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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 51   Question The functions  and  are defined by   for     for       i.       Express  in terms of  and solve the equation .    ii.       On the same diagram sketch the graphs of  and , showing the coordinates of their point of intersection and the relationship between the graphs.   iii.       Find the set of values of  which satisfy . Solution i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 50 Question The diagram shows the line  and the curve , meeting at  and .     i.       Find the area of the shaded region.    ii.       Find the volume obtained when the shaded region is rotated through 360◦ about the y-axis. Solution     i.   It is evident from the diagram that; To find the area of region under the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 31 Question A curve  has a stationary point at . It is given that, where k is a constant. i.       Show that  and hence find the x-coordinate of the other stationary point, Q.    ii.       Find  and determine the nature of each of the stationary points P and Q.   iii.       Find . Solution i.   A stationary point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 45 Question i.   A straight line passes through the point (2, 0) and has gradient . Write down the equation of the line. ii.  Find the two values of  for which the line is a tangent to the curve . For each value of , find the coordinates of the point where the line touches the curve. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 100 Question Relative to an origin , the position vectors of points A and B are  and , respectively.      i.       Use a scalar product to calculate angle BOA. The point C is the mid-point of AB. The point D is such that .    ii.       Find . Solution      i.   We recognize that angle BOA is between  and . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 54 Question      i.       Given that  Show that, for real values of      ii.       Hence solve the equation  for . Solution i.   We have the equation; We have the trigonometric identity; We can rewrite it as; Thus Now we have two options; NOT POSSIBLE So we are left with ONLY option;      ii.   To solve the equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 305 Question In the diagram, ABCD is a parallelogram with AB=BD=DC=10cm and angle ABD= 0.8 radians. APD and BQC are arcs of circles with centres B and D respectively.     i.       Find the area of the parallelogram ABCD.    ii.       Find the area of the complete figure ABQCDP.   iii.       Find the perimeter of the complete figure ABQCDP. Solution i.   Expression for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 45 Question The diagram shows the curve  and the line  intersecting at points A, O and B.     i.       Show that the x-coordinates of A and B satisfy the equation .    ii.       Solve the equation  and hence find the coordinates of A and B, giving your answers in an exact form. Solution i.   We are given that points A & […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 62 Question The first and second terms of a progression are 4 and 8 respectively. Find the sum of the first 10  terms given that the progression is     i.       an arithmetic progression    ii.       a geometric progression. Solution i.   From the given information, we can compile following data about Arithmetic Progression (A.P); Expression for the sum of  number of […]