# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#3

Question The polynomial  is given by . where b and c are integers. a.   Given that  is a factor of  show that . b.   The remainder when  is divided by  is -30. Obtain a further equation in b and c. c.   Use equations from parts (a) and (b) to find the value of b and the value of c. Solution […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#2

Question A curve has the equation . The curve has a stationary point at the point M where . a.  Find the coordinates of the other stationary point of the curve. b.  Find the value of  at the point M, and hence determine, with a reason, whether M is a  minimum point or a maximum point. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#4

Question The polynomial  is given by . a.                                i.       Use the Factor Theorem to show that  is a factor of .                          ii.      Express  as a product of three linear factors. b.                                i.       Use Remainder Theorem  to find the remainder when  is divided by .                          ii.       Express  in the form , where b and c are integers. Solution a.                               i.   Factor […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#7

Question a.   Sketch the curve with equation . 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.                         iv.       Hence show that the equation  has exactly 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 | January | Q#4

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 . Find the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#5

Question The polynomial  is given by . where c and d are integers. a.    Given that  is a factor of  show that b.   The remainder when  is divided by  is 65. Obtain a function in c and d. c.   Use equations from parts (a) and (b) to find the value of c and the value of d. Solution a.   Factor […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#6

Question a.   The polynomial f(x) is given by  .                                                i.    Use the Factor Theorem to show that (x-1) is a factor of f(x).                                               ii.    Express f(x) in the form  , where p and q are integers.                                             iii.    Hence show that the equation f(x)=0 has exactly one real root and state its value. b.   The curve with equation  is sketched below. The […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#4

Question a.   The polynomial f(x) is given by .                     i.       Use the Factor Theorem to show that x+3 is a factor of f(x).                   ii.       Express f(x) in the form  , where p and q are integers. b.   A curve has equation .                     i.       Find .                   ii.       Show that the x-coordinates of any stationary points of the curve satisfy the equation                  iii.       Use the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#5

Question The polynomial  is given by a.   Use the Remainder Theorem to find the remainder when  is divided by x+1. b.                         i.       Use the Factor Theorem to show that x-3 is a factor of .                   ii.       Express  as a product of linear factors. c.   Sketch the curve with equation  , stating the values of where the curve meets the […]

# 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 2011 | June | Q#5

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 theorem states […]

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

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.   Hence show that […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | 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.   Use the Remainder Theorem to find the remainder when  is divided by . c.                                i.       Verify that .                          ii.  […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#1

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. Solution a.   Factor theorem states that if  is a factor of   then; For the given case  is factor of . We can write the factor in standard form as; Here  and . […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#4

Question a.  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.               iv.       The equation  has one root equal to -2. Show that equation has no other real roots. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#6

Question a.  The polynomial  is given by .                     i.       Use the Factor Theorem to show that  is a factor of .                   ii.       Express  in the form  , where a and b are constants. b. The curve C with equation  , sketched below, crosses the x-axis at the point .                     i.       Find the gradient of the curve C at the point Q.                   ii.       Hence find an […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#6

Question The polynomial p(x) is given by  . a.   Use the Remainder Theorem to find the remainder when p(x) is divided by x-1 . b.                         i.       Use the Factor Theorem to show that x+2 is a factor of p(x).                   ii.       Express p(x) as the product of linear factors. c.                         i.       The curve with equation  passes through the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#6

Question a.   The polynomial  is given by .                   i.       Use the Factor Theorem to show that  is a factor of  .                 ii.       Express  as the product of three linear factors. b.   The curve with equation  is sketched below. The curve cuts the x-axis at the point A and the points […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January| Q#1

Question The polynomial  is given by where k is a constant.   a.           i.       Given that  is a factor of , show that .              ii.       Express   as the product of three linear factors. b.   Use the Remainder Theorem to find the remainder when  is divided by . c.   Sketch the curve […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#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,  express  in […]