Hits: 151

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 151   Question The polynomial x3 + 4×2 + ax + 2, where a is a constant, is denoted by p(x). It is given that the  remainder when p(x) is divided by (x + 1) is equal to the remainder when p(x) is divided by (x − 2).     i.       Find the value […]

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: 17   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: 7   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: 28     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: 29 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 | (P2-9709/22) | Q#5

Hits: 101   Question The polynomial , where a is a and b are constants, is denoted by . It is given that  and (x − 2) are factors of p(x). i.       Find the values of a and b.    ii.       When a and b have these values, find the other linear factor […]

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: 45   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: 92   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: 84   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 | (P2-9709/23) | Q#2

Hits: 22   Question i.       Find the quotient and remainder when  is divided by .    ii.       Hence find the values of the constants p and q such that x2 − 2x + 5 is a factor of 2×3 − 7×2 + px + q. Solution      i.   Hence quotient is and […]

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

Hits: 32   Question i.       Find the quotient and remainder when  is divided by .    ii.       Hence find the values of the constants p and q such that x2 − 2x + 5 is a factor of 2×3 − 7×2 + px + q. Solution      i.   Hence quotient is and […]

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: 51   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: 12   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: 39   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 | (P2-9709/21) | Q#4

Hits: 15   Question The polynomials f(x) and g(x) are defined by;  and where a and b are constants. It is given that (x + 2) is a factor of f(x). It is also given that, when g(x)  is divided by (x + 1), the remainder is −18. i.       Find the values of a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#6

Hits: 22   Question The polynomial p(x) is defined by where a is a constant.     i.       Given that (x + 2) is a factor of p(x), find the value of a. ii.       When a has this value, find the quotient when p(x) is divided by (x + 2) and hence show that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#6

Hits: 57   Question The polynomial p(x) is defined by where a is a constant.     i.       Given that (x + 2) is a factor of p(x), find the value of a. ii.       When a has this value, find the quotient when p(x) is divided by (x + 2) and hence show that […]

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: 27    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: 10   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. […]