# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#6

Question The parametric equations of a curve are x = 1 + 2 sin2θ , y = 4 tanθ , i. Show that    ii. Find the equation of the tangent to the curve at the point where , giving your answer in  the form y = mx + c. Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#3

Question The diagram shows the curve y= x − 2 ln x and its minimum point M.      i. Find the x-coordinates of M.    ii. Use the trapezium rule with three intervals to estimate the value of giving your answer correct to 2 decimal places.   iii. State, with a reason, whether […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#7

Question The parametric equations of a curve are  ,  , i.       Show that . ii.       Show that the tangent to the curve at the point (1, 3) is parallel to the x-axis. iii.       Find the exact coordinates of the other point on the curve at which the tangent is parallel to the  x-axis. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#5

Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/22) | Q#5

Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/23) | Q#2

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . It can be written as; We have to deal with two separate cases; When ; When Therefore; Therefore; Hence, Hence, We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/21) | Q#1

Question Solve the inequality . Solution SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; Hence, the only solution for the given equation is; SOLVING EQUATION: […]