Hits: 108

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#8

Hits: 108     Question      i.       Given that   and find in terms of .    ii.       Solve the equation giving all solutions in the interval 0◦ ≤ x ≤ 360◦. Solution      i.   We are given; We are given that ; therefore;    ii.   We are required to solve  giving all solutions […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 137     Question The diagram shows the part of the curve  for .      i.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       The line y=x intersects the curve at point P. Use the iterative formula to determine the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#2

Hits: 77     Question The curve with equation has one stationary point  in the interval . Find the exact  x-coordinate of this point. Solution We are required to find the x-coordinate of stationary point of the curve with equation; A stationary point on the curve is the point where gradient of the curve is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 159     Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the  point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region  R is bounded by the curve and by the lines x = and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 75     Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of   to find other solutions (roots):  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 134     Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the  point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded  region R is bounded by the curve and by the lines x = and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 76     Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of   to find other solutions (roots):  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#7

Hits: 107   Question (i)          Show that (2 sin x + cos x)2 can be written in the form (ii)        Hence find the exact value of  Solution      i.   We are given that; We have formula; Therefore; Therefore; Therefore;    ii.   We are required to find the exact value of; From (i) we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#4

Hits: 53     Question      i.       Given that , find the value of .    ii.       Hence, showing the use of an appropriate formula in each case, find the exact value of a.   b.   Solution      i.   We are given that; We have trigonometric identity; Let , then; Since , therefore;      […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#7

Hits: 156   Question (i)          Show that and hence find the exact value of; (ii)   The region enclosed by the curve y = tan x + cos x and the lines x = 0,  and y = 0 is shown in  the diagram. Find the exact volume of the solid produced when this region […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#6

Hits: 170   Question The diagram shows the curve , for . The x-coordinate of the maximum point  M is denoted by . i.       Find  and show that  satisfies the equation tan 2x = 2x + 4.    ii.       Show by calculation that  lies between 0.6 and 0.7.   iii.       Use the iterative formula to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#4

Hits: 93   Question i. Express  in the form , where  and , Give the value of  correct to 2 decimal places.    ii.Hence solve the equation for .   iii. State the largest value of k for which the equation  has any solutions. Solution      i.   We are given the expression; We are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#7

Hits: 147   Question (i)       Show that (2 sin x + cos x)2 can be written in the form (ii)        Hence find the exact value of  Solution      i.   We are given that; We have formula; Therefore; Therefore; Therefore;    ii.   We are required to find the exact value of; From […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#4

Hits: 112     Question      i.       Given that , find the value of .    ii.       Hence, showing the use of an appropriate formula in each case, find the exact value of a.   b.   Solution      i.   We are given that; We have trigonometric identity; Let , then; Since , therefore;      […]