# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#11

Question The diagram shows the curve . i.       Find the equation of the tangent to the curve at the point . ii.    Show that the x-coordinates of the points of intersection of the line   and the curve are given by the equation . Hence find these x- coordinates. iii.     The region shaded in the diagram is rotated through […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#3

Question The point A has coordinates  and the point B has coordinates . The  point C is the mid-point of AB.   i.       Find the equation of the line through A that is perpendicular to .  ii.     Find the distance AC. Solution i.   We are required to find equation of a line that passes through  and is  perpendicular to the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#6

Question In the diagram, S is the point  and T is the point . The point Q lies on ST,  between S and T, and has coordinates . The points P and R lie on the x-axis  and y-axis respectively and OPQR is a rectangle.      i.       Show that the area, A, of the rectangle OPQR is given by […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#5

Question The diagram shows a rectangle ABCD in which point A is  and point B is . The diagonal AC has equation . Find, by calculation, the coordinates of  C and D. Solution We are required to find coordinates of the points C and D. First we find the coordinates of point C. It is evident from the diagram that point C […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#10

Question The diagram shows the curve  and the tangent to the curve at the point . i.         Find the equation of this tangent, giving your answer in the form . ii.       Find the area of the shaded region. Solution i.   We are required to find equation of the tangent to the curve at point […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#7

Question The point A has coordinates  and the point B has coordinates . i.       Find the equation of the perpendicular bisector of AB, giving your answer in the form .    ii.       A point C on the perpendicular bisector has coordinates . The distance OC is 2 units, where O is the origin. Write down two equations involving  and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#11

Question The diagram shows part of the curve  and a point  and  which lie on the curve. The tangent to the curve at B intersects the line  at the point C.      i. Find the coordinates of C.    ii. Find the area of the shaded region. Solution i.   We are required to find the coordinates of point C. It is evident […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#7

Question The diagram shows three points ,  and . The point X lies on  AB, and CX is perpendicular to AB. Find, by calculation,       i.       the coordinates of X,    ii.       the ratio AX : XB. Solution i.   We are required to find the coordinates of point X. It is evident from the diagram that point X is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#11

Question The diagram shows the curve  , which intersects the x-axis at A and the  y-axis at B. The normal to the curve at B meets the x-axis at C. Find      i.       the equation of BC,    ii.       the area of the shaded region. Solution      i.   To find the equation of the line either we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#8

Question The volume of a solid circular cylinder of radius  cm is  cm3.      i.       Show that the total surface area, S cm2, of the cylinder is given by     ii.       Given that  can vary, find the stationary value of .   iii.       Determine the nature of this stationary value. Solution      i.   We are given that volume of solid circular cylinder; Expression […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#7

Question The point R is the reflection of the point  in the line . Find by calculation the coordinates of R. Solution We are given equation of the line ; Slope-Intercept form of the equation of the line; Where  is the slope of the line. We can rearrange this equation to write it in standard point-intercept form. Therefore […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#4

Question The diagram shows a square ABCD of side 10 cm. The mid-point of AD is O and BXC is an arc of a circle with centre O.      i.       Show that angle BOC is 0.9273 radians, correct to 4 decimal places.    ii.       Find the perimeter of the shaded region.   iii.       Find the area of the shaded region. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#3

Question The straight line  is a tangent to the curve  at the point P. Find the value of the constant  and the coordinates of P. Solution If line  is tangent to the curve that means it intersects the curve at a single point.  Now we need to find the coordinates of the ONLY point of intersection […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#10

Question The diagram shows part of the curve  and the point  on the curve. The tangent at A cuts the x-axis at B and the normal at A cuts the y-axis at C.      i.       Find the coordinates of B and C.  ii.   Find the distance AC, giving your answer in the form  , where a and b are integers.   iii.       Find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#7

Question A curve has equation  and a line has equation , where  is a constant.      i.       For the case where , the curve and the line intersect at the points A and B. Find the coordinates of the mid-point of AB.    ii.       Find the non-zero value of  for which the line is a tangent to the curve, and find […]