# 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 | May-Jun | (P2-9709/22) | Q#6

Question a)   Find b)  Without using a calculator, find the exact value of giving your answer in the form . c)     The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and  the lines x = 0, x = 6 and y = 0 is denoted by […]

# 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#5

Question The equation of a curve is  . At the point on the curve with x-coordinate p, the gradient of  the curve is .      i.       Show that .      ii.       Show by calculation that 3.3 < p < 3.5.     iii.       Use an iterative formula based on the equation in part (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#4

Question Show that i.Hence a)   find the exact value of , b)  Solve the equation , for . Solution      i.   We are given that; We know that; Therefore;      ii.   a)     We are required to find the exact value of From (i) we have found that; Therefore; b)    We […]

# 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#3

Question      i.       Solve the equation .    ii.       Hence solve the equation  for , giving your answer  correct to 3 significant figures. Solution i.   SOLVING EQUALITY: 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 […]

# 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#2

Question i.       Find the quotient and remainder when  is divided by .    ii.       Hence find the values of the constants p and q such that x2 − 2x + 5 is a factor of 2×3 − 7×2 + px + q. Solution      i.   Hence quotient is and remainder is […]

# 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#2

Question i.       Find the quotient and remainder when  is divided by .    ii.       Hence find the values of the constants p and q such that x2 − 2x + 5 is a factor of 2×3 − 7×2 + px + q. Solution      i.   Hence quotient is and remainder is […]

# 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#1

Question Given that 53x = 74y, use logarithms to find the value of correct to 4 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule; Answer correct to 4 significant figures is;