Hits: 445

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#7

Hits: 445     Question The diagram shows the part of the curve y=ex cos x for . The curve meets the y-axis at the  point A. The point M is a maximum point. i. Write down the coordinates of A. ii. Find the x-coordinate of M. iii. Use the trapezium rule with three intervals […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 264   Question The diagram shows the curve and its maximum point M.      i.       Find the x-coordinate of M.    ii.       Show that the tangent to the curve at the point where x = 1 passes through the origin.   iii.       Use the trapezium rule with two intervals to estimate […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#3

Hits: 353   Question The parametric equations of a curve are for t > 1.      i.       Express in terms of t.     ii.       Find the coordinates of the only point on the curve at which the gradient of the curve is equal to 1. Solution      i.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#3

Hits: 228       Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let  and , then; We consider two separate cases. When When We have the inequality; We have to consider two separate cases; When When Therefore the inequality will hold for ; Hence; SOLVING INEQUALITY: ALGEBRAICALLY Let, . Since given equation/inequality is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#2

Hits: 371   Question The variables x and y satisfy the relation .      i.       By taking logarithms, show that the graph of y against x is a straight line. Find the exact value  of the gradient of this line.    ii.       Calculate the x-coordinate of the point of intersection of this line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#1

Hits: 184     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 | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 516 Question A curve is such that  and the point P(2, 9) lies on the curve. The normal to the curve at P meets the curve again at Q. Find i.       the equation of the curve,    ii.       the equation of the normal to the curve at P   iii.       the coordinates of Q. Solution      i.   We are given the equation; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#6

Hits: 1266 Question The three points A (3, 8), B (6, 2) and C (10, 2) are shown in the diagram. The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. Solution It is evident that point D is the intersection of lines AD & […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#1

Hits: 338 Question Determine the set of values of the constant k for which the line  does not intersect the curve . Solution First we find the conditions when line and the curve intersect. This we can do by equating equations of line and the curve. If line and the curve do not intersect then above equation has […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#6

Hits: 2605 Question The diagram shows a rectangle ABCD. The point A is (2, 14), B is (−2, 8) and C lies on the x-axis. Find     i.       the equation of BC    ii.       the coordinates of C and D. Solution      i.   To find the equation of the line either we need coordinates of the two points on the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#1

Hits: 496 Question Find the value of the constant  for which the line  is a tangent to the curve . Solution Since line is tangent to the curve i.e. both intersect each other at a single point. To find that point; If two lines (or a line and a curve) intersect each other at a point then that point […]