Hits: 272

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 204     Question Find the exact coordinates of the point on the curve   at which . Solution We are given that; We are required to find; Second derivative is the derivative of the derivative. If we have derivative of the curve   as , then  expression for the second derivative of the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#7

Hits: 252   Question The equation of the curve is .     i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#6

Hits: 209     Question It is given that the curve has one stationary point.      i.       Find the x-coordinates of this point.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required to find the coordinates of stationary point of the curve; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#8

Hits: 489 Question The equation of a curve is . i.       Show that the equation of the normal to the curve at the point  is This normal meets the curve again at the point Q.    ii.       Find the coordinates of Q.   iii.       Find the length of PQ. Solution i.   We are required to find the equation of the normal to the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#7

Hits: 2036 Question A wire, 80 cm long, is cut into two pieces. One piece is bent to form a square of side x cm and the other piece is bent to form a circle of radius r cm (see diagram). The total area of the square and the circle is Acm2. i.       Show that    ii.       Given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#4

Hits: 462 Question The equation of a curve C is  and the equation of a line L is . i. Find the x-coordinates of the points of intersection of L and C.    ii. Show that one of these points is also the stationary point of C. Solution i.   If two lines (or a line and […]