\hfill \mbox{\textit{AQA Paper 3 2023 Q4 [5]}}