Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#8

Question Solve each of the following inequalities: a.   b.   . Solution a.   b.     We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are  & . Standard form of quadratic equation is; The graph of quadratic equation is […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#7

Question A circle with center C has the equation . The point A(3,-2) lies on the  circle. a.   Express the equation of the circle in the form b.                                i.       Write down the coordinates of C.                          ii.       Show that the circle has radius , where n is an integer. c.                         i.       Find the equation of the tangent to the circle […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#6

Question The diagram shows a curve and a line which intersect at the points A, B and C. The curve has equation  and the straight line has equation . The point B has coordinates (0,7). a.                           i. Show that the x-coordinates of the points A and […]

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 2014 | June | Q#4

Question a.                                i.       Express  in the form  where p and q are integers.                          ii.       Hence write down the maximum value of . b.                                i.       Factorise  .                            ii.       Sketch the curve with equation  , stating the values of x where the curve  crosses the x-axis and the value of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#3

Question A curve has equation . a.   Find:                          i.       ;                          ii.        b.   The point on the curve where  is P.                            i.       Determine whether y is increasing or decreasing at P, giving a reason for your answer.                          ii.       Find an equation of the tangent to the curve at […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#2

Question A rectangle has length  cm and area  cm2.  Find the width of the rectangle, giving your answer in the form  cm, where m and n are  integers. Solution Expression for the area of the rectangle is; For the given case; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” […]

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

Question The point A has coordinates (-1,2) and the point B has coordinates (3,-5). a.                         i.       Find the gradient of AB.                   ii.       Hence find an equation of the line AB, giving your answer in the form  , where p, q  and r are integers. b.   Midpoint of AB is M.                     i.       Find the coordinates of M.                   ii.       Find an equation […]