Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#7

Question The equation of a curve is 2×3+y3=24      i.       Express in terms of x and y, and show that the gradient of the curve is never positive.    ii.       Find the coordinates of the two points on the curve at which the gradient is −2. Solution      i.   Gradient (slope) of the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#6

Question The diagram shows the part of the curve  for , and the stationary point M.        i.       Find the equation of the tangent to the curve at the origin.    ii.       Find the coordinates of M, giving each coordinate correct to 3 decimal places. Solution      i.   We are given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | 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 2016 | Oct-Nov | (P2-9709/23) | Q#2

Question The variables x and y satisfy the equation y = Kxp, where K and p are constants. The graph of ln y  against ln x is a straight line passing through the points (1.28, 3.69) and (2.11, 4.81), as shown in  the diagram. Find the values of K and p correct to 2 decimal […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#7

Question The diagram shows the curve with parametric equations for .     i.       Show that can be expressed in the form    ii.       Find the equation of the normal to the curve at the point where the curve crosses the positive y-axis. Give your answer in the form y = mx +c, where the constants […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#6

Question The equation of a curve is 3×2 + 4xy + y2 = 24. Find the equation of the normal to the curve at the point (1, 3), giving your answer in the form ax +by +c = 0 where a, b and c are integers. Solution      i.   We are given equation of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#2

Question The variables x and y satisfy the equation y = Aepx, where A and p are constants. The graph of ln y  against x is a straight line passing through the points (5, 3.17) and (10, 4.77), as shown in the diagram. Find the values of A and p correct to 2 decimal places. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/23) | Q#7

Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q.     i.       Show that .    ii.       Find the coordinates of M.   iii.       Find the gradient of the curve at P and at Q. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/22) | Q#7

Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q.     i.       Show that .    ii.       Find the coordinates of M.   iii.       Find the gradient of the curve at P and at Q. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#1

Question Solve the equation . Solution SOLVING EQUATION: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the equation; It  can be written as; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given equation are; […]