# 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 | June | Q#4

Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .      i.   Find the coordinates of the vertex of the curve.     ii.   State the equation of the line of symmetry of the curve.    iii.   Sketch the curve, stating the value of the intercept on […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#7

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 a […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#8

Question A circle has centre C(3,-8) and radius 10 . a.   Express the equation of the circle in the form b.   Find the x-coordinates of the points where the circle crosses the x-axis. c.   The tangent to the circle at the point A has gradient . Find an equation of the line CA, giving your answer […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#6

Question The curve with equation  is sketched below. The curve cuts the x-axis at the point A(-1,0) and passes through the point B(1,2). a.   Find b.   Hence find the area of the shaded region bounded by the curve  and the line AB. Solution a.   Rule for integration of  is: Rule for integration of  is: Rule […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#3

Question The volume, V m3 , of water in a tank after time t seconds is given by a.   Find . b.                         i.       Find the rate of change of volume, in m3 s-1, when .                   ii.       Hence determine, with a reason, whether the volume is increasing or decreasing when . c.                         i.       Find the positive value of t […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#2

Question a.                        i.       Express  in the form , where k is an integer.                  ii.       Simplify  , giving your answer as an integer. b.   Express  in the form , where m and n are integers. Solution a.                               i.   We are given; Since ; ii.   Since ; Since ; b.   […]

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

Question The line AB has equation  . a.   Find the gradient of AB. b.   The point C has coordinates .                     i.       Find an equation of the line which passes through the point C and which is parallel to AB.                   ii.       The point  is the mid-point of AC . Find the coordinates of the point A.  c.   The line […]