Hits: 289

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 289   Question The angle x, measured in degrees, satisfies the equation      i.       By expanding each side, show that the equation may be simplified to    ii.       Find the two possible values of x lying between  and .   iii.       Find the exact value of , giving your answer as a fraction. Solution      i.   We are given; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2002 | Oct-Nov | (P1-9709/01) | Q#5

Hits: 573 Question      i.       Show that the equation  can be expressed as    ii.       Hence solve the equation , for . Solution i.   We have; Using the relation ; We have the trigonometric identity; It can be written as; Therefore; Becomes; ii.   As demonstrated in (i) we can write the equation  as,  To solve this equation for , let; Therefore  can be […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2002 | Oct-Nov | (P1-9709/01) | Q#6

Hits: 624 Question In the diagram, triangle ABC is right-angled and D is the mid-point of BC. Angle  and angle . Denoting the length of AD by ,      i.       express each of AC and BC exactly in terms of , and show that .     ii.       show that . Solution i.   Expression for  trigonometric ratio in right-triangle […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2002 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 1938 Question In the diagram, OPQ is a sector of a circle, centre O and radius r cm. Angle QOP= radians. The tangent to the circle at Q meets OP extended at R. i.     Show that the area, Acm2, of the shaded region is given by .    ii.       In the case where   and , evaluate the length […]