Hits: 53

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: 53   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: 63   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 2011 | May-Jun | (P2-9709/23) | Q#7

Hits: 37   Question The cubic polynomial  is defined by where  and  are constants. It is given that  is a factor of  and that, when is divided by , the remainder is 24.      i.       Find the values of  and .    ii.       When  and  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 2011 | May-Jun | (P2-9709/22) | Q#7

Hits: 100   Question The cubic polynomial  is defined by where  and  are constants. It is given that  is a factor of  and that, when is divided by , the remainder is 24.      i.       Find the values of  and .    ii.       When  and  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 2011 | May-Jun | (P2-9709/21) | Q#4

Hits: 121   Question The polynomial  is defined by where  is a constant. i.       Given that  is a factor of , find the value of . ii.       When  has the value found in part (i), find the quotient when  is divided by . Solution      i.   We are given that; We are […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#10

Hits: 40   Question a.   On the axes below, sketch the graphs of i.        ii.     showing clearly the coordinates of all the points where the curves cross the coordinate axes. b.   Using your sketch state, giving a reason, the number of real solutions to the equation Solution a.   i.   We are required to sketch; We need to […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#5

Hits: 63 Question The polynomial  is given by . a.   Use the Remainder Theorem to find the remainder when  is divided by . b.   Use the Factor Theorem to show that  is a factor of . c.                         i.       Express  in the form , where b and c are integers.                   ii.       Hence show that the equation  has exactly one real root. Solution a.   Remainder […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#5

Hits: 47   Question a.                         i.       Sketch the curve with equation         ii.       Show that the equation  can be expressed as b.   The polynomial  is given by  .                     i.       Find the remainder when  is divided by .                   ii.       Use the Factor Theorem to show that  is a factor of .                  iii.       Express  in the form  , where b and c are integers. c.   […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#6

Hits: 65   Question A circle has centre C(-3,1) and radius . a.                         i.       Express the equation of the circle in the form                   ii.       Hence find the equation of the circle in the form where m, n and p are integers. b.   The circle cuts the y-axis at the points A and B. Find the distance AB. c.                         i.       Verify […]