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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: 36   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#5

Hits: 17   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 2016 | June | Q#8

Hits: 11   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: 19   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 2015 | June | Q#6

Hits: 10   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#3

Hits: 17   Question The diagram shows a sketch of a curve and a line. The curve has equation  . The points A(-1,6) and B(2,30) lie on the curve. a.   Find an equation of the tangent to the curve at the point A. b.                 i.       Find           ii.       Calculate the area of the shaded region bounded by the curve and the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#3

Hits: 8   Question A curve has equation . a.   Find:                          i.       ;                          ii.        b.   The point on the curve where  is P.                            i.       Determine whether y is increasing or decreasing at P, giving a reason for your answer.                          ii.       Find an equation of the tangent to the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#4

Hits: 28   Question a.   The polynomial f(x) is given by .                     i.       Use the Factor Theorem to show that x+3 is a factor of f(x).                   ii.       Express f(x) in the form  , where p and q are integers. b.   A curve has equation .                     i.       Find .                   ii.       Show that the x-coordinates of any stationary points of the curve satisfy the equation […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#6

Hits: 23   Question a.  The polynomial  is given by .                     i.       Use the Factor Theorem to show that  is a factor of .                   ii.       Express  in the form  , where a and b are constants. b. The curve C with equation  , sketched below, crosses the x-axis at the point .                     i.       Find the gradient of the curve C at the point Q.                   ii.       Hence […]

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

Hits: 7   Question a.   The polynomial  is given by .                   i.       Use the Factor Theorem to show that  is a factor of  .                 ii.       Express  as the product of three linear factors. b.   The curve with equation  is sketched below. The curve cuts the x-axis at the point A and […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#6

Hits: 18   Question A curve has equation . The point P with coordinates (-1,6) lies on the curve.  a.   Find the equation of the tangent to the curve at the point P, giving your answer in the form   . b.   The point Q with coordinates (2,k) lies on the curve.                     i.       Find the value of k.                   ii.       Verify that […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#6

Hits: 7   Question The gradient, , of a curve at the point (x,y) is given by The curve passes through the point P(1,4). a.   Find the equation of the tangent to the curve at the point P, giving your answer in the form . b.   Find the equation of the curve. Solution a.   We are required to […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#2

Hits: 7   Question A bird flies from a tree. At time t seconds, the bird’s height, y metres, above the horizontal ground is given by ,   a.   Find . b.                 i.       Find the rate of change of height of the bird in metres per second when .          ii.       Determine, […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#7

Hits: 8   Question The gradient,  , of a curve C at the point (x,y) is given by a.                         i.       Show that y is increasing when .                   ii.       Solve the inequality . b.   The curve C passes through the point P(2,3).                     i.       Verify that the tangent to the curve at P is parallel to the x-axis.                   ii.       The point Q(3,-1) also […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#4

Hits: 23     Question The diagram shows a solid cuboid with sides of lengths x cm, 3x cm and y cm. The total surface area of the cuboid is 32 cm2. a.                         i.       Show that .                   ii.       Hence show that the volume, V cm3 , of the cuboid is given by b.   Find . c.       […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#4

Hits: 8  Question The curve with equation  is sketched below. The point O is at the origin and the  curve passes through the points A(-1,0) and B(1,4). a.   Given that  , find:                            i.       ;                          ii.        b.   Find an equation of the tangent to the curve at the point A(-1,0). c.   Verify that the point B, where  , is a […]

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

Hits: 7   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 […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#4

Hits: 9   Question The curve sketched below passes through the point A(-2,0) . The curve has equation and the point P(1,12) lies on the curve. a.                         i.       Find the gradient of the curve at the point P.                   ii.       Hence find the equation of the tangent to the curve at the point P, giving your answer […]