Hits: 22

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 68 Question     i.      Show that the equation  can be expressed as Where   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; Let ;      ii.   We are required to solve the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 65 Question a)   Given that x > 0, find the two smallest values of x, in radians, for which . Show  all necessary working. b)  The function is defined for . i.     Express f(x) in the form , where a and b are constants. ii.      Find the range of f. Solution a)   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 81 Question The diagram shows a sector OAC of a circle with centre O. Tangents AB and CB to the circle meet  at B. The arc AC is of length 6 cm and angle  radians. i.       Find the length of OA correct to 4 significant figures.    ii.       Find the perimeter of the shaded […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 42   Question     i.      Given that , show, without using a calculator, that .    ii.       Hence, showing all necessary working, solve the equation  for Solution i.   We are given that; Since ; We have the trigonometric identity; From this we can write; Therefore; Let ; Now we have two options. Since […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#9

Hits: 69 Question The functions is defined for , where and are positive constants. The diagram shows the graph of y = f(x).     i.      In terms of and state the range of .    ii.       State the number of solutions of the following equations.                  a)    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#6

Hits: 275 Question The equation of a curve is and the equation of a line is . i.State the smallest and largest values of y for both the curve and the line for . ii.Sketch, on the same diagram, the graphs of and for . iii.State the number of solutions of the equation for . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#9

Hits: 269 Question The functions f is defined by  for  ,     i.      State the range of .   ii.     Sketch the graph of . The functions g is defined by for , where is a constant.  iii.     State the largest value of for which g has an inverse.  iv.     For this value of , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#6

Hits: 463  Question      i.       Prove the identity    ii.       Hence solve the equation  for Solution i.   First, we are required to show that; Since ; We have the trigonometric identity; From this we can write; Therefore; We have the algebraic formula;      ii.   We are required to solve the equation;   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#7

Hits: 176 Question a)  Solve the equation   for . b)    The diagram shows part of the graph of , where is measured in radians and and are constants. The curve intersects the x-axis at  and the y-axis at . Find the values of and . Solution a)   We are required to solve the […]

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

Hits: 174 Question i.       Show that   ii.       Hence, showing all necessary working, solve the equation For . Solution i.   We are given the expression;   We have the algebraic identity; We have the trigonometric identity;               Since ; We can write; Therefore; ii.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 383 Question The diagram shows an arc BC of a circle with centre A and radius 5 cm. The length of the arc BC is  4 cm. The point D is such that the line BD is perpendicular to BA and DC is parallel to BA.      i.       Find angle BAC in radians.    […]

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: 286 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: 225 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: 901 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: 241 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 […]