Year 2010 June (6360-MPC1) Archives — O/A Level Solutions

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#3

  Question The polynomial  is given by a.                                i.       Use the Factor Theorem to show that  is a factor of .                          ii.       Express  as the product of three linear factors. b.   Use the Remainder Theorem to find the remainder when  is divided by . c.                                i.       Verify that .                          ii.  […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#7

Question a. i.Express  in the form  , where p and q are integers. ii.Use your result from part (a)(i) to explain why the equation  has no real roots. b.The quadratic equation  has real roots. i.Show that . ii.Hence find the possible values of k.   Solution a. i. We have the expression; We use method of “completing square” to obtain the desired form. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#6

  Question The diagram shows a block of wood in the shape of a prism with triangular cross-section. The end  faces are right-angled triangles with sides of lengths 3x cm, 4x cm and 5x cm, and the length of the  prism is y cm, as shown in the diagram. The total surface area of the five faces is 144 […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#5

  Question A circle with centre  touches the y-axis, as shown in the diagram. a.   Find the equation of the circle in the form b.                          i.       Verify that the point  lies on the circle.                   ii.       Find an equation of the normal to the circle at the point P.                 iii.       The mid-point […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#4

  Question The curve with equation  is sketched below. The point  lies on the curve. a.                                i.       Find                          ii.       Hence find the area of the shaded region bounded by the curve and the line  . b.   The point  lies on the curve with equation   .                            i.       Find the gradient of the curve at the point A.                          ii.       Hence find an equation of the tangent to […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#2

  Question a.   Express  in the form  , where m and n are integers. b.   Hence express  in the form  , where p and q are integers. Solution a.   We have algebraic formula; For the given case; b.   We are given the expression; We have found in (a) that; Therefore; If we need a rational number in the denominator […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#1

  Question The trapezium ABCD is shown below. The line AB has equation  and DC is parallel to AB. a.   Find the gradient of AB. b.   The point D has coordinates .                            i.       Find an equation of the line DC.                          ii.       The angle BAD is a right angle. Find an equation of the line AD, giving your answer in  the form […]