CAIE IGCSE Additional Math 6 Logarithmic and Exponential Functions Topic Practice

B1 for correct shape in first three quadrants tending towards a
vertical asymptote in the second and third quadrants.
Dep B1 for curve passing through x=-0.5 oe on the x-axis, or stated
and no other points on the x-axis
Dep B1 for curve passing through y$=5 \ln 3$ oe on the y-axis, or stated
and no other points on the y-axis
B1 for $x=-\frac{3}{4}$ oe shown on graph
or stated as the equation of the asymptote. May be implied by a
dotted or straight vertical line
through $x=-\frac{3}{4}$. This is not a
dependent mark.

$\log _{a}\left(\frac{5(p+1) p}{p+2}\right)=\log _{a} 12$ oe, nfww
or $\frac{5(p+1) p}{p+2}=12$ oe, nfww
M1 for correct use of one log law in a correct equation e.g.

$\log _{a}(p+1)+\log _{a} p-\log _{a}(p+2)$$+\log _{a} 5=\log _{a} 12$

or $\log _{a} p(p+1)-\log _{a}(p+2)$$=\log _{a} 12-\log _{a} 5$

or $\log _{a} \frac{p+1}{p+2}+\frac{1}{\log _{p} a}$$+\log _{a} 5=\log _{a} 12$$5 p^{2}-7 p-24=0$
(5 p+8)(p-3)=0 or formula
FT their 3-term quadratic

p=3 and no other solution nfww

$$e^{2x-3-(5-x)}=\frac74$$$$e^{3x-8}=\frac74$$$$3x-8=\ln\frac74$$$$x=\frac{\ln1.75+8}{3}=2.85\ldots$$