# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#8

Question      i.       By differentiating , show that if y = cot x then    ii.       By expressing in terms of and using the result of part (i), show that   iii.       Express cos 2x in terms of sin2 x and hence show that can be expressed as .  Hence using the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#7

Question      i.       By sketching a suitable pair of graphs, show that the equation  has only one root.    ii.       Verify, by calculation that this root lies between x=0 and x=0.5.   iii.       Show that, if a sequence of values given by the iterative formula converges, then it converges to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#6

Question The equation of the curve is .     i.       Show that    ii.       Find the equation of the tangent to the curve at the point (1,2), giving your answer in the form  ax+by=c. Solution      i.   We are given that; Therefore; Rule for differentiation of  is: Rule for differentiation of  is: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#3

Question      i.       Show that the equation can be written in the form    ii.       Hence solve the equation  for . Solution      i.   We are given; We apply following addition formula on left side of given equation. Therefore; Since;      ii.   We are required to solve following […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#2

Question Show that Solution We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#5

Question      i.       Given that y = 2x, show that the equation 2x + 3(2−x) = 4 can be written in the form y2 − 4y + 3 = 0.    ii.       Hence solve the equation 2x + 3(2−x) = 4  giving the values of x correct to 3 significant figures where […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#4

Question The polynomial  is denoted by . i.       Find the quotient and remainder when  is divided by .    ii.       Use the factor theorem to show that  is a factor of . Solution      i.   Hence quotient is and remainder is .    ii.   We are given that; We are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will hold for ; SOLVING INEQUALITY: ALGEBRAICALLY […]