Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#6

Question The polynomial p(x) is given by  . a.   Use the Remainder Theorem to find the remainder when p(x) is divided by x-1 . b.                         i.       Use the Factor Theorem to show that x+2 is a factor of p(x).                   ii.       Express p(x) as the product of linear factors. c.                         i.       The curve with equation  passes through the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#1

Question The straight line L has equation  and the curve C has equation a.   Sketch on the same axes the line L and the curve C, showing the values of the intercepts on the  x-axis and the y-axis. b.   Show that the x-coordinates of the points of intersection of L and C satisfy the equation  . c.   Hence find the coordinates […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#8

Question The quadratic equation  has real roots. a.   Show that  . b.   Hence find the possible values of k. Solution a.   We are given following quadratic equation which has real roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two roots. If , […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#7

Question The circle S has centre C(8,13) and touches the x-axis, as shown in the diagram. a.   Write down an equation for S, giving your answer in the form b.   The point P with coordinates (3,1) lies on the circle.                     i.       Find the gradient of the straight line passing through P and C.                   ii.       Hence […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#5

Question The curve with equation  is sketched below. The points A(-2,0) , B(2,0) and C(1,15) lie on the curve.  a.   Find an equation of the straight line AC . b.                          i.       Find .                   ii.       Hence calculate the area of the shaded region bounded by the curve and the line AC . Solution a.   We are required to […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#4

Question a.   Express  in the form  , where p and q are rational numbers. b.   Hence write down the minimum value of the expression . c.   Describe the geometrical transformation that maps the graph of  onto the graph of . Solution a.   We are given; We use method of “completing square” to obtain the desired form. Next we complete the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#3

Question Two numbers, x and y, are such that  , where  and . It is given that  .  a.   Show that  . b.                         i.       Show that , and state the value of the integer k.                   ii.       Hence find the two values of x for which c.    Find d.                         i.       Find the value of  for each of the two values […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#2

Question It is given that  and . Find, in the simplest form, the value of : a.   b.   c.   . Solution a.   We are given that  and . b.     We are given that  and . c.     We are given that  and . We have the algebraic formula; From (a) we have; Therefore;