# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#7

Question      i.       Express in the form , where  and , giving the  exact value of R and the value of a correct to 2 decimal places.    ii.      Hence solve the equation Giving all solutions in the interval  correct to 1 decimal place.   iii.       Determine the least value of  as […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#6

Question      i.       By sketching a suitable pair of graphs, show that the equation where x is in radians, has only one root for .    ii.       Verify by calculation that this root lies between x= 0.7 and x=0.9.   iii.       Show that this root also satisfies the equation   iv.       Use the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#5

Question The parametric equations of a curve are  ,  ,     i.       Show that .  ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is given parametrically […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#3

Question i.       Show that  .  ii.       Hence show that Solution      i.   We are given that; From this we can write; From this we can write; It can be formulated as; Hence;    ii.   We are required to show that; We have found in (i) that; Therefore; Rule for integration of  is: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#1

Question Solve the equation , giving answers correct to 2 decimal places where appropriate. Solution i.   Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Taking logarithm of both sides. Power […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#4

Question The polynomial , where  and  are constants, is denoted by . It is given that   is a factor of , and that when  is divided by  the remainder is 8. i.       Find the values of a and b. ii.       When a and b have these values, factorise p(x) completely. Solution      […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#2

Question Solve the equation ln(3 − 2x) − 2 ln x = ln 5. Solution We are given; Power Rule; Division Rule; Taking anti-logarithm of both sides;  for any Now we have two options. Since logarithm of a negative number is not possible, therefore is not possible because we  have the term in the […]