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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#8

Hits: 20 Question      i.       Show that .    ii.       Using the identity in part (i),                a.   find the least possible value of as x varies.                             b.  find the exact value of Solution      […]

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

Hits: 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 […]

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

Hits: 11   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 […]

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#4

Hits: 12 Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Determine the value of correct to 3 decimal places, giving the result of each iteration to 5  decimal places.    ii.       State an equation satisfied by and hence find the exact value of . […]

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#3

Hits: 8   Question It is given that k is a positive constant. Solve the equation 2 ln x = ln(3k + x) + ln(2k – x), expressing  x in terms of k. Solution We are given that; Power Rule; Multiplication Rule;  and are inverse functions. The composite function is an identity function, with  domain […]

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

Hits: 15   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 […]