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 | June | Q#7

Question The quadratic equation  has real roots. (a)  Show that . (b)  Find the possible values of k. Solution a.    We are given the quadratic equation; For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two distinct roots. If , the equation will have two identical/repeated […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#6

Question A curve has equation . The point P with coordinates (-1,6) lies on the curve.  a.   Find the equation of the tangent to the curve at the point P, giving your answer in the form   . b.   The point Q with coordinates (2,k) lies on the curve.                     i.       Find the value of k.                   ii.       Verify that Q also […]

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

Question a.                        i.       Express  in the form  , where p and q are rational numbers.                   ii.       Hence write down the minimum value of . b.   The point A has coordinates (-3,5) and the point B has coordinates (x,3x+9).                     i.       Show that .                   ii.       Use your result from part (a)(ii) to find the minimum […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#3

Question A circle C has the equation a.   Write the equation of C in the form Where a, b and k are integers. b.   Hence, for the circle C write down:                            i.       the coordinates of its center;                          ii.       its radius. c.                         i.       Sketch the circle C.                   ii.       Write down the coordinates of the point on C that is furthest […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#2

Question a.                              i.       Express  in the form , where k is an integer.                          ii.       Solve the equation                   giving your answer in its simplest form. b.   Express  in the form , where m is an integers. Solution a.   i.   […]

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

Question The line AB has equation . a.   The point with coordinates (p,p+2) lies on the line AB. Find the value of the constant p. b.   Find the gradient of AB. c.   The point A has coordinates (1,2). The point C(-5,k) is such that AC is perpendicular to AB. Find  the value of k. d.   The line AB […]