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

MATHEMATICS 9709

Cambridge International AS and A Level

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

Qtn No. 1 2 3 4 5 6 7 8 9 10 11 12 Total
Marks 4 4 5 5 6 7 5 8 8 7 8 8 75
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 questions Question 1 Code: 9709/12/M/J/10/2, Topic: Integration The diagram shows part of the curve$y=\displaystyle \frac{a}{x}$, where$a$is a positive constant. Given that the volume obtained when the shaded region is rotated through$360^{\circ}$about the$x$-axis is$24 \pi$, find the value of$a$.$[4]$Question 2 Code: 9709/11/M/J/18/2, Topic: Differentiation A point is moving along the curve$\displaystyle y=2 x+\frac{5}{x}$in such a way that the$x$-coordinate is increasing at a constant rate of$0.02$units per second. Find the rate of change of the$y$-coordinate when$x=1$.$[4]$Question 3 Code: 9709/12/M/J/18/2, Topic: Quadratics The equation of a curve is$y=x^{2}-6 x+k$, where$k$is a constant.$\text{(i)}$Find the set of values of$k$for which the whole of the curve lies above the$x$-axis.$[2]\text{(ii)}$Find the value of$k$for which the line$y+2 x=7$is a tangent to the curve.$[3]$Question 4 Code: 9709/12/M/J/18/3, Topic: Series A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by$2 \%$of the amount obtained in the preceding week. It is given that in the first week after the change the company obtained$8000 \mathrm{~kg}$of salt.$\text{(i)}$Find the amount of salt obtained in the 12 th week after the change.$[3]\text{(ii)}$Find the total amount of salt obtained in the first 12 weeks after the change.$[2]$Question 5 Code: 9709/12/M/J/16/4, Topic: Series Find the term that is independent of$x$in the expansion of$\text{(i)}\displaystyle\left(x-\frac{2}{x}\right)^{6}$,$[2]\text{(ii)}\displaystyle\left(2+\frac{3}{x^{2}}\right)\left(x-\frac{2}{x}\right)^{6}$.$[4]$Question 6 Code: 9709/11/M/J/10/5, Topic: Quadratics The function$\mathrm{f}$is such that$\mathrm{f}(x)=2 \sin ^{2} x-3 \cos ^{2} x$for$0 \leqslant x \leqslant \pi$.$\text{(i)}$Express$\mathrm{f}(x)$in the form$a+b \cos ^{2} x$, stating the values of$a$and$b$.$[2]\text{(ii)}$State the greatest and least values of$\mathrm{f}(x)$.$[2]\text{(iii)}$Solve the equation$f(x)+1=0$.$[3]$Question 7 Code: 9709/12/M/J/19/5, Topic: Circular measure The diagram shows a semicircle with diameter$A B$, centre$O$and radius$r$. The point$C$lies on the circumference and angle$A O C=\theta$radians. The perimeter of sector$B O C$is twice the perimeter of sector$A O C$. Find the value of$\theta$correct to 2 significant figures.$[5]$Question 8 Code: 9709/13/M/J/13/7, Topic: Coordinate geometry The diagram shows three points$A(2,14), B(14,6)$and$C(7,2).$The point$X$lies on$A B$, and$C X$is perpendicular to$A B$. Find, by calculation,$\text{(i)}$the coordinates of$X$,$[6]\text{(ii)}$the ratio$A X: X B$.$[2]$Question 9 Code: 9709/13/M/J/14/8, Topic: Quadratics$\text{(i)}$Express$2 x^{2}-10 x+8$in the form$a(x+b)^{2}+c$, where$a, b$and$c$are constants, and use your answer to state the minimum value of$2 x^{2}-10 x+8$.$[4]\text{(ii)}$Find the set of values of$k$for which the equation$2 x^{2}-10 x+8=k x$has no real roots.$[4]$Question 10 Code: 9709/11/M/J/16/8, Topic: Coordinate geometry A curve has equation$\displaystyle y=3 x-\frac{4}{x}$and passes through the points$A(1,-1)$and$B(4,11)$. At each of the points$C$and$D$on the curve, the tangent is parallel to$A B$. Find the equation of the perpendicular bisector of$C D$.$[7]$Question 11 Code: 9709/12/M/J/19/9, Topic: Coordinate geometry The curve$C_{1}$has equation$y=x^{2}-4 x+7$. The curve$C_{2}$has equation$y^{2}=4 x+k$, where$k$is a constant. The tangent to$C_{1}$at the point where$x=3$is also the tangent to$C_{2}$at the point$P$. Find the value of$k$and the coordinates of$P$.$[8]$Question 12 Code: 9709/11/M/J/21/10, Topic: Coordinate geometry The equation of a circle is$x^{2}+y^{2}-4 x+6 y-77=0$.$\text{(a)}$Find the$x$-coordinates of the points$A$and$B$where the circle intersects the$x$-axis.$[2]\text{(b)}$Find the point of intersection of the tangents to the circle at A and B.$[6]\$

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/51 ).
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).