# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#2

Question                     i.       Solve the equation                   ii.       Hence, using logarithms, solve the equation giving the answer correct to 3 significant figures. Solution SOLVING EQUALITION: PIECEWISE      i.   Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/21) | Q#5

Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of and that  remainder is 27 when  is divided by .     i.       Find the values of a and b.    ii.       Hence factorise   completely.   iii.       State the number of roots of the equation p(2y) = 0, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/21) | Q#2

Question      i.       Solve the inequality .    ii.       Hence find the greatest integer satisfying the inequality  Solution SOLVING INEQUALITY: PIECEWISE      i.   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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#4

Question The polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Find the value of a .    ii.       Using this value of a, factorise completely.    iii.       Hence solve the equation , giving the answer correct to 2 significant figures. Solution      i.   We are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#1

Question      i.       Solve the inequality .    ii.       Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE      i.   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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/21) | Q#4

Question The polynomial  is defined by where  is a constant. It is given that  is a factor of .     i.       Find the value of  .    ii.       Using this value of a, factorise  completely.   iii.       Hence solve the equation , giving the answer correct to 2 significant  figures. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/21) | Q#1

Question      i.       Solve the inequality .    ii.       Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE      i.   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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/23) | Q#2

Question      i.       Solve the equation .    ii.       Hence solve the equation , giving the answer correct to 3  significant figures. Solution i.   SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/22) | Q#2

Question      i.       Solve the equation .    ii.       Hence solve the equation , giving the answer correct to 3  significant figures. Solution i.   SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Feb-Mar | (P2-9709/22) | Q#4

Question     i.       Find the quotient when   is divided by  ,  and show  that the remainder is 5.    ii.       Show that the equation  has exactly one real root. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to show that following equation has exactly one real […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Feb-Mar | (P2-9709/22) | Q#2

Question Given that satisfies the equation find the value of Solution SOLVING EQUALITION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; This cannot be solved. Hence, the solution for […]