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### AS MATHEMATICS

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade 11 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 4 6 6 5 6 7 8 7 9 8 9 80
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 questions Question 1 Code: 9709/12/M/J/14/1, Topic: Coordinate geometry Find the coordinates of the point at which the perpendicular bisector of the line joining$(2,7)$to$(10,3)$meets the$x$-axis.$[5]$Question 2 Code: 9709/13/M/J/17/3, Topic: Coordinate geometry Find the coordinates of the points of intersection of the curve$y=x^{\frac{2}{3}}-1$with the curve$y=x^{\frac{1}{3}}+1$.$[4]$Question 3 Code: 9709/12/M/J/10/4, Topic: Coordinate geometry In the diagram,$A$is the point$(-1,3)$and$B$is the point$(3,1)$. The line$L_{1}$passes through$A$and is parallel to$O B$. The line$L_{2}$passes through$B$and is perpendicular to$A B$. The lines$L_{1}$and$L_{2}$meet at$C$. Find the coordinates of$C$.$[6]$Question 4 Code: 9709/12/M/J/20/6, Topic: Quadratics The equation of a curve is$y=2 x^{2}+k x+k-1$, where$k$is a constant.$\text{(a)}$Given that the line$y=2 x+3$is a tangent to the curve, find the value of$k$.$[3]$It is now given that$k=2$.$\text{(b)}$Express the equation of the curve in the form$y=2(x+a)^{2}+b$, where$a$and$b$are constants, and hence state the coordinates of the vertex of the curve.$[3]$Question 5 Code: 9709/11/M/J/21/6, Topic: Quadratics The equation of a curve is$y=(2 k-3) x^{2}-k x-(k-2)$, where$k$is a constant. The line$y=3 x-4$is a tangent to the curve. Find the value of$k[5]$Question 6 Code: 9709/13/M/J/21/6, Topic: Functions Functions$\mathrm{f}$and$\mathrm{g}$are both defined for$x \in \mathbb{R}and are given by \begin{aligned} &\mathrm{f}(x)=x^{2}-2 x+5 \\ &\mathrm{~g}(x)=x^{2}+4 x+13 \end{aligned}\text{(a)}$By first expressing each of$\mathrm{f}(x)$and$\mathrm{g}(x)$in completed square form, express$\mathrm{g}(x)$in the form$\mathrm{f}(x+p)+q$, where$p$and$q$are constants.$[4]\text{(b)}$Describe fully the transformation which transforms the graph of$y = f(x)$to the graph of$y = g(x)$.$[2]$Question 7 Code: 9709/12/M/J/19/7, Topic: Functions Functions$\mathrm{f}$and$\mathrm{g}are defined by \begin{aligned} \mathrm{f}: x & \mapsto 3 x-2, \quad x \in \mathbb{R} \\ \mathrm{g}: x & \mapsto \frac{2 x+3}{x-1}, \quad x \in \mathbb{R}, x \neq 1 \end{aligned}\text{(i)}$Obtain expressions for$\mathrm{f}^{-1}(x)$and$\mathrm{g}^{-1}(x)$, stating the value of$x$for which$\mathrm{g}^{-1}(x)$is not defined.$[4]\text{(ii)}$Solve the equation$\mathrm{fg}(x)=\frac{7}{3}$.$[3]$Question 8 Code: 9709/12/M/J/16/8, Topic: Coordinate geometry Three points have coordinates$A(0,7), B(8,3)$and$C(3 k, k).$Find the value of the constant$k$for which$\text{(i)}C$lies on the line that passes through$A$and$B$,$[4]\text{(ii)}C$lies on the perpendicular bisector of$A B$.$[4]$Question 9 Code: 9709/12/M/J/18/8, Topic: Coordinate geometry Points$A$and$B$have coordinates$(h, h)$and$(4 h+6,5 h)$respectively. The equation of the perpendicular bisector of$A B$is$3 x+2 y=k$. Find the values of the constants$\mathrm{h}$and$k$.$[7]$Question 10 Code: 9709/11/M/J/12/9, Topic: Coordinate geometry The coordinates of$A$are$(-3,2)$and the coordinates of$C$are$(5,6).$The mid-point of$A C$is$M$and the perpendicular bisector of$A C$cuts the$x$-axis at$B$.$\text{(i)}$Find the equation of$M B$and the coordinates of$B$.$[5]\text{(ii)}$Show that$A B$is perpendicular to$B C$.$[2]\text{(iii)}$Given that$A B C D$is a square, find the coordinates of$D$and the length of$A D$.$[2]$Question 11 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.$[6]$Question 12 Code: 9709/13/M/J/14/11, Topic: Coordinate geometry The diagram shows a parallelogram$A B C D$, in which the equation of$A B$is$y=3 x$and the equation of$A D$is$4 y=x+11$. The diagonals$A C$and$B D$meet at the point$E\left(6 \frac{1}{2}, 8 \frac{1}{2}\right)$. Find, by calculation, the coordinates of$A, B, C$and$D$.$[8]\$

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