# 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

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; We apply […]

# 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

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 written as, […]

# 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

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 is; It is […]

# 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

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 of the […]