# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#7

Question (i)          Show that and hence find the exact value of; (ii)   The region enclosed by the curve y = tan x + cos x and the lines x = 0,  and y = 0 is shown in  the diagram. Find the exact volume of the solid produced when this region is rotated […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#6

Question The diagram shows the curve , for . The x-coordinate of the maximum point  M is denoted by . i.       Find  and show that  satisfies the equation tan 2x = 2x + 4.    ii.       Show by calculation that  lies between 0.6 and 0.7.   iii.       Use the iterative formula to find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#5

Question The parametric equations of a curve are      i.       Find an expression for in terms of t.      i.       Find the equation of the normal to the curve at the point for which t = 0. Give your answer in  the form ax + by + c = 0, where a, b and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#4

Question i. Express  in the form , where  and , Give the value of  correct to 2 decimal places.    ii.Hence solve the equation for .   iii. State the largest value of k for which the equation  has any solutions. Solution      i.   We are given the expression; We are required to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#3

Question i.       Find the quotient when the polynomial   is divided by  ,  and  show that the remainder is 4.    ii.       Hence, or otherwise, factorise the polynomial Solution      i.   Hence quotient is and remainder is .      ii.   We are required to factorise; When a polynomial, , is divided by […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#2

Question      i.       Given that 52x + 5x = 12, find the value of 5x.    ii.       Hence, using logarithms, solve the equation 52x + 5x = 12, giving the value of x correct to 3  significant figures. Solution i.   We are given; Let , then; Therefore; It is a quadratic […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | 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 […]