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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#2

Hits: 46   Question The polynomial  is denoted by .     i.       Find the remainder when  is divided by .    ii.       Find the quotient and remainder when   is divided by . Solution      i.   We are given that;    We are required to find the remainder when is divided by […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#4

Hits: 45   Question The polynomial  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  and  have these values, factorise . Solution      i.   We are given […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#4

Hits: 12   Question a.   The function f is defined for all values of  by  .                            i.       Find the remainder when  is divided by .                          ii.       Given that  and  , write down two linear factors of .                        iii.       Hence express  as the product of three linear factors. b.   The curve with equation  is sketched below.                            i.       The curve intersects the y-axis at the point […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#6

Hits: 9   Question The cubic polynomial  is given by . a.   Show that  can be written in the form  , where   and   are constants  whose values are to be found. b.   Use the Remainder Theorem to find the remainder when    is divided by  . c.   Prove that the equation  has only one real root and state its value. Solution […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#4

Hits: 20   Question The curve with equation  is sketched below. The curve touches the x-axis at the point  and cuts the x-axis at the point  . a.                               i.       Use the factor theorem to show that  is a factor  of                          ii.       Hence find the coordinates of B b. The point , shown on  the  diagram, is  a   minimum point  of  the  curve with equation […]