Hits: 66

# 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#5

Hits: 66     Question Solve the equation , giving all solutions in the interval . Solution We are required to solve; We have trigonometric identity; To solve this equation for , we can substitute . Hence, Since given interval is  , for interval can be found as follows; Multiplying the entire inequality with 2; […]

# 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: 60   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 | (P2-9709/22) | Q#8

Hits: 101   Question i.       Express  in the form , where  and , stating the  exact value of R and and giving the value of  correct to 2 decimal places.    ii.       Hence solve the equation Giving all solutions in the interval .   iii.       Write down the least value of  as  varies. Solution      […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 137     Question The parametric equations of a curve are x = 1 + 2 sin2θ , y = 4 tanθ , i. Show that    ii. Find the equation of the tangent to the curve at the point where , giving your answer in  the form y = mx + c. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 107     Question      i.       By sketching a suitable pair of graphs, show that the equation Where x is in radians, has only one root for .      ii.       Verify by calculation that this root lies between x=1.1 and x=1.2.   iii.       Use the iterative formula to determine this root correct to […]

# 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: 77     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#8

Hits: 61   Question i.       Prove that    ii.       Hence a.   Solve for  the equation b.   find the exact value of . Solution      i.   We are given that; We utilize following relations;   provided that   provided that Therefore; We utilize following relation; Therefore;    ii.   We are required to solve; As […]

# 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#8

Hits: 124   Question i.       Prove that    ii.       Hence a.   Solve for  the equation b.   find the exact value of . Solution      i.   We are given that; We utilize following relations;   provided that   provided that Therefore; We utilize following relation; Therefore;    ii.   We are required to solve; As […]

# 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#8

Hits: 152   Question i.       Express  in the form , where  and , Give the exact value of R and the value of  correct to 2 decimal places.    ii.       Hence solve the equation for .   iii.       Find the greatest and least possible values of  as  varies. Solution      i.   We are given […]

# 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#2

Hits: 156   Question A curve has parametric equations Find the exact gradient of the curve at the point for which . Solution      i.   Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that  particular point. Gradient (slope) of the curve at a particular […]