# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#10

Question Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x2(9 –2x) There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point  A. a.   Write down the coordinates of the point A. b.   On separate […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#9

Question The line L1 has equation 4y + 3 = 2x. The point A (p, 4) lies on L1. a.   Find the value of the constant p. The line L2 passes through the point C (2, 4) and is perpendicular to L1. b.   Find an equation for L2 giving your answer in the form ax + by […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#8

Question Where p and q are integers. a.   Find the value of p and the value of q. b.   Calculate the discriminant of  . c.  On the axes on page 17, sketch the curve with equation  showing clearly the  coordinates of any points where the curve crosses the coordinate axes. Solution a.   We have the expression; We […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#7

Question The point P(4,–1) lies on the curve C with equation y = f(x), x > 0, and a.   Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c,  where m and c are integers. b.   Find f(x). Solution a.   We are required to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#10

Question Figure 2 shows a sketch of the curve C with equation  , x ≠ 0 The curve crosses the x-axis at the point A. a.   Find the coordinates of A. b.   Show that the equation of the normal to C at A can be written as 2x+8y−1=0 The normal to C at A meets C again at the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#6

Question The line  has equation 2x − 3y +12 = 0. a.   Find the gradient of . The line  crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure. The line  is perpendicular to  and passes through B. b.   Find an equation of . The line  crosses the x-axis at the point […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#5

Question The curve C has equation y=x(5−x) and the line L has equation 2y=5x+4. a.   Use algebra to show that C and L do not intersect. b.   In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the  points at which C and L meet the axes. Solution […]

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

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 lies on the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#6

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    , where s, t […]

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

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. ii.       Find iii.       Find […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#2

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 equation  at […]

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

Question A circle with centre C has . a.   Express the equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   Sketch the circle. d.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the line and the circle satisfy  […]

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

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 minimum point […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#2

Question a.   Factorise . b.   Sketch the graph with equation  , stating the values where the curve crosses  the coordinate axes. c.                   i.       Express  in the form , where p and q are positive integers.               ii.       Hence find the minimum value of . d.   The curve with […]

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

Question The point A has coordinates (6,-4) and the point B has coordinates (-2,7). a.   Given that the point O has coordinates (0,0), show that the length of OA is less than the length of OB. b.                         i.       Find the gradient of AB.                   ii.       Find an equation of the line AB in the form  , where p, q and r are […]