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### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo Subject Pure Mathematics 3 (P3) Variant(s) P31, P32, P33 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 7 5 5 6 6 7 36
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/31/M/J/11/3, Topic: Vectors Points$A$and$B$have coordinates$(-1,2,5)$and$(2,-2,11)$respectively. The plane$p$passes through$B$and is perpendicular to$A B$.$\text{(i)}$Find an equation of$p$, giving your answer in the form$a x+b y+c z=d$.$\text{(ii)}$Find the acute angle between$p$and the$y$-axis.$$Question 2 Code: 9709/32/M/J/11/3, Topic: Trigonometry Solve the equation $$\cos \theta+4 \cos 2 \theta=3$$ giving all solutions in the interval$0^{\circ} \leqslant \theta \leqslant 180^{\circ}$.$$Question 3 Code: 9709/33/M/J/11/3, Topic: Integration Show that$\displaystyle\int_{0}^{1}(1-x) \mathrm{e}^{-\frac{1}{2} x} \mathrm{~d} x=4 \mathrm{e}^{-\frac{1}{2}}-2$.$$Question 4 Code: 9709/31/O/N/11/3, Topic: Algebra The polynomial$x^{4}+3 x^{3}+a x+3$is denoted by$\mathrm{p}(x)$. It is given that$\mathrm{p}(x)$is divisible by$x^{2}-x+1$.$\text{(i)}$Find the value of$a$.$\text{(ii)}$When$a$has this value, find the real roots of the equation$\mathrm{p}(x)=0$.$$Question 5 Code: 9709/32/O/N/11/3, Topic: Algebra Question 6 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.$\text{(ii)}$Hence solve the equation$8 \cos \theta+15 \sin \theta=12$, giving all solutions in the interval$0^{\circ}< \theta <360^{\circ}$.$\$

Worked solutions: P1, P3 & P6 (S1)

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