Hits: 54

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#3

Hits: 54   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.   Verify that . c.   Sketch the curve with equation  , indicating the values where the curve  crosses the x-axis. Solution […]

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

Hits: 32   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#6

Hits: 113   Question The circle with centre C(5,8) touches the y-axis, as shown in the diagram. a.   Express the equation of the circle in the form b.                         i.       Verify that the point A(2,12) lies on the circle.                   ii.       Find an equation of the tangent to the circle at the point A, giving your answer in the form    , […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#5

Hits: 65   Question a.                         i.       Express  in the form .                   ii.       Hence write down the equation of the line of symmetry of the curve with equation . b.   The curve C with equation  and the straight line  intersect at the point  A(0,5) and at the point B, as shown in the diagram below. i.       Find the coordinates of the point B. […]

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

Hits: 261     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 | June | Q#2

Hits: 37   Question The line AB has equation  . a.                         i.       Find the gradient of AB.                   ii.       Find an equation of the straight line that is parallel to AB and which passes through the  point C(3,-5), giving your answer in the form , where p, q and r are integers. b.   The line AB intersects the line with […]

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

Hits: 33   Question Express  in the form , where m and n are integers. Solution 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 denominator is of the form  then multiply both numerator and denominator by .  ü If the […]