Hits: 18

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

Hits: 18   Question The polynomial  is denoted by p(x). i.       Find the quotient when p(x) is divided by  .  ii.       Hence solve the equation  p(x)=0. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to solve; When a polynomial, , is divided by a non-constant […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 34   Question The polynomial , where a and b are constants, is denoted by . It is given that  when  is divided by  the remainder is 4, and that when  is divided by the remainder is 12. i.       Find the values of  and .    ii.       When a and b have these values, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 11   Question The polynomial , where a and b are constants, is denoted by . It is given that  when  is divided by  the remainder is 4, and that when  is divided by the remainder is 12.     i.       Find the values of  and .    ii.       When a and b have these […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#3

Hits: 22   Question The polynomial  is defined by where  is a constant. i.       Given that  is a factor of , find the value of .    ii.       When  has this value,                      a.  Factorise p(x) completely,                   […]

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

Hits: 9   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#3

Hits: 14   Question The polynomial  is defined by where  is a constant. i.       Given that  is a factor of , find the value of .    ii.       When  has this value,               a.  Factorise p(x) completely,              b.   Find the remainder when p(x) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 16   Question i.       The polynomial , where  and  are constants, is denoted by . It is  given that   and  are factors of . Find the values of  and .    ii.       When  and  have these values, find the quotient when p(x) is divided by x2 + x − 2. Solution      i.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 28   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 12. 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 2010 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 28   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 10. i.       Find the values of a and b.    ii.       When a and b have these values, solve the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 15   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 10.  i.       Find the values of a and b.    ii.       When a and b have these values, solve the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#8

Hits: 58     Question a)   Find the equation of the tangent to the curve at the point where . b)                  i.       Find the value of the constant A such that           ii.       Hence show that Solution a.     We are given that curve with […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#7

Hits: 58 Question      i.       Differentiate ln(2x + 3).    ii.       Hence, or otherwise, show that   iii.       Find the quotient and remainder when 4×2 + 8x is divided by 2x + 3.   iv.       Hence show that Solution      i.   We are required to find; If we define , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 87   Question The polynomial , where a is a constant, is denoted by . It is given that  is a factor of . i.Find the value of  .    ii. When  has this value, factorise  completely. Solution      i.  We are given that;    We are also given that is a factor of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#2

Hits: 65   Question The polynomial , where a is a constant, is denoted by . It is given that is a factor of . i.       Find the value of  .    ii.       When  has this value, factorise  completely. Solution      i.  We are given that;    We are also given that is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 121   Question The polynomial , where a is a constant, is denoted by . It is given that  is a factor of .     i.       Find the value of  .    ii.       When  has this value, solve the equation . Solution      i.  We are given that;    We are also […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#3

Hits: 102   Question The polynomial , where a is a constant, is denoted by . It is given that is a factor of . i.       Show that . ii.       Hence, or otherwise, solve the equation . Solution      i.   We are given that;    We are also given that is a […]