20N.1.SL.TZ0.S_6

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

evidence of integration      (M1)

eg    $\int f\text{'}\left(x\right) \text{d}x , \int 6{\text{e}}^{2x}$

correct integration (accept missing $+c$)      (A1)

eg    $\frac{1}{2}\times 6{\text{e}}^{2x} , 3{\text{e}}^{2x}+c$

substituting initial condition into their integrated expression (must have $+c$)       M1

eg    $3{\text{e}}^{2\times \ln 4}+c=20$

 

Note: Award M0 if candidate has substituted into $f\text{'}$ or $f\text{'}\text{'}$.

 

correct application of $\log \left(a^b\right)=b \log a$ rule (seen anywhere)      (A1)

eg    $2 \ln 4=\ln 16 , {\text{e}}^{\ln 16} , \ln 4^2$

correct application of ${\text{e}}^{\ln a}\text{=}\mathit{\text{a}}$ rule (seen anywhere)      (A1)

eg    ${\text{e}}^{\ln 16}=16 , {\left({\text{e}}^{\ln 4}\right)}^2=4^2$

correct working      (A1)

eg    $3\times 16+c=20 , 3\times {\left(4\right)}^2+c=20 , c=-28$

$f\left(x\right)=3{\text{e}}^{2x}-28$        A1 N4

 

[7 marks]

[N/A]