# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#10

Question The points Q (1, 3) and R (7, 0) lie on the line , as shown in Figure. The length of QR is . a.   Find the value of a. The line l2 is perpendicular to , passes through Q and crosses the y-axis at the point P, as shown  in Figure. Find b.   an […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#9

Question The curve C has equation , where k is a constant. a.   Find . Point A with x-coordinate  lies on C. The tangent to C at A is parallel to the line with equation  . Find b.   The value of k. c.   The value of y-coordinate of A. Solution a.   Gradient (slope) of the curve […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#10

Question The curve C has equation y=(x + 3)(x −1)2 . a.   Sketch C showing clearly the coordinates of the points where the curve meets the coordinate  axes. b.   Show that the equation of C can be written in the form y = x3 + x2 − 5x + k, where k is a positive integer, and […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#9

Question The curve C has equation y = f(x), x > 0, and . Given that the point P(4,1) lies on C, a.   find f(x) and simplify your answer. b.   Find an equation of the normal to C at the point P(4, 1). Solution a.   We are required to find f(x), when; We are also given that […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#4

Question The point A(–6, 4) and the point B (8, –3) lie on the line L. a.  Find an equation for L in the form ax + by + c = 0, where a, b and c are integers. b.  Find the distance AB, giving your answer in the form , where k is an integer.` Solution a. […]

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

Question The straight line L has equation  and the curve C has equation a.   Sketch on the same axes the line L and the curve C, showing the values of the intercepts on the  x-axis and the y-axis. b.   Show that the x-coordinates of the points of intersection of L and C satisfy the equation  . c.   Hence find the coordinates […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#5

Question The curve with equation  is sketched below. The points A(-2,0) , B(2,0) and C(1,15) lie on the curve.  a.   Find an equation of the straight line AC . b.                          i.       Find .                   ii.       Hence calculate the area of the shaded region bounded by the curve and the line AC . Solution a.   We are required to […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#7

Question The curve C has equation  . The line L has equation  , where k is a constant. a.   Show that the x-coordinates of any points of intersection of the line L with the curve C satisfy the  equation b.   The curve C and the line L intersect in two distinct points. Show that c.   Solve the inequality […]

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

Question The triangle ABC has vertices A(-2,3), B(4,1) and C(2,-5). a.   Find the coordinates of the mid-point of BC . b.                 i.  F ind the gradient of AB, in its simplest form.           ii.  Hence find an equation of the line AB , giving your answer in the form  , where q  and r are […]