Hits: 4113

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#1

Hits: 4113   Question  Solve the equation , for  Solution i.   We have the equation; Dividing both sides of the equation by ; We have the relation , therefore, To solve this equation, we can substitute . Hence,   Since given interval is  , for  interval can be found as follows; Multiplying both sides of the inequality with […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#4

Hits: 424 Question      i. Solve the equation  for . ii. How many solutions has the equation  for ? Solution    i.   We are given; 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; Since ; Hence the given interval for  is . To solve  equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 1102   Question In the diagram, D lies on the side AB of triangle ABC and CD is an arc of a circle with centre A and radius 2 cm. The line BC is of length 2√3 cm and is perpendicular to AC. Find the area of the shaded region BDC, giving your answer in terms of  and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#11

Hits: 5470   Question The diagram shows a sector of a circle with centre  and radius 20 cm. A circle with centre  and radius  cm lies within the sector and touches it at P, Q and R. Angle POR = 1.2 radians. i. Show that , correct to 3 decimal places. ii. Find the total area of the three parts […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#1

Hits: 524   Question i. Prove the identity ii. Use this result to explain why  for . Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; We can rewrite the identity as; Therefore; Again using the relation , we can rewrite; ii.   It is evident that in equation  for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 248   Question Solve the equation , for . Solution We have the equation; We have the trigonometric identity; We can rewrite the identity as; Therefore; To solve this equation  for ,  we can substitute . Hence, Now we have two options; Since; NOT POSSIBLE Using calculator we can find the values of . We utilize the symmetry property of   to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 396   Question i.       Show that the equation  can be written as a quadratic equation in . ii.       Solve the equation , for . Solution i.   We have the equation; To write the given equation in terms of , we utilize the trigonometric relation; Hence; Multiplying both sides with ; We have the trigonometric identity; We can rewrite the identity as; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 1140   Question i.       Solve the equation  , for .          ii.    The smallest positive solution of the equation , where  is a positive integer, is . State the value of  and hence find the largest solution of this equation in the interval . Solution i.   We have the equation; We have the trigonometric identity; We can rewrite the identity as; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 3630   Question The diagram shows a sector OAB of a circle with centre O and radius . Angle AOB is  radians. The point C on OA is such that BC is perpendicular to OA. The point D is on BC and the circular arc AD has centre C.     i.       Find AC in terms of  and .    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#8

Hits: 1904 Question In the diagram, AB is an arc of a circle with centre O and radius . The line XB is a tangent to the circle at B and A is the mid-point of OX. i. Show that angle  radians. Express each of the following in terms of,  and : ii. the perimeter of the shaded region, iii. the area of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#5

Hits: 525 Question i.       Prove the identity ii.       Solve the equation      for . Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; Therefore; ii.   Solve the equation   for . We can rewrite the given equation as; As demonstrated in (i), we can rewrite the given equation as; To […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#3

Hits: 1701 Question In the diagram, ABC is an equilateral triangle of side 2 cm. The mid-point of BC is Q. An arc of a circle with centre A touches BC at Q, and meets AB at P and AC at R. Find the total area of the shaded regions, giving your answer in terms of  and . […]