Hits: 1204

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 1204   Question The diagram shows parts of the graphs of  and  intersecting at points A and B.      i.       Write down an equation satisfied by the x-coordinates of A and B. Solve this equation and  hence find the coordinates of A and B.    ii.             Find by integration the area of the shaded region. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 602   Question A curve  has a stationary point at  and is such that .       i.       State, with a reason, whether this stationary point is a maximum or a minimum.    ii.       Find  and . Solution i.   Once we have the coordinates of the stationary point  of a curve, we can determine its  nature, whether minimum or maximum, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 588   Question A curve is such that . The curve has a stationary point at  where .      i.            State, with a reason, the nature of this stationary point.    ii.              Find an expression for .   iii.       Given that the curve passes through the point , find the coordinates […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 614 Question The diagram shows part of the curve . Find the volume obtained when the shaded region  is rotated through  about the y-axis. Solution Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the y-axis is; We are given; We can rearrange it to change the subject; We can see […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 1187   Question The diagram shows parts of the curves  and  intersecting at points  and . The angle between the tangents to the two curves at  is .      i.       Find , giving your answer in degrees correct to 3 significant figures.    ii.       Find by integration the area of the shaded region. Solution i.   Angle between two curves is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 644   Question The function  is defined for  and is such that . The curve  passes through the point .      i.       Find the equation of the normal to the curve at P.    ii.       Find the equation of the curve.    iii.     Find the x-coordinate of the stationary point and state with a reason whether this point is a maximum […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#10

Hits: 481 Question The diagram shows the curve  and the line . Find, showing all necessary working, the area of the shaded region. Solution It is evident from the diagram that; First we find area under the curve. We are given equation of the curve as; We are also given equation of the line as; To find the area of region […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#6

Hits: 438 Question A curve is such that  , where a is  constant. The point  lies on the curve and the normal to the curve at  is .      i. Show that .    ii. Find the equation of the curve. Solution i.   If two lines (or one line and a curve) are perpendicular (normal) to each other, then […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#9

Hits: 794   Question The diagram shows part of the curve   and the tangent to the curve at .      i.       Find expressions for  and .    ii.       Find the equation of the tangent to the curve at P in the form .   iii.       Find, showing all necessary working, the area of the shaded region. Solution i.   First we find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#8

Hits: 677   Question The equation of a curve is such that . Given that the curve has a  minimum point at , find the coordinates of the maximum point. Solution To find the coordinates of a stationary point (in this case a maximum point) we need derivative of equation of the curve. We are given the second derivative of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#12

Hits: 586   Question A curve is such that  . The curve passes through the point .      i.       Find the equation of the curve.    ii.       Find  .   iii.       Find the coordinates of the stationary point and determine its nature. Solution i.   We are given that curve  passes through the point  and we are  required to find the equation of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#11

Hits: 795   Question A line has equation  and a curve has equation .      i.       For the case where the line is a tangent to the curve, find the value of the  constant .    ii.              For the case where , find the x-coordinates of the points of intersection  of the line and […]