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### AS MATHEMATICS - LY

#### 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 Total
Marks 3 4 3 4 7 8 29
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 A line has equation$y=2 x-7$and a curve has equation$y=x^{2}-4 x+c$, where$c$is a constant. Find the set of possible values of$c$for which the line does not intersect the curve.$[3]$Question 2$\text{(i)}$Express$x^{2}+6 x+2$in the form$(x+a)^{2}+b$, where$a$and$b$are constants.$[2]\text{(ii)}$Hence, or otherwise, find the set of values of$x$for which$x^{2}+6 x+2>9$.$[2]$Question 3 Showing all necessary working, solve the equation$4 x-11 x^{\frac{1}{2}}+6=0$.$[3]$Question 4$\text{(i)}$Express$4 x^{2}-12 x$in the form$(2 x+a)^{2}+b$.$[2]\text{(ii)}$Hence, or otherwise, find the set of values of$x$satisfying$4 x^{2}-12 x>7$.$[2]$Question 5 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.$[4]\text{(ii)}$Find the value of$k$for which the line is a tangent to the curve.$[3]$Question 6 A curve for which$\displaystyle\frac{\mathrm{d} y}{\mathrm{~d} x}=7-x^{2}-6 x$passes through the point$(3,-10)$.$\text{(i)}$Find the equation of the curve.$[3]\text{(ii)}$Express$7-x^{2}-6 x$in the form$a-(x+b)^{2}$, where$a$and$b$are constants.$[2]\text{(iii)}$Find the set of values of$x$for which the gradient of the curve is positive.$[3]\$

Worked solutions: P1, P3 & P6 (S1)

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