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Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#8

Hits: 9   Question The water level in a reservoir rises and falls during a four-hour period of heavy rainfall. The height, h cm, of water above its normal level, t hours after it starts to rain, can be modelled by the equation , a.   Find the rate of change of the height of water, in cm per […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#7

Hits: 7   Question The diagram shows the right-angled corner AFE of a building and four sections of fencing running  parallel to the walls of the building. Each of the sections of fencing AB and DE has length x metres and each of the sections of wall AF  and FE has length y metres. The total length of the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#6

Hits: 5   Question A circle with centre C has .  a.   Express this equation in the form b.   Show that the circle touches the y-axis and crosses the x-axis in two distinct points. c.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the circle and the line […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#5

Hits: 5   Question A curve and the line AB are sketched below. The curves has the equation  and the points A(-1,9) and B(2,12) lie on the curve. a.   Find the equation of the normal to the curve at the point A, giving your answer in the form  . b.                         i.       Find .                   ii.       Hence find the area of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#4

Hits: 3   Question The point A has coordinates (-2,5) and the point B has coordinates (8,-6). a.   Find and equation for the straight line AB, giving your answer in the form , where p, q and r are integers. b.   The point C has coordinates (k,k+1). Given that the angle ACB is a right angle, find the two  […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#3

Hits: 1   Question The polynomial  is given by . where b and c are integers. a.   Given that  is a factor of  show that . b.   The remainder when  is divided by  is -30. Obtain a further equation in b and c. c.   Use equations from parts (a) and (b) to find the value of b and the value of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#1

Hits: 4   Question a.  Express  in the form , where m and n are integers.  b. Solve the equation giving your answer in its simplest form. Solution a.   We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#8

Hits: 4   Question The gradient, , at the point (x,y) on a curve is given by a.                        i.               Find                   ii.               The curve passes through the point . Verify that the curve has a minimum point at P. b.                       i.               Show that at the points on the curve where y is decreasing                   ii.               Solve the inequality Solution a.   We are given;                     i. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#7

Hits: 8   Question The diagram shows the sketch of a curve and the tangent to the curve at P. The curve has equation  and the point P(-2,24) lies on the curve. The tangent at P  crosses the x-axis at Q. a.                       i.               Find the equation of the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#6

Hits: 4   Question a.  A curve has equation .                     i.               Find the values of x where the curve crosses the x-axis, giving your answer in the form   , where m and n are integers.                   ii.               Sketch the curve, giving the value of the y-intercept. b. A line has equation  , where k is a constant.                     i.               Show that the x-coordinates of any points […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#5

Hits: 4   Question A circle with center C(5,-3) passes through the point A(-2,1). a.   Find the equation of the circle in the form b.   Given that AB is a diameter of the circle, find the coordinates of the point B. c.   Find an equation of the tangent to the circle at the point A, giving your answer […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#4

Hits: 1   Question The polynomial  is given by . a.                                i.       Use the Factor Theorem to show that  is a factor of .                          ii.      Express  as a product of three linear factors. b.                                i.       Use Remainder Theorem  to find the remainder when  is divided by .                          ii.       Express  in the form , where b and c are integers. Solution a.                               i. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#3

Hits: 2   Question a.                         i.       Express  in the form  , where p and q are rational numbers.                   ii.       Hence write down the minimum value of . a.   Describe the geometrical transformation which maps the graph of  onto the graph  of  . Solution a.                               i.   We have the expression; We use method of “completing square” to obtain the desired form. First we […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#2

Hits: 3   Question a.   Simplify . b.   Express  in the form  , where m and n are integers. Solution a.   b.   If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#1

Hits: 0   Question The line AB has equation . a.   The line AB is parallel to the line with equation .  Find the value of m. b.    The line AB intersects the line with equation  at the point B. Find the coordinates of B. c.    The point with coordinates  lies on the line AB. Find the value of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#8

Hits: 3   Question A curve has equation  and a line has equation  , where k is a  constant. a.   Show that the x-coordinate of any point of intersection of the curve and the line satisfies the equation b.   Given that the line and the curve do not intersect:.                    i.       Show […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#7

Hits: 2   Question a.   Sketch the curve with equation . b.   The polynomial  is given by .                            i.       Find the remainder when  is divided by .                          ii.       Use the Factor Theorem to show that  is a factor of .                        iii.       Express  in the form , where B and c are integers.                         iv.       Hence show that the equation  has exactly one real root and state its […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#6

Hits: 2   Question The diagram shows a cylindrical container of radius r cm and height h cm. The container has an  open top and a circular base. The external surface area of the container’s curved surface and base is 48 cm2. When the radius of the base is r cm, the volume of the container is V cm3. a. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#5

Hits: 1   Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .                     i.       Use the result from part (a) to write down the coordinates of the vertex of the curve.                   ii.       State the equation of the line of symmetry of the curve. c.   The curve with equation  is translated by vector . Find the […]