Hits: 262

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 262   Question      i.                     a.   Prove the identity                  b.   Hence prove that    ii.       By differentiating , show that if  then .     iii.       Using the results of parts (i) and (ii), […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#4

Hits: 166   Question      i.       Show that the equation Can be written in the form    ii.       Hence solve the equation to For . Solution      i.   We are given; We apply following two addition formulae on both sides of given equation. Therefore;    ii.   We are required to solve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#5

Hits: 173 Question i.       Express  in the form , where  and , giving 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 that; We are required to write it […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#3

Hits: 132     Question Find the exact value of Solution We are required to find exact value of; 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 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#5

Hits: 504   Question The function f is such that  for , where  and  are positive constants. The maximum value of  is 10 and the minimum value is −2.      i.       Find the values of  and .    ii.       Solve the equation .   iii.       Sketch the graph of . Solution i.   We have the function; We know that; For ; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 3920   Question The diagram shows the curve  and the points P(0,1) and Q(1,2) on the curve. The shaded region is bounded by the curve, the y-axis and the line y = 2.     i.       Find the area of the shaded region.    ii.       Find the volume obtained when the shaded region is rotated through 360◦ about the x-axis. Tangents are drawn […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#2

Hits: 396 Question Prove the identity Solution We are given the equation; We can rewrite it as; We have the trigonometric identity; We can rewrite it as; Therefore;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#2

Hits: 373 Question      i.       Show that the equation  can be written in the  form .    ii.       Hence solve the equation , for . Solution i.   We are given the equation; We can rewrite it as; We have the trigonometric relation; Substituting  in the above equation; We have the trigonometric identity; We can rewrite this as; Therefore; ii.   To solve  equation for […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#1

Hits: 443 Question In the triangle ABC, AB = 12 cm, angle BAC = 60o and angle ACB = 45o. Find the exact length of BC. Solution From the given data we can write the following; Expression for Law of Sines is; For the given case;