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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 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 2006 | May-Jun | (P2-9709/02) | Q#4

Hits: 68  Question The cubic polynomial , where  and  are constants, is denoted by . It is given that   and  are factors of .     i.       Find the values of  and .    ii.       When  and  have these values, find the other linear factor of . Solution      i.   We are given […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#6

Hits: 6   Question The polynomial  is given by  . a.   Use the Factor Theorem to show that  is a factor of  . b.   Express as the product of three linear factors. c.                 i.  Use the Remainder Theorem to find the remainder, , when is divided by .             ii. Using algebraic division, or otherwise,  […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#6

Hits: 6   Question The polynomial  is given by a.                                i.       Using the factor theorem, show that  is a factor  of .                          ii.       Hence express  as the product of three linear factors.   b.       Sketch the curve with equation  , showing the coordinates of the points  where the curve cuts the axes. (You are not required to calculate the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#5

Hits: 3   Question The curve with equation  is sketched below. The curve crosses the x-axis at the origin  and the point  lies on the curve.  a.                                i.       Find                          ii.       Hence show that the curve has a stationary  point when  and find the x-coordinate  of the other stationary point. b.                             […]