# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#3

Question The length,  metres, of a Green Anaconda snake which is t years old is given  approximately by the formula where 1 t 10. Using this formula, find      i.           ii.       the rate of growth of a Green Anaconda snake which is 5 years old. Solution      i.   We are given; We are required to find  . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#6

Question A curve has equation  and a line has equation , where  is a non-zero constant.     i.       Find the set of values of  for which the curve and the line have no common points.    ii.       State the value of  for which the line is a tangent to the curve and, for this case, find the coordinates of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#11

Question The diagram shows part of the curve  . The curve cuts the y-axis at A and the line  at B.     i.       Show that the equation of the line AB is .    ii.       Find the volume obtained when the shaded region is rotated through 360o about the x-axis. 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 2010 | Oct-Nov | (P1-9709/12) | Q#10

Question The diagram shows an open rectangular tank of height  meters covered with a lid. The base of the tank has sides of length  meters and  meters and the lid is a rectangle with sides of length  meters  meters. When full the tank holds 4m3 of water. The material from which the tank is made is of negligible thickness. The […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#9

Question The diagram shows a pyramid OABCP in which the horizontal base OABC is a square of side 10 cm and the vertex P is 10 cm vertically above O. The points D, E, F, G lie on OP, AP, BP, CP respectively and DEFG is a horizontal square of side 6 cm. The height of DEFG above […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#8

Question The diagram shows part of the curve  and the line . The curve and the line meet at points A and B. i.       Find the coordinates of A and B.    ii.       Find the length of the line AB and the coordinates of the mid-point of AB. Solution i.   If two lines (or a line and a curve) […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#4

Question The diagram shows points A, C, B, P on the circumference of a circle with centre O and radius 3 cm. Angle AOC = angle BOC = 2.3 radians.     i.       Find angle AOB in radians, correct to 4 significant figures.    ii. Find the area of the shaded region ACBP, correct to 3 significant figures. Solution i.   We know that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#2

Question Prove the identity Solution We have the equation; We have the relation , therefore, We have the trigonometric identity; We can write it as; Therefore; We have the relation , therefore,

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#7

Question The function f is defined by  for .      i.       Express  in the form of  and hence state the range of .    ii.       Obtain an expression for  and state the domain of . The function g is defined by  for . The function  is such that  and the domain of  is .   iii.       Obtain an expression for . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#1

Question i.        Find the first three terms in the expansion, in ascending powers of .    ii.       Find the coefficient  in the expansion of . Solution i.   Expression for the Binomial expansion of  is: First rewrite the given expression in standard form. In the given case: Hence; ii.   To find the coefficient of   in the expansion of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#5

Question a)   The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum  of the first  terms is zero. Find the value of . b)  A geometric progression, in which all the terms are positive, has common ratio r. The sum of the  first  terms is less than 90% of the sum […]