FPM(2023) June Paper 02 Question 7/8/9 and solution
Question 7 (a) Expand $\left(1+\frac{x}{3}\right)^{-3}$ in ascending powers of $x$ up to and inc…
Question 7 (a) Expand $\left(1+\frac{x}{3}\right)^{-3}$ in ascending powers of $x$ up to and inc…
Question 4 The curve $S$ with equation $y=\frac{x^2}{4}+2$ where $x \geqslant 0$ and the line …
Question 1 Given that $\frac{a+2 \sqrt{5}}{3-\sqrt{5}}=\frac{11+b \sqrt{5}}{2}$ where $a$ is an…
Question 9 (a) Using the formulae on page 2, show that $$ \cos^2 A=\frac{\cos 2A+1}{2} $$ …
Question 7 The equation of a curve is $$ y=\sqrt{\frac{\mathrm{e}^{4x}}{2x-3}} $$ When $x$ is i…
Question 5 A solid cuboid has width $x \mathrm{~cm}$, length $4x \mathrm{~cm}$ and height $h \mat…
Question 3 Figure 1 shows part of the curve with equation $$ y=\frac{x}{2}+\frac{4}{x^2} $$…
Question 1 (a) Show that $$ \sum_{r=1}^{n} (3r+2)=\frac{n}{2}(3n+7) $$ (3) (b) Hence, or …
Question 11 Figure 4 shows an open container in the shape of a cylinder with radius $r \ma…
Question 10 (a) Show that $\frac{9^{3 y}}{243}=3^{(6 y-5)}$ (4) (b) Solve the simultaneous …