Hits: 85

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#5

Hits: 85     Question The diagram shows part of the curve and its maximum point M. The shaded region is bounded by the curve, the axes and the line  through M parallel to the y-axis.      i.       Find the exact value of the x-coordinate of M.    ii.       Find the exact value of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 105 Question The diagram shows part of the curve  and its maximum point M. The x-coordinate of M is denoted by m.      i.       Find  and hence show that m satisfies the equation .    ii.       Show by calculation that m lies between 0.7 and 0.8.   iii.       Use an iterative formula based on the […]

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

Hits: 62 Question For each of the following curves, find the exact gradient at the point indicated: i.        at   ii.        at Solution      i.   We are required to find the gradient of the curve at the point . Therefore first we need to find the expression for gradient of the given curve. Gradient […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 75   Question The diagram shows part of the curve  and its maximum point M. The x-coordinate of M is denoted by m.      i.       Find  and hence show that m satisfies the equation .    ii.       Show by calculation that m lies between 0.7 and 0.8.   iii.       Use an iterative formula based […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 82 Question For each of the following curves, find the exact gradient at the point indicated: i.        at  ii.        at Solution      i.   We are required to find the gradient of the curve at the point .  Therefore first we need to find the expression for gradient of the given curve. Gradient (slope) […]

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 | (P2-9709/22) | Q#8

Hits: 134 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 | (P2-9709/21) | Q#7

Hits: 268     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 | May-Jun | (P2-9709/21) | Q#2

Hits: 168 Question Find the gradient of each of the following curves at the point for which x = 0.     i.           ii.         Solution      i.   We are required to find the gradient of the curve at the point for which x = 0. Therefore first we need to find the […]

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

Hits: 21 Question Differentiate with respect to x, giving each answer in its simplest form. a)   b)  Solution a.     We are given;   We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: Therefore; We have algebraic formula; Rule for differentiation […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#3

Hits: 51   Question A curve has equation . a.   Find:                          i.       ;                          ii.        b.   The point on the curve where  is P.                            i.       Determine whether y is increasing or decreasing at P, giving a reason for your answer.                          ii.       Find an equation of the tangent to the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 920 Question a.   The functions  and  are defined for by  , where  and  are positive constants  , Given that  and ,       (i)          calculate the values of  and ,      (ii)         obtain an expression for  and state the domain of .   b.   A point P travels along the curve  in such a way that the x-coordinate of P at time t  […]