Hits: 193

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 193 Question i.       Express  in the form , where  and , giving the exact  value of R and the value of  correct to 2 decimal places.    ii.       Hence solve the equation Giving all solutions in the interval . Solution      i.   We are given the expression; We are required to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 185   Question a.   Find . b.   Express  in terms of  and hence find . Solution a.     We are required to find; Rule for integration of , or ; b.     We know that , therefore; Hence; Therefore; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#8

Hits: 183   Question The diagram shows the curve , for . The point  lies on the curve. i.       Show that the normal to the curve at Q passes through the point .    ii.       Find .   iii.       Hence evaluate Solution      i.   If a point P(x,y) lies on a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 67   Question Solve the equation , giving all solutions in the interval . Solution We are given; We know that ; Let , then we can write; Now we have two options. Since ; We know that except where  or undefined, therefore; Using calculator we can find that; Properties of Domain Range Periodicity […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#8

Hits: 109   Question The diagram shows the curve , for . The point  lies on the curve.     i.       Show that the normal to the curve at Q passes through the point .    ii.       Find .   iii.       Hence evaluate Solution      i.   If a point P(x,y) lies on […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 71   Question Solve the equation , giving all solutions in the interval . Solution We are given; We know that ; Let , then we can write; Now we have two options. Since ; We know that except where  or undefined, therefore; Using calculator we can find that;   Properties of Domain Range […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#8

Hits: 77   Question i.       Prove the identity    ii.       Hence solve the equation For . Solution      i.   We are given that; We utilize following two addition formulae;    ii.   We are required to solve; As demonstrated in (i); Therefore; Since   provided that ; Since ; Therefore, we solve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#4

Hits: 74   Question a.   Show that b.   By using an appropriate trigonometrical identity, find the exact value of Solution a.     We are required to show that; Rule for integration of  is: b.     We are required to find exact value of; We know that , therefore; Hence; Rule for integration of  is: Rule […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#8

Hits: 117 Question i.       Prove the identity    ii.       Hence solve the equation For . Solution      i.   We are given that; We utilize following two addition formulae;    ii.   We are required to solve; As demonstrated in (i); Therefore; Since   provided that ; Since ; Therefore, we solve  for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#4

Hits: 108     Question a.   Show that b.   By using an appropriate trigonometrical identity, find the exact value of Solution a.     We are required to show that; Rule for integration of  is:   b.     We are required to find exact value of; We know that , therefore; Hence; Rule for integration of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#8

Hits: 149 Question      i.       By differentiating , show that if y = cot x then    ii.       By expressing in terms of and using the result of part (i), show that   iii.       Express cos 2x in terms of sin2 x and hence show that can be expressed as .  Hence […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#3

Hits: 97     Question      i.       Show that the equation can be written in the form    ii.       Hence solve the equation  for . Solution      i.   We are given; We apply following addition formula on left side of given equation. Therefore; Since;      ii.   We are required to […]