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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 6 7 8 9 10 11 12 Total
Marks 5 5 4 4 6 3 5 8 9 8 8 9 74
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 questions Question 1 Code: 9709/13/M/J/10/1, Topic: Series The first term of a geometric progression is 12 and the second term is$-$6. Find$\text{(i)}$the tenth term of the progression,$[3]\text{(ii)}$the sum to infinity.$[2]$Question 2 Code: 9709/12/M/J/13/2, Topic: Series Find the coefficient of$x^{2}$in the expansion of$\text{(i)}\displaystyle\left(2 x-\frac{1}{2 x}\right)^{6}$,$[2]\text{(ii)}\displaystyle\left(1+x^{2}\right)\left(2 x-\frac{1}{2 x}\right)^{6}$.$[3]$Question 3 Code: 9709/13/M/J/15/2, Topic: Integration A curve is such that$\displaystyle\frac{\mathrm{d} y}{\mathrm{~d} x}=(2 x+1)^{\frac{1}{2}}$and the point$(4,7)$lies on the curve. Find the equation of the curve.$[4]$Question 4 Code: 9709/11/M/J/18/2, Topic: Differentiation A point is moving along the curve$\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 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/21/4, Topic: Trigonometry The diagram shows part of the graph of$y=a \tan (x-b)+c$Given that$0 < b < \pi$, state the values of the constants$a, b$and$c$.$[3]$Question 7 Code: 9709/12/M/J/21/4, Topic: Series The coefficient of$x$in the expansion of$\displaystyle \left(4 x+\frac{10}{x}\right)^{3}$is$p$. The coefficient of$\displaystyle \frac{1}{x}$in the expansion of$\displaystyle \left(2 x+\frac{k}{x^{2}}\right)^{5}$is$q$. Given that$p=6 q$, find the possible values of$k$.$[5]$Question 8 Code: 9709/13/M/J/18/8, Topic: Differentiation$\text{(i)}$The tangent to the curve$y=x^{3}-9 x^{2}+24 x-12$at a point$A$is parallel to the line$y=2-3 x$. Find the equation of the tangent at$A$.$[6]\text{(ii)}$The function$\mathrm{f}$is defined by$\mathrm{f}(x)=x^{3}-9 x^{2}+24 x-12$for$x>k$, where$k$is a constant. Find the smallest value of$k$for$\mathrm{f}$to be an increasing function.$[2]$Question 9 Code: 9709/11/M/J/11/9, Topic: Circular measure In the diagram,$O A B$is an isosceles triangle with$O A=O B$and angle$A O B=2 \theta$radians. Arc$P S T$has centre$O$and radius$r$, and the line$A S B$is a tangent to the$\operatorname{arc} P S T$at$S$.$\text{(i)}$Find the total area of the shaded regions in terms of$r$and$\theta$.$[4]\text{(ii)}$In the case where$\theta=\frac{1}{3} \pi$and$r=6$, find the total perimeter of the shaded regions, leaving your answer in terms of$\sqrt{3}$and$\pi$.$[5]$Question 10 Code: 9709/13/M/J/12/9, Topic: Integration, Differentiation A curve is such that$\displaystyle\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-4 x.$The curve has a maximum point at$(2,12)$.$\text{(i)}$Find the equation of the curve.$[6]$A point$P$moves along the curve in such a way that the$x$-coordinate is increasing at$0.05$units per second.$\text{(ii)}$Find the rate at which the$y$-coordinate is changing when$x=3$, stating whether the$y$-coordinate is increasing or decreasing.$[2]$Question 11 Code: 9709/13/M/J/14/9, Topic: Differentiation The base of a cuboid has sides of length$x \mathrm{~cm}$and$3 x \mathrm{~cm}$. The volume of the cuboid is$288 \mathrm{~cm}^{3}$.$\text{(i)}$Show that the total surface area of the cuboid,$A \mathrm{~cm}^{2}$, is given by$[3]$$$A=6 x^{2}+\frac{768}{x}.$$$\text{(ii)}$Given that$x$can vary, find the stationary value of$A$and determine its nature.$[5]$Question 12 Code: 9709/13/M/J/13/11, Topic: Coordinate geometry, Integration The diagram shows part of the curve$\displaystyle y=\frac{8}{\sqrt{x}}-x$and points$A(1,7)$and$B(4,0)$which lie on the curve. The tangent to the curve at$B$intersects the line$x=1$at the point$C$.$\text{(i)}$Find the coordinates of$C$.$[4]\text{(ii)}$Find the area of the shaded region.$[5]\$

Worked solutions: P1, P3 & P6 (S1)

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