Hits: 121

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 121 Question A curve has equation Find the equation of the normal to the curve at the point (1, 2). Give your answer in the form ax + by  + c = 0, where a, b and c are integers. Solution We are given equation of the curve as; We are required to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#4

Hits: 86   Question The parametric equations of a curve are Find the equation of the tangent to the curve at the point for which t = 0. Give your answer in the  form ax + by + c = 0, where a, b and c are integers. Solution We are required to find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#8

Hits: 93 Question The diagram shows the curve , for and its maximum point M.     i.       Show that    ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#1

Hits: 74 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x.   Hence, the only solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#8

Hits: 137 Question The diagram shows the curve , for and its maximum point M. i.       Show that      ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#4

Hits: 104   Question The parametric equations of a curve are Find the equation of the tangent to the curve at the point for which t = 0. Give your answer in the  form ax + by + c = 0, where a, b and c are integers. Solution We are required to find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#1

Hits: 83     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#7

Hits: 279     Question The equation of a curve is 3×2+3xy+y2=3      i.       Find the equation of the tangent to the curve at the point (2, −1), giving your answer in the form  ax +by +c = 0, where a, b and c are integers.    ii.       Show that the curve has no stationary […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 81     Question Solve the equation. Solution SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; Hence, the only solution for the given equation is; SOLVING […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#1

Hits: 190     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 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#11

Hits: 216   Question A sketch of part of the curve C with equation , x>0 is shown in Figure. Point A lies on C and has an x coordinate equal to 2 a.   Show that the equation of the normal to C at A is y = –2x + 7. The normal to C at A […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#9

Hits: 62   Question The curve C has equation . The line L has equation y = 3x + k, where k is a positive constant. a.   Sketch C and L on separate diagrams, showing the coordinates of the points at which C and L cut the axes. Given that line L is a tangent to C, b.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#7

Hits: 1782   Question Figure 2 shows a right angled triangle LMN. The points L and M have coordinates (–1, 2) and (7, –4) respectively. a.   Find an equation for the straight line passing through the points L and M. Give your answer in the  form ax + by + c = 0, where a, b and c […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#11

Hits: 54   Question Given that f(x) = 2×2 + 8x + 3 a.   find the value of the discriminant of f(x). b.   Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found. The line y = 4x + c, where c is a constant, is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#10

Hits: 50   Question A curve with equation y=f(x) passes through the point (4,25). Given that a.   find f(x) simplifying each term. b.   Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#9

Hits: 87 Question The line , shown in figure has equation 2x+3y = 26. The line  passes through the origin O and is perpendicular to . a.   Find an equation for the line . The line  intersects the line  at the point C. Line  crosses the y-axis at the point B as shown in Figure. b.   Find the area of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#4

Hits: 79   Question Figure 1 shows a sketch of the curve C with equation  , x ≠ 0. The curve C crosses the x-axis at the point A. a.   State the x coordinate of the point A. The curve D has equation y = x2(x – 2), for all real values of x. b.   A copy of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#10

Hits: 104   Question The curve C has equation . The point P, which lies on C, has coordinates (2, 1). a.   Show that an equation of the tangent to C at the point P is y = 3x – 5. The point Q also lies on C. Given that the tangent to C at Q is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#9

Hits: 107   Question A curve with equation y=f(x) passes through the point (3,6). Given that a.   use integration to find f(x). Give your answer as a polynomial in its simplest form. b.   Show that , where p is a positive constant. State the value of p. c.   Sketch the graph of y = f(x), showing the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#6

Hits: 98   Question The straight line  has equation 2y = 3x + 7. The line  crosses the y-axis at the point A as shown in Figure. a.                         i.       State the gradient of .                   ii.       Write down the coordinates of the point A. Another straight line  intersects  at the point B (1, 5) and crosses the x-axis at the point C, as  […]