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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 167   Question The diagram shows part of the curve  and the normal to the curve at the point P(2, 3).  This normal meets the x-axis at Q.      i.       Find the equation of the normal at P.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are required to find the equation of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 171   Question The diagram shows a trapezium OABC in which OA is parallel to CB. The position vectors of A and  B relative to the origin O are given by and                           i.       Show that angle OAB is 90o. The magnitude of  is three times the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 141   Question A curve is such that .                    i.       Find the x-coordinate of each of the stationary point on the curve.                  ii.       Obtain an expression for  and hence or otherwise find the nature of each of the  stationary points.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 150   Question Points A and B lie on the curve . Point A has coordinates (4,7) and B is the  stationary point of the curve. The equation of a line L is , where m is a constant.                             i.       In the case where L passes through the mid-point of AB, find the value of m.                           ii.       Find the set of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 128   Question a.   The function f, defined by   for , is such that  and .                             i.       Find the values of the constants a and b.                           ii.       Evaluate . b.   The function g is defined by  for for . The range of g is given by  . Find the values of the constants c and d. Solution a.   i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 97   Question      i.       Show that the equation  can be expressed as    ii.       Hence solve the equation  for . Solution      i.   We are given equation as; Utilising , we can write the given equation as; We have the trigonometric identity; It can be arranged to get; Substituting in the above equation obtained.    ii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 294   Question The diagram shows a semicircle with centre O and radius 6 cm. The radius OC is perpendicular to  the diameter AB. The point D lies on AB, and DC is an arc of a circle with centre B.      i.       Calculate the length of the arc DC.    ii.       Find the value of giving your answer […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 112   Question a)   Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the  year. A collector bought the stamp for $10 000 at the beginning of 2005. Find its value at the  beginning of 2015 correct to the nearest $100.  b)   The sum of the first n […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#2

Hits: 81   Question A function f is defined by  for .      i.       Find an expression for  and find the point of intersection of the graphs of  and  .    ii.       Sketch, on the same diagram, the graphs of  and , making clear the  relationship between the graphs. Solution i.   We have; We write it as; To find the inverse of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 73   Question Find the term independent of x in the expansion of . Solution Expression for the general term in the Binomial expansion of  is: For the given case: Hence; Since we are looking for the coefficient of the term independent of  i.e. , so we can  equate Hence, substituting ; Becomes; Hence coefficient of the term independent […]