Hits: 31

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 23 Question The functions f and g are defined by  for  ,  for      i.      Solve the equation .   ii.     Sketch the graph of . Solution i.   We are given;  for  for We are required to solve equation ; To solve this equation for , we can substitute . Hence, Since given […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 67 Question     i.      Show that the equation  may be expressed as      ii.      Hence solve the equation   for . Solution i.   We are given the equation; We have the trigonometric identity; From this we can substitute in above equation; ii.   We are required to solve the equation for . From […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#6

Hits: 134 Question The diagram shows a sector POQ of a circle of radius 10 cm and centre O. Angle POQ is 2.2  radians. QR is an arc of a circle with centre P and POR is a straight line.     i.       Show that the length of PQ is 17.8 cm, correct to 3 significant […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#5

Hits: 51 Question a.   Express the equation  as a quadratic equation in  and hence solve the equation for . b.   The diagram shows part of the graph of , where  and  are constants and . Find the value of  and the value of . Solution a.     We are required to solve this quadratic equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#4

Hits: 49 Question A straight line cuts the positive x-axis at A and the positive y-axis at B(0, 2). Angle radians, where O is the origin.      i.       Find the exact value of the x-coordinate of A.    ii.       Find the equation of the perpendicular bisector of AB, giving your answer in the form y […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#7

Hits: 234 Question a.                         i.       Express  in the form , where  and are constants to be  found.       ii.       Hence, or otherwise, and showing all necessary working, solve the equation  For .   b.     The diagram shows the graphs of  and  for . The  graphs intersect at the points A […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#10

Hits: 491 Question     i.       Solve the equation  for .    ii.       Sketch, on the same diagram, the graphs of  and for  .   iii.       Use your answers to parts (i) and (ii) to find the set of values of x for   for which . Solution      i.   We have the equation; We know that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#6

Hits: 1201 Question The diagram shows points A and B on a circle with centre O and radius r. The  tangents to the circle at A and B meet at T. The shaded region is bounded by the  minor arc AB and the lines AT and BT. Angle AOB is  radians.      i.       In the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#4

Hits: 411 Question The function f, is such that   for . It is given that  and .                             i.       Find the values of the constants a and b.                           ii.       Find the set of values of k for which the equation f(x) = k has no  solution. Solution i.   We are given the function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#6

Hits: 1000 Question The diagram shows a circle with centre O and radius r cm. The points A and B lie on  the circle and AT is a tangent to the circle. Angle radians and OBT is a  straight line.      i.       Express the area of the shaded region in terms of r and . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#4

Hits: 321 Question i.Prove the identity    ii.Hence solve the equation  for . Solution i.       We have the trigonometric identity;         ii. We have the equation;   From (i) we know that left hand side of given equation can be written as;      Therefore;         […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#8

Hits: 145 Question     i.       Express  in the form , where and  , giving the value of  correct to 2 decimal places.    ii.       Hence solve the equation  for . Solution      i.   We are given the expression; We are required to write it in the form; If  and are positive, then; can be written […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 132 Question A curve is defined by the parametric equations for .       i.       Find the exact gradient of the curve at the point for which .    ii.       Find the value of at the point where the gradient of the curve is 2, giving the value correct to 3 significant figures. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 127 Question a.   Show that b.   Find the exact value of Show all necessary working. Solution a.     We are required to show; Rule for integration of  is: Division Rule; Power Rule; b.     We are required to find; Since , we can rearrange to write; Rule for integration of  is: Rule for integration […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/21) | Q#7

Hits: 110   Question      i.       Show that    ii.       Hence, show that   iii.       Solve the equation For . Show all the necessary working. Solution i.   First we are required to show that;   provided that   provided that   provided that ii.   We are required to show that; As shown in […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/21) | Q#4

Hits: 95 Question a.   Find b.   Find the exact value of Show all necessary working. Solution a.   We are given that; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: b.   We are required to find the exact value of; Rule for integration of  is: Rule for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 72   Question a.   Showing all necessary working, solve the equation for . b.   Showing all necessary working, solve the equation for . Solution a.     We are given;   provided that   provided that Let , then; We are given that ; interval for  can be found as follows. Multiplying entire inequality with […]