# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#2

Question The diagram shows the curve y = x4 +2x −9. The curve cuts the positive x-axis at the point P. i.               Verify by calculation that the x-coordinate of P lies between 1.5 and 1.6. ii.               Show that the x-coordinate of P satisfies the equation iii.               Use the iterative formula to determine the x-coordinate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#5

Question The parametric equations of a curve are      i.       Find the exact value of the gradient of the curve at the point P where y = 6.    ii.       Show that the tangent to the curve at P passes through the point . Solution      i.   We are need  for the parametric […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#2

Question The diagram shows the curve y = x4 +2x −9. The curve cuts the positive x-axis at the point P. i.               Verify by calculation that the x-coordinate of P lies between 1.5 and 1.6. ii.            Show that the x-coordinate of P satisfies the equation iii.               Use the iterative formula to determine the x-coordinate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#6

Question      i.       By sketching a suitable pair of graphs, show that the equation   has only one root.    ii.       Verify by calculation that this root lies between x = 0.7 and x = 0.8.   iii.       Show that this root also satisfies the equation   iv.       Use the iterative formula  to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#5

Question The equation of a curve is x2− 2 x2y+ 3y = 9.      i. Show that    ii. Find the equation of the normal to the curve at the point where x = 2, giving your answer in the  form ax + by + c = 0. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#5

Question The parametric equations of a curve are  ,  ,     i.       Show that .  ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is given parametrically […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/21) | Q#5

Question The parametric equations of a curve are  ,  , i.       Show that .    ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is given parametrically […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#2

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]

# 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#3

Question A circle C has the equation a.   Write the equation of C in the form Where a, b and k are integers. b.   Hence, for the circle C write down:                            i.       the coordinates of its center;                          ii.       its radius. c.                         i.       Sketch the circle C.                   ii.       Write down the coordinates of the point on C that is furthest […]