# 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 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 2007 | June | Q#5

Question A circle with centre C has equation  . a.   Write down:                            i.       the coordinates of C;                           ii.       the radius of the circle. b.                                i.       Verify that the point N(0,-2) lies on the circle.                           ii.       Sketch the circle.                         iii.       Find an equation of the normal to the circle at the point N. c.   The point P has coordinates (2, 6).                            i.       Find […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#7

Question The quadratic equation where k is a constant, has real roots. a.   Show that . b.                 i.               Factorise .          ii.               Hence, or otherwise, solve the quadratic inequality  Solution a.   We are given a quadratic equation as follows; We are also given that it has real roots. For a quadratic equation , […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#4

Question A model helicopter takes off from a point O at time t=0 and moves vertically so that its height, y cm,  above O after time t seconds is given by  , a.   Find:                            i.                                  ii.        b.   Verify that y has a stationary value when  and determine whether this stationary value is a  maximum value or a […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#3

Question a.                           i.       Express  in the form  , where p and q are integers.                    ii.       Write down the coordinates of the vertex (minimum point) of the curve with equation                     iii.    […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#2

Question a.   Express  in the form  , where  is an integer. b.   Express  in the form  , where  and  are integers. Solution a.   b.     We have algebraic formula;

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

Question The point  and  have coordinates  and  respectively. a.                          i.    Show that the gradient of AB is .                   ii.    Hence find an equation of the line AB, giving your answer in the form  , where a, b and c are integers. b.                          i.    Find an equation of the line which passes through […]