$\require{\cancel}$ $\require{\stix[upint]}$

### MATHEMATICS 9709

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade Stream Subject Pure Mathematics 3 (P3) Variant(s) P33 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 4 7 6 8 9 9 43
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/33/O/N/20/2, Topic: Complex numbers On a sketch of an Argand diagram, shade the region whose points represent complex numbers$z$satisfying the inequalities$|z| \geqslant 2$and$|z-1+\mathrm{i}| \leqslant 1$.$[4]$Question 2 Code: 9709/33/O/N/11/3, Topic: Trigonometry$\text{(i)}$Express$8 \cos \theta+15 \sin \theta$in the form$R \cos (\theta-\alpha)$, where$R>0$and$0^{\circ}< \alpha <90^{\circ}$. Give the value of$\alpha$correct to 2 decimal places.$[3]\text{(ii)}$Hence solve the equation$8 \cos \theta+15 \sin \theta=12$, giving all solutions in the interval$0^{\circ}< \theta <360^{\circ}$.$[4]$Question 3 Code: 9709/33/O/N/12/4, Topic: Differential equations The variables$x$and$y$are related by the differential equation $$\left(x^{2}+4\right) \displaystyle\frac{\mathrm{d} y}{\mathrm{~d} x}=6 x y.$$ It is given that$y=32$when$x=0$. Find an expression for$y$in terms of$x$.$[6]$Question 4 Code: 9709/33/O/N/12/6, Topic: Numerical solutions of equations The diagram shows the curve$y=x^{4}+2 x^{3}+2 x^{2}-4 x-16$, which crosses the$x$-axis at the points$(\alpha, 0)$and$(\beta, 0)$where$\alpha<\beta$. It is given that$\alpha$is an integer.$\text{(i)}$Find the value of$\alpha$.$[2]\text{(ii)}$Show that$\beta$satisfies the equation$x=\sqrt[3]{(8-2 x)}$.$[3]\text{(iii)}$Use an iteration process based on the equation in part$\text{(ii)}$to find the value of$\beta$correct to 2 decimal places. Show the result of each iteration to 4 decimal places.$[3]$Question 5 Code: 9709/33/O/N/18/7, Topic: Differentiation, Integration The diagram shows the curve$y=5 \sin ^{2} x \cos ^{3} x$for$0 \leqslant x \leqslant \frac{1}{2} \pi$, and its maximum point$M$. The shaded region$R$is bounded by the curve and the$x$-axis.$\text{(i)}$Find the$x$-coordinate of$M$, giving your answer correct to 3 decimal places.$[5]\text{(ii)}$Using the substitution$u=\sin x$and showing all necessary working, find the exact area of$R$.$[4]$Question 6 Code: 9709/33/O/N/19/7, Topic: Vectors The plane$m$has equation$x+4 y-8 z=2$. The plane$n$is parallel to$m$and passes through the point$P$with coordinates$(5,2,-2)$.$\text{(i)}$Find the equation of$n$, giving your answer in the form$a x+b y+c z=d$.$[2]\text{(ii)}$Calculate the perpendicular distance between$m$and$n$.$[3]\text{(iii)}$The line$l$lies in the plane$n$, passes through the point$P$and is perpendicular to$O P$, where$O$is the origin. Find a vector equation for$l$.$[4]\$

Worked solutions: P1, P3 & P6 (S1)

If you need worked solutions for P1, P3 & P6 (S1), contact us @ [email protected] | +254 721 301 418.

1. Send us the link to these questions ( https://stemcie.com/view/150 ).
2. We will solve the questions and provide you with the step by step worked solutions.
3. We will then schedule a one to one online session to take you through the solutions (optional).