Hits: 66

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#2

Hits: 66   Question The diagram shows the curve y = x4 +2x −9. The curve cuts the positive x-axis at the point P. i.               Verify by calculation that the x-coordinate of P lies between 1.5 and 1.6. ii.               Show that the x-coordinate of P satisfies the equation iii.               Use the iterative formula to determine […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 83   Question The parametric equations of a curve are      i.       Find the exact value of the gradient of the curve at the point P where y = 6.    ii.       Show that the tangent to the curve at P passes through the point . Solution      i.   We are need  for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#2

Hits: 56 Question The diagram shows the curve y = x4 +2x −9. The curve cuts the positive x-axis at the point P. i.               Verify by calculation that the x-coordinate of P lies between 1.5 and 1.6. ii.            Show that the x-coordinate of P satisfies the equation iii.               Use the iterative formula to determine […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#6

Hits: 100     Question      i.       By sketching a suitable pair of graphs, show that the equation   has only one root.    ii.       Verify by calculation that this root lies between x = 0.7 and x = 0.8.   iii.       Show that this root also satisfies the equation   iv.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#5

Hits: 310     Question The parametric equations of a curve are  ,  ,     i.       Show that .  ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/21) | Q#5

Hits: 146     Question The parametric equations of a curve are  ,  , i.       Show that .    ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#1

Hits: 124     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 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#1

Hits: 88     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 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#2

Hits: 109     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 2013 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 489 Question The diagram shows the curve . i.       Find the equation of the tangent to the curve at the point . ii.    Show that the x-coordinates of the points of intersection of the line   and the curve are given by the equation . Hence find these x- coordinates. iii.     The region shaded in the diagram is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 392 Question The point A has coordinates  and the point B has coordinates . The  point C is the mid-point of AB.   i.       Find the equation of the line through A that is perpendicular to .  ii.     Find the distance AC. Solution i.   We are required to find equation of a line that passes through  and is  […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 974 Question In the diagram, S is the point  and T is the point . The point Q lies on ST,  between S and T, and has coordinates . The points P and R lie on the x-axis  and y-axis respectively and OPQR is a rectangle.      i.       Show that the area, A, of the rectangle OPQR is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 2399 Question The diagram shows a rectangle ABCD in which point A is  and point B is . The diagonal AC has equation . Find, by calculation, the coordinates of  C and D. Solution We are required to find coordinates of the points C and D. First we find the coordinates of point C. It is evident from the diagram that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 553   Question The diagram shows the curve  and the tangent to the curve at the point . i.         Find the equation of this tangent, giving your answer in the form . ii.       Find the area of the shaded region. Solution i.   We are required to find equation of the tangent to the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 2410   Question The point A has coordinates  and the point B has coordinates . i.       Find the equation of the perpendicular bisector of AB, giving your answer in the form .    ii.       A point C on the perpendicular bisector has coordinates . The distance OC is 2 units, where O is the origin. Write down two equations […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#11

Hits: 494 Question The diagram shows part of the curve  and a point  and  which lie on the curve. The tangent to the curve at B intersects the line  at the point C.      i. Find the coordinates of C.    ii. Find the area of the shaded region. Solution i.   We are required to find the coordinates of point C. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#7

Hits: 1157   Question The diagram shows three points ,  and . The point X lies on  AB, and CX is perpendicular to AB. Find, by calculation,       i.       the coordinates of X,    ii.       the ratio AX : XB. Solution i.   We are required to find the coordinates of point X. It is evident from the diagram that point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#11

Hits: 1141   Question The diagram shows the curve  , which intersects the x-axis at A and the  y-axis at B. The normal to the curve at B meets the x-axis at C. Find      i.       the equation of BC,    ii.       the area of the shaded region. Solution      i.   To find the equation of the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#8

Hits: 497 Question The volume of a solid circular cylinder of radius  cm is  cm3.      i.       Show that the total surface area, S cm2, of the cylinder is given by     ii.       Given that  can vary, find the stationary value of .   iii.       Determine the nature of this stationary value. Solution      i.   We are given that volume of solid circular […]