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 2009 | January | Q#4

Question a.                 i.               Express  in the form  , where p and q are integers.           ii.               Hence show that  is always positive. b.   A curve has equation  .                            i.               Write down the coordinates of the minimum point of the curve.                          ii.               Sketch the curve, showing the value of the intercept on the y-axis. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#7

Question A circle with center C has equation .  a.   Express this equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   The point D has coordinates (7,-2).                            i.       Verify that point D lies on the circle.                          ii.       Find an equation of the normal to the circle at the point D, giving […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#5

Question A model car moves so that its distance, x centimeters, from a fixed point O after time t seconds is given by  , a.   Find:                            i.                                  ii.        b.   Verify that x has a stationary value when  and determine whether this stationary value is a  maximum value or a minimum value. c.   Find the rate of change […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#3

Question a.   Express  in the form  , where m and n are integers. b.   Express   in the form , where k is an integer. Solution a.   We are given the expression;   We have algebraic formula; Since b.     We are given the expression; Since ; Since ;

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#2

Question a.   Factorise . b.   Hence, or otherwise, solve the inequality Solution a.   We are given the expression; b.     We are required to solve the inequality; We solve the following equation to find critical values of ; From (a) we know that this equation can be written as; Now we have two options. Hence the critical points on […]

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

Question The points A and B have coordinates (1,6) and (5,-2) respectively. The mid-point of AB is M. a.   Find the coordinates of M. b.   Find the gradient of AB, giving your answer in its simplest form. c.   A straight line passes through M and is perpendicular to AB.                     i.       Show that this line has equation  .                   ii.       Given […]