Year 2007 January (6360-MPC1) Archives — O/A Level Solutions

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Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January| Q#1

Hits: 7   Question The polynomial  is given by where k is a constant.   a.           i.       Given that  is a factor of , show that .              ii.       Express   as the product of three linear factors. b.   Use the Remainder Theorem to find the remainder when  is divided by . c.   Sketch […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#7

Hits: 1   Question The quadratic equation  has real roots. i.       Show that .  ii.       Hence find the possible values of . Solution i.   We are given the equation It is a quadratic equation and we are also given that it has real roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#6

Hits: 13   Question The curve with equation  is sketched below. The curve cuts the x-axis at the point A (-1, 0) and cuts the y-axis at the point B. a.                                i.       State the coordinates of the point B and hence find the area of the triangle AOB, where  O is the origin.          […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#5

Hits: 1   Question The diagram shows an open-topped water tank with a horizontal rectangular base and four vertical  faces. The base has width  metres and length  metres, and the height of the tank is  metres. The combined internal surface area of the base and four vertical faces is 54m2. a.                        i.       Show that .                   ii.       Hence express  in terms of . […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#4

Hits: 2   Question A circle with centre C has equation  . a.  By completing the square, express this equation in the form b. Write down:                     i.       the coordinates of C;                   ii.       the radius of the circle. c.   Show that the circle does not intersect the x-axis. d.  The line with equation  intersects the circle at the points P and Q. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#3

Hits: 4   Question a.  Express  in the form of , where  and  are integers. b.                      i.       Express  in the form  , where n is an integer.                   ii.       Solve the equation giving your answer in its simplest form. Solution a.   We are given;   If we need a rational number in […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#2

Hits: 1   Question The line AB has equation  and the point A has coordinates . a.    i.  Find the gradient of AB. ii. Hence find an equation of the straight line which is perpendicular to AB and which passes through A. b.  The line AB intersects the line with equation  at the point B. Find the coordinates of  B. c.  The […]