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### CHRISTIAN DJURIT

#### Cambridge International AS and A Level

 Name of student CHRISTIAN DJURIT Date Adm. number Year/grade 1991 Stream Christian Djurit Subject Pure Mathematics 3 (P3) Variant(s) P31, P32, P33 Start time Duration Stop time

Qtn No. 1 2 3 Total
Marks 10 10 10 30
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 3 questions Question 1 Code: 9709/33/M/J/12/9, Topic: Vectors The lines$l$and$m$have equations$\mathbf{r}=3 \mathbf{i}-2 \mathbf{j}+\mathbf{k}+\lambda(-\mathbf{i}+2 \mathbf{j}+\mathbf{k})$and$\mathbf{r}=4 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}+\mu(a \mathbf{i}+b \mathbf{j}-\mathbf{k})$respectively, where$a$and$b$are constants.$\text{(i)}$Given that$l$and$m$intersect, show that$[4]$$$2 a-b=4.$$$\text{(ii)}$Given also that$l$and$m$are perpendicular, find the values of$a$and$b$.$[4]\text{(iii)}$When$a$and$b$have these values, find the position vector of the point of intersection of$l$and$m$.$[2]$Question 2 Code: 9709/31/O/N/12/9, Topic: Algebra The complex number$1+(\sqrt{2}) \mathrm{i}$is denoted by$u$. The polynomial$x^{4}+x^{2}+2 x+6$is denoted by$\mathrm{p}(x)$.$\text{(i)}$Showing your working, verify that$u$is a root of the equation$\mathrm{p}(x)=0$, and write down a second complex root of the equation.$[4]\text{(ii)}$Find the other two roots of the equation$\mathrm{p}(x)=0$.$[6]\$

Question 3 Code: 9709/32/O/N/12/9, Topic: Algebra

Worked solutions: P1, P3 & P6 (S1)

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