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.

$\log_5(5x-2)^2-\log_5 x=1$ oe
B1 for $\log_{25}x=\frac{\log_5 x}{\log_5 25}=\frac{\log_5 x}{2}$
B1 for $2\log_5(5x-2)=\log_5(5x-2)^2$ oe
$\log_5\frac{(5x-2)^2}{x}=1$
M1 dep on one of the previous B1 marks;
accept $\log_5 5$ for 1.
$25x^2-25x+4=0$ oe
M1 dep for forming and attempting to solve a 3-term quadratic;
must have at least 2 B marks.
$x=\frac{4}{5}$ only
A1
Alternative methods using base 25, square-root logarithms, or common logs are accepted as in the markscheme.

$\mathrm{e}^{x^{2}-3-\left(7-x^{2}\right)}=25$ oe
Arrange as equation with one power of e

$2 x^{2}-10=\ln 25$$x^{2}=\frac{\ln 25+10}{2}$$x= \pm \sqrt{\frac{\ln 25+10}{2}}$ oe or $\pm \sqrt{\ln 5+5}$
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