# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#7

Question The diagram shows part of the curve The shaded region is bounded by the curve and the two axes.        i. Show that  can be expressed in the form where the values of the constants  and are to be determined.    ii.Find the exact area of the shaded region. Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#6

Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of and that remainder is 28  when  is divided by .     i.       Find the values of a and b.    ii.       Hence factorise   completely.   iii.       State the number of roots of the equation p(2y) = 0, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#5

Question It is given that a is a positive constant such that i.       Show that    ii.       Use an iterative formula based on the equation in part (i) to find the value of a correct to 4  significant figures. Give the result of each iteration to 6 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 2017 | Feb-Mar | (P2-9709/22) | Q#4

Question Find the gradient of the curve at the point . Solution We are required to find the gradient of the curve at point . Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that  particular point. Gradient (slope) of the curve at a particular […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#3

Question      i.       Solve the inequality .    ii.       Hence find the largest integer y 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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#2

Question      i.       Given that , show that .    ii.       Hence solve the equation  for . Solution i.   We are given that; except where  or undefined ii.   We are required to solve the following equation for ; As demonstrated in (i), the given equation can be written as; Now we have two […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#1

Question Solve the equation 2 ln(2x) − ln(x + 3)= ln(3x + 5). Solution We are given that; Power Rule; Multiplication Rule;  and are inverse functions. The composite function is an identity function, with  domain the positive real numbers. Therefore; Taking anti-logarithm of both sides; Now we have two options. If  then will be undefined […]