# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#11

Question The line  meets the the curve  at the points A and B as shown in the figure. a.   Find the coordinates of A and the coordinates of B. b.   Find the distance AB in the form  where r is a rational number. Solution a.   We are required to find the coordinates of the points […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#4

Question The line  has equation 4x + 2y – 3 = 0. a.   Find the gradient of . The line  is perpendicular to  and passes through the point (2,5). b.   Find an equation of  in the form y = mx + +c, where m and c are constants. Solution a.     We are given equation of line ; We are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#11

Question Figure  shows a sketch of the curve H with equation;  , a.   Give the coordinates of the point where H crosses the x-axis. b.   Give the equations of the asymptotes to H. c.   Find an equation for the normal to H at the point P(–3, 3). This normal crosses the x-axis at A […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#8

Question Figure 1 shows a sketch of the curve with equation y = f(x) where  , The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis at (0, –9). a.   In the space below, sketch the curve C with equation y=f(x+2) and state the coordinates of the  points where the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#6

Question The straight line L1 passes through the points (–1, 3) and (11, 12). a.   Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers. The line L2 has equation 3y + 4x – 30 = 0. b.   Find the coordinates of the point of intersection […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#11

Question The curve C has equation , a.   Find , giving each term in its simplest form. The point P on C has x-coordinate equal to . b.   Find the equation of the tangent to C at P, giving your answer in the form y = ax + b, where a and  b are constants. The […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#6

Question Figure 1 shows a sketch of the curve with equation  , x ≠ 0. The curve C has equation , x ≠ 0, and the line  has equation y = 4x + 2. a.   Sketch and clearly label the graphs of C and  on a single diagram. On your diagram, show clearly the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#5

Question The line L1 has equation y = -2x+3. The line L2 is perpendicular to L1 and passes through the point (5, 6). a.   Find an equation for L2 in the form ax + by + c = 0, where a, b and c are integers. The line L2 crosses the x-axis at the point A and the y-axis […]

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

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 Q also […]

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

Question The line AB has equation . a.   The point with coordinates (p,p+2) lies on the line AB. Find the value of the constant p. b.   Find the gradient of AB. c.   The point A has coordinates (1,2). The point C(-5,k) is such that AC is perpendicular to AB. Find  the value of k. d.   The line AB […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#8

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.   The curve and the line intersect at two distinct points.                     i.       Show that .                   ii.       Find the possible values of k. Solution a.   […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#7

Question A circle with centre C(-3,2) has equation a.   Find the y-coordinates of the points where the circle crosses the y-axis. b.   Find the radius of the circle.  c.   The point P(2,5) lies outside the circle.                     i.       Find the length of CP, giving your answer in the form  , where n is an integer.                   ii.       The point Q lies […]

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

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 find the […]

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

Question a.                        i.       Express  in the form .                  ii.       Use the result from part (a)(i) to show that the equation  has no real  solutions. b.   A curve has equation .                            i.       Find the coordinates of the vertex of the curve.                          ii.       Sketch the curve, […]

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

Question The point A has coordinates (-3,2) and the point B has coordinates (7,k). The line AB has equation . a.                         i.       Show that .                   ii.       Hence find the coordinates of the midpoint of AB. b.   Find the gradient of AB. c.   A line which passes through the point A is perpendicular to the line AB. Find an equation […]