# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#7

Question      i.       Given that y = tan 2x, find .    ii.       Hence, or otherwise, show that and, by using an appropriate trigonometrical identity, find the exact value of   iii.       Use the identity cos 4x ≡ 2cos2 2x − 1 to 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 2006 | Oct-Nov | (P2-9709/02) | Q#6

Question The diagram shows the part of the curve  for , and its minimum point M.      i.       Find the coordinates of M.    ii.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 1 decimal place.   iii.       State, with a reason, whether the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#5

Question The diagram shows a chord joining two points, A and B, on the circumference of a circle with centre  O and radius r. The angle AOB is radians, where . The area of the shaded  segment is one sixth of the area of the circle.     i.       Show that  satisfies the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#4

Question i. Prove the identity    ii. Hence, solve the equation Solution      i.   We are given that; Utilizing addition formulae; We have algebraic formulae; We have double angle formula as; From this we can write; Substituting in above equation;    ii.   We are required to solve the equation; As demonstrated in […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#3

Question The polynomial , where a is a constant, is denoted by . It is given that is a factor of . i.       Show that . ii.       Hence, or otherwise, solve the equation . Solution      i.   We are given that;    We are also given that is a factor of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#2

Question      i.       Express 4x in terms of y, where y = 2x.    ii.       Hence find the values of x that satisfy the equation 3(4x) -10 (2x) + 3= 0 giving your answers correct to 2 decimal places. Solution i.   We are given; We are also given that; Writing given expression […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#1

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 following […]