Hits: 582

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#8

Hits: 582   Question The function f is defined by  for . It is given that  and  .      i.       Find the values of  and .    ii.       Find the x-coordinates of the points where the curve  intersects the x-axis.   iii.       Sketch the graph of . Solution i.   We have the function; We are given that; Adding both equations gives us; Substituting  in […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#5

Hits: 282 Question      i.       Show that the equation  can be written as .    ii.       Hence solve the equation   for . Solution i.   We are given the equation; We have the trigonometric relation; Substituting  in the above equation; We have the trigonometric identity; We  can rewrite it as; Substituting it in above equation; ii.   To solve  for , as demonstrated in (i) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#7

Hits: 1214 Question In the diagram, AB is an arc of a circle, centre O and radius r cm, and angle  radians. The point X lies on OB and AX is perpendicular to OB. i.       Show that the  area, Acm2, of the shaded region AXB is given by     ii.       In the case where  and , find the perimeter […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#5

Hits: 1918 Question In the diagram, OAB is a sector of a circle with centre O and radius 12 cm. The lines AX and BX are tangents to the circle at A and B respectively. Angle  radians. i.       Find the exact length of AX, giving your answer in terms of .    ii.       Find the area of the shaded region, giving […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#3

Hits: 453 Question Prove the identity Solution We have the trigonometric relation; Therefore we can write the given expression as; We have the trigonometric identity; Therefore we can write the above expression as; We have the trigonometric identity; We can also rewrite the identity as; Therefore we can write; As;