Hits: 606

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 606  Question i.    Sketch, on the same diagram, the graphs of  and  for . ii.       Verify that  is a root of the equation , and state the other root of this equation for which .  iii.       Hence state the set of values of , for , for which Solution i.   We are required to sketch  and  for . First we sketch  for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 1020   Question The diagram represents a metal plate , consisting of a sector  of a circle with centre  and radius , together with a triangle  which is right-angled at C. Angle  radians and  is perpendicular to . i.       Find an expression in terms of  and  for the perimeter of the plate. ii.    For the case where  and […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#9

Hits: 1091   Question The function f is such that , for , where  is a constant.      i.       In the case where ,         a.   Find the range of ,        b.   Find the exact solutions of the equation .    ii.       In the case where ,        a.   Sketch the graph of  ,     […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#4

Hits: 895   Question A curve has equation  and P(2, 2) is a point on the curve.     i.       Find the equation of the tangent to the curve at P.    ii.       Find the angle that this tangent makes with the x-axis. Solution i.   To find the equation of the line either we need coordinates of the two points on the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 386 Question      i.       Given that  Show that, for real values of      ii.       Hence solve the equation  for . Solution i.   We have the equation; We have the trigonometric identity; We can rewrite it as; Thus Now we have two options; NOT POSSIBLE So we are left with ONLY option;      ii.   To solve the equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 1730 Question In the diagram, ABCD is a parallelogram with AB=BD=DC=10cm and angle ABD= 0.8 radians. APD and BQC are arcs of circles with centres B and D respectively.     i.       Find the area of the parallelogram ABCD.    ii.       Find the area of the complete figure ABQCDP.   iii.       Find the perimeter of the complete figure ABQCDP. Solution i.   Expression for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 1244 Question The diagram shows a circle  touching a circle  at a point . Circle  has centre A and radius 6cm, and circle  has centre B and radius 10 cm. Points D and E lie on  and  respectively and DE is parallel to AB. Angle  radians and angle  radians.     i.       By considering the perpendicular distances of D […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 545 Question      i.       Sketch, on a single diagram, the graphs of  and  for .    ii.       Write down the number of roots of the equation  in the interval .   iii.       Deduce the number of roots of the equation  in the interval . Solution     i.        ii.   If two lines (or a line and a curve) intersect each other […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#8

Hits: 377 Question i.  Prove the identity    ii.  Hence solve the equation   , for .   Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; We can rewrite it as; Therefore; Using formula;      ii.   To solve the equation  , for , as demonstrated in (i), we […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#7

Hits: 1489 Question In the diagram, AB is an arc of a circle, centre O and radius 6 cm, and angle  radians. The line AX is a tangent to the circle at A, and OBX is a straight line.     i.       Show that the exact length of AX is  cm.  Find, in terms of  and ,    ii.       the area of the shaded […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#5

Hits: 705 Question      i.       Prove the identity    ii.       Hence solve the equation  , for . Solution i.   We have the equation; We have the relation , therefore, We have the trigonometric identity; We can rewrite it as; Therefore; Using formula;      ii.   To solve the equation  , for , as demonstrated in (i), we can write […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#5

Hits: 483 Question      i.       Show that the equation   can be written in the form    ii.        Hence solve the equation  for . Solution i.   We have the equation; We have the relation , therefore, Multiplying entire equation with We have the trigonometric identity; We can rewrite it as; Therefore;      ii.   To solve the […]