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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 1 Question     i.       Use the factor theorem to show that (2x+3) is a factor of    ii.       Show that the equation  can be expressed as   iii.       Solve the equation For . Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#2

Hits: 1 Question Given that , find the value of 3x and hence, using logarithms, find the  value of x correct to 4 significant figures. Solution We are given that; Let ; Now we have two options. Since ; Taking logarithm of both sides; Since logarithm of negative number is nt possible, only possible solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/23) | Q#1

Hits: 8 Question      i.       Solve the equation .    ii.       Hence, using logarithms, solve the equation , giving the  answer correct to 3 significant figures. Solution i.   SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/21) | Q#1

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

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/23) | Q#3

Hits: 14 Question     i.       Find the quotient when   is divided by  ,  and show that the  remainder is 1.    ii.        Show that the equation  has no real root. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to show that following equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/22) | Q#3

Hits: 1 Question i.       Find the quotient when   is divided by  ,  and show that the remainder is 1.    ii.       Show that the equation  has no real root. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to show that following equation has no real […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#6

Hits: 5 Question The cubic polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Use the factor theorem to find the value of  and hence factorise f(x) completely.    ii.       Hence, without using a calculator, solve the equation f(2x) = 3f(x). Solution      i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#7

Hits: 45 Question The diagram shows part of the curve defined by the parametric equations The curve has a minimum point at M and crosses the x-axis at the point P.     i.       Find the gradient of the curve at P.    ii.       Find the coordinates of the point M.   iii.       The value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#4

Hits: 14 Question The polynomial p(x) is defined by     i.       Use the factor theorem to show that (x+3) is a factor of p(x).    ii.       Factorise p(x) completely.   iii.       Hence, given that find the value of 2u and, using logarithms, find the value of u correct to 3 significant figures. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#1

Hits: 6   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#6

Hits: 9 Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of and that remainder is 28  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) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#3

Hits: 15 Question      i.       Solve the inequality .    ii.       Hence find the largest integer y 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#2

Hits: 8   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 14 Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of . It is also given that the remainder is 40 when  is divided by .     i.       Find the values of a and b.    ii.       When a and b have these values, factorise p(x) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 7 Question The polynomials p(x) and g(x) are defined by;  and where a and b are constants. It is given that (x + 3) is a factor of f(x) and also of q(x).     i.       Find the values of a and b.    ii.       Show that the equation q(x) – p(x) = 0 has […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 3 Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of . It is also given that the remainder is 40 when  is divided by .     i.       Find the values of a and b.    ii.       When a and b have these values, factorise p(x) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/23) | Q#6

Hits: 13 Question     i.       Use the factor theorem to show that (x+2) is a factor of the expression and hence factorise the expression completely.    ii.       Deduce the roots of the equation Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/22) | Q#6

Hits: 11 Question     i.       Use the factor theorem to show that (x+2) is a factor of the expression and hence factorise the expression completely.    ii.       Deduce the roots of the equation Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#2

Hits: 23   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 […]