Hits: 488

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 488 Question i.       Show that .    ii.  Hence solve the equation  for . Solution      i.   We are given; We choose the left hand side; It can be rewritten as; Utilizing the algebraic formula; Utilizing the trigonometric identity; We can write now; We can rewrite the trigonometric identity as; Therefore; Hence;    ii.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 3054   Question In the diagram, OADC is a sector of a circle with centre O and radius 3 cm. AB and CB are tangents  to the circle and angle  radians. Find, giving your answer in terms of  and ,       i.       the perimeter of the shaded region,    ii.       the area of the shaded region. Solution     i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#11

Hits: 2187   Question The function  is defined for .      i.       Find the exact value of  for which .    ii.       State the range of .   iii.       Sketch the graph of .   iv.       Find an expression for . Solution i.   We are given that; We can write it as; We are given that , therefore; Using calculator; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 565 Question      i.       Show that the equation  can be expressed as    ii.       Hence solve the equation  for . Solution i.   We are given; We know that; We can write the given equation as; We have the trigonometric identity; We can rearrange this identity as; Substituting in above equation; ii.   From (i) we know that we can write the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 592 Question Solve the equation  for . Solution We are given the equation; We have the trigonometric identity; We can rewrite it as; Substituting this in above equation; Now we have two options. Using calculator we can find that; Since we are required to solve the equation  for , we consider angles only in this range. Therefore; We utilize  the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 769 Question Find the value of  satisfying the equation . Solution We are given the equation; Using calculator we can find; Therefore; Using calculator we can find; Therefore;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#4

Hits: 504 Question      i.       Prove the identity    ii.       Hence solve the equation  for . Solution i.   We utilize the relation; We have the trigonometric identity; ii.   We are required to solve the equation  for . From (i), we know that; Therefore; Using calculator; We utilize the periodic/symmetry property of   to find other solutions (roots) of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#5

Hits: 627   Question      i.       Prove the identity    ii.       Solve the equation  for . Solution i.   We have the trigonometric identity; From this we can substitute  in the above equation. Since ; ii.   We are required to solve the equation  for . From (i), we know that; Therefore; Using calculator; We utilize the periodic/symmetry property of   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#3

Hits: 711   Question The reflex angle  is such that , where .      i.       Find an expression, in terms of , for a.   b.      ii.       Explain why  is negative for . Solution i.   A Reflex Angle is one which is more than 180° but less than 360°. a.     We are given that; We have the trigonometric identity; From […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#9

Hits: 676   Question i.       Prove the identity ii.     Hence solve the equation   , for .   Solution i.   We have the equation; We have the identity; Substituting  in above equation; We have the identity , therefore,      ii.   To solve the equation   , for , as demonstrated in (i), we can write the given equation as; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#6

Hits: 2809   Question The diagram shows triangle ABC in which AB is perpendicular to BC. The length of AB is 4 cm and angle CAB is  radians. The arc DE with centre A and radius 2 cm meets AC at D and AB at E. Find, in terms of,      i.       the area of the shaded region,    […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#1

Hits: 978   Question The diagram shows part of the graph of . State the values of the constants a and b. Solution We know that; We also know that; We can see from the given diagram that at ; Substituting  in the above equation yields value of . We can see from the given diagram that at ; Substituting   and  in the above […]