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: 266   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: 372   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: 186     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 (C1-6663/01) | Year 2007 | June | Q#5

Hits: 27   Question Figure 1 shows a sketch of the curve with equation  , x ≠0. a.   On a separate diagram, sketch the curve with equation , x≠−2, showing the coordinates of  any point at which the curve crosses a coordinate axis. b.   Write down the equations of the asymptotes of the curve in part (a). Solution […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#10

Hits: 49   Question a.   On the same axes sketch the graphs of the curves with equations i.       y=x2(x –2), ii.     y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves  cross the x-axis. b.   Use algebra to find the coordinates of the points where the graphs intersect. Solution a.     […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#5

Hits: 114   Question A circle with centre C has equation  . a.   Write down:                            i.       the coordinates of C;                           ii.       the radius of the circle. b.                                i.       Verify that the point N(0,-2) lies on the circle.                           ii.       Sketch the circle.                         iii.       Find an equation of the normal to the circle at the point N. c.   The point P has coordinates (2, […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#1

Hits: 113   Question The point  and  have coordinates  and  respectively. a.                          i.    Show that the gradient of AB is .                   ii.    Hence find an equation of the line AB, giving your answer in the form  , where a, b and c are integers. b.                          i.    Find an equation of the line which […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#6

Hits: 117   Question The curve with equation  is sketched below. The curve cuts the x-axis at the point A (-1, 0) and cuts the y-axis at the point B. a.                                i.       State the coordinates of the point B and hence find the area of the triangle AOB, where  O is the origin.          […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#4

Hits: 59   Question A circle with centre C has equation  . a.  By completing the square, express this equation in the form b. Write down:                     i.       the coordinates of C;                   ii.       the radius of the circle. c.   Show that the circle does not intersect the x-axis. d.  The line with equation  intersects the circle at the points P and Q. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#2

Hits: 45   Question The line AB has equation  and the point A has coordinates . a.    i.  Find the gradient of AB. ii. Hence find an equation of the straight line which is perpendicular to AB and which passes through A. b.  The line AB intersects the line with equation  at the point B. Find the coordinates of  B. c.  The […]

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; […]