# 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#5

Question It is given that  and , where .      i.       Show that  has a constant value for all values of .    ii.       Find the values of  for which . Solution      i.   We are given that; Taking squares of both sides of each equation. We have the algebraic formulae; We can simplify these to; Adding both sides of these […]

# 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 | (P1-9709/12) | Q#1

Question A curve is such that  and  is a point on the curve. Find the equation of the curve. Solution i.   We are given that curve with   passes through the point  and we are  required to find the equation of the curve. We can find equation of the curve from its derivative through integration; For the given case; […]

# 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#6

Question Relative to an origin , the position vectors of three points A and B are given by , and where  and  are constants.      i.       State the values of p and q for which  is parallel to .    ii.       In the case where , find the value of  for which angle BOA is .   iii.       In the case where  and , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#9

Question A function f is defined by , for .      i.       Find an expression for .    ii.       Determine, with a reason, whether  is an increasing function, a decreasing function or neither.   iii.       Find an expression for  and state the domain and range of . Solution i.   We have the function; The expression for  represents derivative of . We can rewrite as; Rule […]

# 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#2

Question Find the coefficient of  in the expansion of      i.           ii.       Solution i.   First rewrite the given expression in standard form. Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the coefficient of the term : we can  equate Finally substituting  in: Therefore the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#10

Question a)   The first and last terms of an arithmetic progression are 12 and 48 respectively. The sum of the  first four terms is 57. Find the number of terms in the progression. b)  The third term of a geometric progression is four times the first term. The sum of the first six  terms is k times the […]