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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#12

Hits: 101   Question A curve is such that  . The curve passes through the point .      i.       Find the equation of the curve.    ii.       Find  .   iii.       Find the coordinates of the stationary point and determine its nature. Solution i.   We are given that curve  passes through the point  and we are  required to find the equation of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#11

Hits: 108   Question A line has equation  and a curve has equation .      i.       For the case where the line is a tangent to the curve, find the value of the  constant .    ii.              For the case where , find the x-coordinates of the points of intersection  of the line and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#10

Hits: 135   Question The diagram shows the function  defined for , where      i.       State the range of .    ii.       Copy the diagram and on your copy sketch the graph of .   iii.       Obtain expressions to define the function , giving also the set of values for which each expression is valid. Solution i.   To find the range of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#9

Hits: 100   Question i.       Prove the identity ii.     Hence solve the equation   , for .   Solution i.   We have the equation; We have the identity; Substituting  in above equation; We have the identity , therefore,      ii.   To solve the equation   , for , as demonstrated in (i), we can write the given equation as; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#8

Hits: 143   Question Relative to an origin , the position vectors of the points  and  are given by and i.          Find the value of p for which angle  is . ii.       For the case where , find the unit vector in the direction of . Solution i.   We are given that angle  , hence,  and  are perpendicular […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#7

Hits: 106   Question The coordinates of points A and B are  and  respectively, where  and  are constants. The distance AB is  units and the gradient of the line AB is 2. Find the possible  values of  and of . Solution Expression for slope of a line joining points  and ; Therefore, slope of line AB with points  and ; Expression […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#6

Hits: 293   Question The diagram shows triangle ABC in which AB is perpendicular to BC. The length of AB is 4 cm and angle CAB is  radians. The arc DE with centre A and radius 2 cm meets AC at D and AB at E. Find, in terms of,      i.       the area of the shaded region,    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#4

Hits: 112   Question A curve has equation  . Find the equation of the tangent to the curve at the point where the line  intersects the curve. Solution We are required to find the equation of the tangent to the curve at the point where curve  and line  intersect. To find the equation of the line either we need […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#2

Hits: 150   Question      i.       Express  in the form  .    ii.       Hence, or otherwise, find the set of values of  satisfying . Solution i.   We have the expression; We use method of “completing square” to obtain the desired form. We complete the square for the terms which involve . We have the algebraic formula; For the given case we can compare […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#1

Hits: 150   Question The diagram shows part of the graph of . State the values of the constants a and b. Solution We know that; We also know that; We can see from the given diagram that at ; Substituting  in the above equation yields value of . We can see from the given diagram that at ; Substituting   and  in the above […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#3

Hits: 147 Question Find the term independent of  in the expansion of . . Solution Expression for the general term in the Binomial expansion of  is: In 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 of  i.e.  is 7. Please […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#5

Hits: 157 Question An arithmetic progression has first term  and common difference . It is given that the sum of the first 200 terms is 4 times the sum of the first 100 terms.      i.       Find  in terms of .    ii.       Find the 100th term in terms of . Solution From the given information, we can compile […]