Hits: 533

# 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#8

Hits: 533   Question The function  is defined by  for .      i.       Solve the equation .    ii.       Find the range of .   iii.       Sketch the graph of . The function  is defined by  for .   iv.       State the maximum value of for which  has an inverse.    v.       Obtain an expression for . Solution i.   We have the function; We can write it as; […]

# 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#5

Hits: 850   Question i.   Sketch, on the same diagram, the curves  and  for  . ii.     Hence state the number of solutions, in the interval , of the equations                      a.                          b.   Solution i.   We are required to […]

# 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#3

Hits: 415 Question   i.      Express the equation  as a quadratic equation in .  ii.       Solve the equation  for , giving solutions in terms of . Solution i.   We are given that; We know that; Therefore; We have the trigonometric identity; It can be rearranged as follows; Substituting this expression of  in the above equation; It can be rewritten as; This […]

# 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#5

Hits: 501 Question It is given that  and , where .      i.       Show that  has a constant value for all values of .    ii.       Find the values of  for which . Solution      i.   We are given that; Taking squares of both sides of each equation. We have the algebraic formulae; We can simplify these to; Adding both sides […]

# 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#7

Hits: 499   Question a)   Find the possible values of  for which , giving your answers correct to 3 decimal places. b)  Solve the equation  for  giving  in terms of  in your answers. Solution a)     We have; We can rearrange the equation as; We know that; Therefore we can write above equation as; b)    To solve the equation  for , let […]

# 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#1

Hits: 448   Question Given that , where  is an acute angle in degrees, find, in terms of ,      i.           ii.          iii.        Solution      i.   We have; Since we are required to write it in terms of  where  , so we first write the given  expression in terms of  . We have the trigonometric identity; […]

# 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#4

Hits: 498   Question      i.       Solve the equation  for .  ii.      Hence find the solution of the equation  for . Solution      i.   We have the equation; Since we are required to write it as a quadratic equation in , we need to eliminate . We have the trigonometric identity; We can rewrite the identity as; Hence; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#5

Hits: 456   Question      i.       Show that    ii.       Hence solve the equation For . Solution      i.   We have the equation; We have the trigonometric identity; Therefore;    ii.   To solve this equation   for ,  as demonstrated in (i), we can rewrite the equation as; We have the trigonometric identity; We can rewrite the identity as; […]