Hits: 29

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

Hits: 53 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) […]

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

Hits: 35 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.   […]

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

Hits: 17 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. […]

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#5

Hits: 23 Question i.       Find the quotient and remainder when is divided by .    ii.       Hence find the exact value of giving the answer in the form where k and a are constants. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to solve; When a […]

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#1

Hits: 15 Question The polynomial  is defined by where  and  are constants. Given that  is a factor of , express in  terms of . Solution We are given that; We are also given that is a factor of . When a polynomial, , is divided by , and  is factor of , then the  remainder […]

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#5

Hits: 40 Question i.       Find the quotient and remainder when is divided by .    ii.       Hence find the exact value of giving the answer in the form where k and a are constants. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to solve; When a […]

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#1

Hits: 52 Question The polynomial  is defined by where  and  are constants. Given that  is a factor of , express in terms of . Solution We are given that; We are also given that is a factor of . When a polynomial, , is divided by , and  is factor of , then the  remainder […]

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

Hits: 192 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 […]

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: 56 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 | (P2-9709/23) | Q#4

Hits: 40 Question The diagram shows the curve with equation . The curve crosses the x-axis at points with coordinates  and .      i.       Use the factor theorem to show that (x +2) is a factor of    ii.       Show that satisfies an equation of the form , and state the  values of p and […]

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#4

Hits: 24   Question The diagram shows the curve with equation . The curve crosses the x-axis at points with coordinates  and .      i.       Use the factor theorem to show that (x +2) is a factor of    ii.       Show that satisfies an equation of the form , and state the  values of p […]

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: 25 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: 43 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: 43 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#4

Hits: 40 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 2017 | Feb-Mar | (P2-9709/22) | Q#6

Hits: 20 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 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 21 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: 32 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 […]