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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 240   Question The diagram shows part of the curve , defined for .      i.       Find, showing all necessary working, the area of the shaded region.    ii.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 360O about the x-axis.   iii.       Find, showing all necessary working, the volume obtained when the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 189   Question Functions f and g are defined for x > 3 by;      i.       Find and simplify an expression for gg(x).    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation .  Solution      i.   We are given that; It can be written as; Therefore for ;    ii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 316   Question a.   Relative to an origin O, the position vectors of two points P and Q are p and q respectively. The  point R is such that PQR is a straight line with Q the mid-point of PR. Find the position vector of R in  terms of p and q, simplifying your answer. b.   The vector […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 461   Question a.   The diagram shows part of the graph of y=a+b sin x. Find the values of the constants a and b. b.                         i.       Show that the equation may be expressed as .       ii.       Hence solve the equation for . Solution a.   We are given graph of the equation; y=a+b sin […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 211   Question The points A(1,1) and B(5,9) lie on the curve .      i.       Show that the equation of the perpendicular bisector of AB is 2y = 13 − x. The perpendicular bisector of AB meets the curve at C and D.    ii.       Find, by calculation, the distance CD, giving your answer in the form  , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 619   Question The diagram shows an isosceles triangle ABC in which AC = 16 cm and AB = BC = 10 cm. The circular arcs BE and BD have centres at A and C respectively, where D and E lie on AC.      i.       Show that angle BAC = 0.6435 radians, correct to 4 decimal places.    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 189   Question Machines in a factory make cardboard cones of base radius r cm and vertical height h cm. The volume, V cm3, of such a cone is given by . The machines produce cones for which h+r=18.      i.       Show that .    ii.       Given that r can vary, find the non-zero value of r for which V […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 476   Question a.   A geometric progression has first term 3a and common ratio r. A second geometric progression  has first term a and common ratio −2r. The two progressions have the same sum to infinity. Find the  value of r. b.   The first two terms of an arithmetic progression are 15 and 19 respectively. The first […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 196   Question A function f is defined by  for . It is given that f is an increasing  function. Find the largest possible value of the constant a. Solution We are given that function f is increasing function. To test whether a function  is increasing or decreasing at a particular point , we  take derivative of a function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#1

Hits: 241   Question A curve has equation . Find the equation of the tangent to the curve at the  point (4,0). Solution To find the equation of the line either we need coordinates of the two points on the line (Two-Point  form of Equation of Line) or coordinates of one point on the line and slope of […]