AQA AS Paper 2 2018 June — Question 3 2 marks

Exam BoardAQA
ModuleAS Paper 2 (AS Paper 2)
Year2018
SessionJune
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeCombine logs into single logarithm
DifficultyEasy -1.2 This is a straightforward application of basic logarithm laws (power rule and subtraction rule) requiring only two steps to reach log_a(12). It's routine manipulation with no problem-solving element, making it easier than average but not trivial since students must recall and apply two laws correctly.
Spec1.06f Laws of logarithms: addition, subtraction, power rules

Express as a single logarithm \(2\log_a 6 - \log_a 3\) [2 marks]

Question 3:
AnswerMarks
3Expresses 2log 6 as log 62 or log 36
a a a
divides by 3 inside the log term (PI)
6
e.g. 2log( ) scores M1 but not
a 3
𝑙𝑜𝑔𝑎6
2
AnswerMarks Guidance
𝑙𝑜𝑔𝑎3AO1.1a M1
log ( ⁄ )
a 3
log 12
a
Obtains correct final answer
(condone the omission of base a)
AnswerMarks Guidance
CAOAO1.1b A1
Total2
QMarking Instructions AO
Question 3:
3 | Expresses 2log 6 as log 62 or log 36
a a a
divides by 3 inside the log term (PI)
6
e.g. 2log( ) scores M1 but not
a 3
𝑙𝑜𝑔𝑎6
2
𝑙𝑜𝑔𝑎3 | AO1.1a | M1 | 62
log ( ⁄ )
a 3
log 12
a
Obtains correct final answer
(condone the omission of base a)
CAO | AO1.1b | A1
Total | 2
Q | Marking Instructions | AO | Marks | Typical Solution
Express as a single logarithm

$2\log_a 6 - \log_a 3$

[2 marks]

\hfill \mbox{\textit{AQA AS Paper 2 2018 Q3 [2]}}