Polynomials (2012) Archives — O/A Level Solutions

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#3

  Question The polynomial  is denoted by p(x). i.       Find the quotient when p(x) is divided by  .  ii.       Hence solve the equation  p(x)=0. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to solve; When a polynomial, , is divided by a non-constant divisor, , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#7

  Question The polynomial , where a and b are constants, is denoted by . It is given that  when  is divided by  the remainder is 4, and that when  is divided by the remainder is 12. i.       Find the values of  and .    ii.       When a and b have these values, find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#7

  Question The polynomial , where a and b are constants, is denoted by . It is given that  when  is divided by  the remainder is 4, and that when  is divided by the remainder is 12.     i.       Find the values of  and .    ii.       When a and b have these values, find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#3

Question The polynomial  is defined by where  is a constant. i.       Given that  is a factor of , find the value of .    ii.       When  has this value,                      a.  Factorise p(x) completely,                      b.  Find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#3

  Question i.       Find the quotient when the polynomial   is divided by  ,  and  show that the remainder is 4.    ii.       Hence, or otherwise, factorise the polynomial Solution      i.   Hence quotient is and remainder is .      ii.   We are required to factorise; When a polynomial, , is divided by […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#3

  Question The polynomial  is defined by where  is a constant. i.       Given that  is a factor of , find the value of .    ii.       When  has this value,               a.  Factorise p(x) completely,              b.   Find the remainder when p(x) is divided […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#8

Question The curve  has equation a.   Find . b.   Sketch , showing the coordinates of the points where C1 meets the x-axis. c.   Find the gradient of  at each point where C1 meets the x-axis. The curve  has equation where k is a constant and . d.   Sketch , showing the coordinates of the points where  meets the x […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#3

  Question The polynomial  is given by . a.                       i.       Use the Factor Theorem to show that  is a factor of .                   ii.       Express  as the product of three linear factors. b.   Verify that . c.   Sketch the curve with equation  , indicating the values where the curve  crosses the x-axis. Solution a.   […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#5

  Question The polynomial  is given by  , where c and d are constants. a.   When  is divided by x+2, the remainder is -150. Show that b.  Given that x-3 is a factor of , find another equation involving c and d.  c.   By solving these two equations, find the value of c and the value of d. Solution a.   Remainder […]