Integration of Trigonometric Functions (2011) Archives — O/A Level Solutions

Hits: 59

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 59   Question i.       Express  in terms of .    ii.       Hence show that Solution      i.   We are given that; From this we can write; We have the trigonometric identity; From this we can write; Hence;      ii.   We are required to show that; We have found in (i) that; Therefore; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#8

Hits: 97   Question i.       By first expanding cos(2x + x), show that    ii.       Hence show that Solution      i.   We are given that   and we are required to express as; Therefore; We have the trigonometric identity; From this we can write; Hence;    ii.   We are required to show that; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 75     Question The diagram shows the part of the curve  for . Find the x-coordinates of the  points on this part of the curve at which the gradient is 4. Solution We are required to find the x-coordinate of the points on the curve where gradient is 4. Therefore first we need […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#4

Hits: 49     Question a.   Find the value of b.   Find Solution a.     We are required to find the value of; Rule for integration of  is: b.     We are required to find; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/22) | Q#4

Hits: 108     Question a.   Find the value of b.   Find Solution a.     We are required to find the value of; Rule for integration of  is: b.     We are required to find; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/21) | Q#6

Hits: 152     Question a.   Find b.   Show that Solution a.     We are required to find; We can expand the integrand as; Rule for integration of  is: Rule for integration of , or ; b.     We are required to show that; We have trigonometric identity; Therefore; Hence; Rule for integration of  is: […]