Hits: 897

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 897 Question a.   Show that the equation  can be expressed as and hence solve the equation  for . b.     The diagram shows part of the graph of , where a and b are constants. The graph  crosses the x-axis at the point  and the y-axis at the point ,. Find c and d in  terms of a […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 926 Question      i.       Prove the identity .    ii.       Hence solve the equation  for . Solution i.   We are given the identity; We have the relation; Therefore; We have the trigonometric identity; It can be rearranged as; Hence; We have the algebraic identity; Therefore, we can write; ii.   We are required to solve following equation. From (i), we know that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 4845 Question The diagram shows a circle with centre A and radius r. Diameters CAD and BAE are perpendicular  to each other. A larger circle has centre B and passes through C and D.      i.       Show that the radius of the larger circle is .    ii.       Find the area of the shaded region in terms of . Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 663 Question      i.       Show that the equation  can be expressed as     ii.       Hence solve the equation  for . Solution i.   We are given that; Since ; We have the trigonometric identity; From this we can write; Therefore; ii.   We are required to solve the equation  for . From (i), we know that; Therefore; Let ; Since; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 569 Question Solve the equation . Solution i.   We are given that; Using calculator; Let ; Now we have two options. Since ;  is not possible

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#11

Hits: 6513 Question In the diagram, OAB is a sector of a circle with centre O and radius r. The point C on OB is such  that angle ACO is a right angle. Angle AOB is  radians and is such that AC divides the sector into  two regions of equal area.     i.       Show that   It […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#4

Hits: 688   Question        i.      Express the equation  in the form  and solve the equation for  .             ii.               Solve the equation  for .   Solution i.   We are given; We know that; Therefore; Now we solve this equation for . Using calculator; We utilize the periodic/symmetry […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#6

Hits: 2568   Question A tourist attraction in a city centre is a big vertical wheel on which passengers can ride. The wheel  turns in such a way that the height, h m, of a passenger above the ground is given by the formula  . In this formula, k is a constant, t is the time in minutes that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#5

Hits: 892 Question i.          Prove the identity .  ii.       Hence solve the equation , for . Solution i.   We have the trigonometric relation; Therefore; ii.   We are required to solve the equation  for . From (i), we know that; Therefore; Let ; Now we have two options. Since ; Using calculator We utilize the periodic/symmetry property […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#2

Hits: 5255   Question In the diagram, AYB is a semicircle with AB as diameter and OAXB is a sector of a circle with centre  O and radius r. Angle AOB = 2 radians. Find an expression, in terms of r and , for the  area of the shaded region. Solution It is evident from the diagram that; First we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#8

Hits: 1328   Question The function  is defined for .      i.       Solve the equation , giving your answer correct to 2 decimal places.    ii.       Sketch the graph of .   iii.       Explain why  has an inverse.   iv.       Obtain an expression for . Solution      i.   We are given; We are required to solve; Therefore; Using calculator;    ii.   Ware required […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#1

Hits: 1888 Question Given that  is an obtuse angle measured in radians and that , find, in terms of , an  expression for                     i.                          ii.                         iii.        Solution We are given that  is an obtuse angle. An obtuse angle  is such that . We are also given that; We know that for an obtuse angle  the sine of that obtuse angle equals […]