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### MATHEMATICS 9709

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade Stream Subject Pure Mathematics 1 (P1) Variant(s) P11, P12, P13 Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 3 7 7 9 9 35
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/13/O/N/16/1, Topic: Quadratics Find the set of values of$k$for which the curve$y=k x^{2}-3 x$and the line$y=x-k$do not meet.$$Question 2 Code: 9709/12/O/N/11/4, Topic: Quadratics The equation of a curve is$y^{2}+2 x=13$and the equation of a line is$2 y+x=k$, where$k$is a constant.$\text{(i)}$In the case where$k=8$, find the coordinates of the points of intersection of the line and the curve.$\text{(ii)}$Find the value of$k$for which the line is a tangent to the curve.$$Question 3 Code: 9709/11/M/J/15/5, Topic: Quadratics A piece of wire of length$24 \mathrm{~cm}$is bent to form the perimeter of a sector of a circle of radius$r \mathrm{~cm}$.$\text{(i)}$Show that the area of the sector,$A \mathrm{~cm}^{2}$, is given by$A=12 r-r^{2}$.$\text{(ii)}$Express$A$in the form$a-(r-b)^{2}$, where$a$and$b$are constants.$\text{(iii)}$Given that$r$can vary, state the greatest value of$A$and find the corresponding angle of the sector.$$Question 4 Code: 9709/11/O/N/11/9, Topic: Quadratics, Coordinate geometry, Differentiation A line has equation$y=k x+6$and a curve has equation$y=x^{2}+3 x+2 k$, where$k$is a constant.$\text{(i)}$For the case where$k=2$, the line and the curve intersect at points$A$and$B$. Find the distance$A B$and the coordinates of the mid-point of$A B$.$\text{(ii)}$Find the two values of$k$for which the line is a tangent to the curve.$$Question 5 Code: 9709/12/O/N/18/10, Topic: Quadratics, Coordinate geometry The equation of a curve is$\displaystyle y=2 x+\frac{12}{x}$and the equation of a line is$y+x=k$, where$k$is a constant.$\text{(i)}$Find the set of values of$k$for which the line does not meet the curve.$$In the case where$k=15$, the curve intersects the line at points$A$and$B$.$\text{(ii)}$Find the coordinates of$A$and$B$.$\text{(iii)}$Find the equation of the perpendicular bisector of the line joining$A$and$B$.$\$

Worked solutions: P1, P3 & P6 (S1)

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