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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: 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 2010 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 6   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: 24     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: 28 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: 75   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: 41   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: 91   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: 83   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/21) | Q#4

Hits: 44   Question The polynomial  is defined by i.       Find the quotient when  is divided by ,  and show that the remainder is 5.    ii.       Hence factorise  completly. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to factorise; When a polynomial, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#2

Hits: 10   Question i.       Given that  is a factor of , find the value of the constant . ii.       When  has this value, factorise  completely. Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, , is divided by , and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#2

Hits: 29   Question i.       Given that  is a factor of , find the value of the constant . ii.       When  has this value, factorise  completely. Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, , is divided by , and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#3

Hits: 25    Question     i.       Find the quotient when  is divided by ,  and confirm that the  remainder is 7. ii.       Hence solve the equation . Solution      i.   Hence quotient is and remainder is .    ii.  We are required to solve; When a polynomial, , is divided by a […]

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

Hits: 9   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. […]