# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#7

Question The equation of a curve is      i.       Find an expression for  and show that the gradient of the curve at the point  (−1, 2)  is .   ii.       Show that the curve has no stationary points.   iii.       Find the x-coordinate of each of the points on the curve at which the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#6

Question a.   Showing all necessary working, solve the equation for . b.   Showing all necessary working, solve the equation for . Solution a.     We are given;   provided that   provided that Let , then; We are given that ; interval for  can be found as follows. Multiplying entire inequality with 2; Hence, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#5

Question It is given that Where  is a constant.     i.       Show that    ii.       Using the equation in part (i), show by calculation that 0.5 < a < 0.75.   iii.       Use an iterative formula, based on the equation in part (i), to find the value of a  correct to 3 significant figures. Give […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#4

Question The polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Find the value of a .    ii.       Using this value of a, factorise completely.    iii.       Hence solve the equation , giving the answer correct to 2 significant figures. Solution      i.   We are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#3

Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the  curve at that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#2

Question Find the exact value of Solution We are given that; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#1

Question      i.       Solve the inequality .    ii.       Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE      i.   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 […]