Hits: 648

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 648   Question i.       Sketch the curve  for . ii.       By adding a suitable straight line to your sketch, determine the number of real roots of the equation State the equation of the straight line. Solution i.   We are required to sketch  for ; We can sketch the graph of  for  as follows. We can find the points of the graph as follows. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 70   Question Solve the equation  for   . Solution We can rearrange the given equation as; We have the trigonometric identity; This identity can be rearranged as; Substituting  expression in the given equation; Let ; We can solve this quadratic equation through factorization. Now we have two options. Since ; Using calculator we can find the values of . We utilize the symmetry […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 1120 Question A function is defined by   for .    i.     State the range of .  ii.     State the exact value of .  iii.      Sketch the graph of .  iv.      Obtain an expression, in terms of , for Solution i.   We have the function;  for This can be written as; We know […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#11

Hits: 2072   Question The function  is defined for the domain .      i.       Solve the equation .    ii.       Sketch the graph of .   iii.       Find the set of values of  for which the equation  has no solution. The function  is defined for the domain .   iv.       State the largest value of  for which g has an inverse.    v.    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 424 Question Solve the equation  for . Solution We have the equation; We have the trigonometric identity; We can write it as; Therefore; To solve this equation for , we can substitute . Hence, Now we have two options; Since; Using calculator we can find the values of . We utilize the symmetry property of   to find other […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 1445 Question      i.       Prove the identity    ii.      Hence solve the equation  for . . Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; We can write it as; Therefore; Using the formula; ii.   To solve the equation  for , as demonstrated in (i), […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/13) | Q#4

Hits: 510 Question      i.       Show that the equation  can be expressed as .    ii.       Solve the equation   for . Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; We can write it as; Therefore; ii.   To solve the equation  for , as demonstrated in (i), we can […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#

Hits: 505 Question      i.       Show that the equation  can be written in the form    ii.       Solve the equation , for . Solution i.   We have the equation; We have the relation , therefore, ii.   To solve the equation , for , as demonstrated in (i), we can write the given equation as; To solve this equation for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/11) | Q#1

Hits: 1004 Question The acute angle  radians is such that tan , where  is a positive constant. Express, in terms of ,      i.           ii.          iii.        Solution      i.   From the diagram below it is evident that if  is acute angle i.e.  lies in the first quadrant, then  will be in second quadrant. From the […]