# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#11

Question The point P(3,5) lies on the curve  .      i.       Find the x-coordinate of the point where the normal to the curve at P intersects the x-axis.    ii.       Find the x-coordinate of each of the stationary points on the curve and determine the nature of  each stationary point, justifying your answers. Solution      i.   The point where […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#10

Question A curve has equation  and it is given that . The point A is the only point  on the curve at which the gradient is −1.      i.       Find the x-coordinate of A.    ii.       Given that the curve also passes through the point (4,10), find the y-coordinate of A, giving  your answer as a fraction. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#9

Question The diagram shows a cuboid OABCDEFG with a horizontal base OABC in which OA = 4 cm and  AB = 15 cm. The height OD of the cuboid is 2 cm. The point X on AB is such that AX = 5 cm and  the point P on DG is such that DP = p cm, where […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#8

Question The functions f and g are defined by  for  for .      i.       Find and simplify an expression for  and state the range of .      ii.       Find an expression for  and find the domain of . Solution      i.   We are given;  for  for . We are required to find expression for ;   We are also […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#7

Question The diagram shows parts of the curves  and , intersecting at points A and  B.      i.       State the coordinates of A.    ii.       Find, showing all necessary working, the area of the shaded region. Solution      i.   It is evident that point A is the intersection point of the two curves given by equations; It is also […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#6

Question      i.       Show that .    ii.       Hence, or otherwise, solve the equation   for . Solution      i.   We have the trigonometric identity; From this we can substitute ; Hence, L.H.S=R.H.S.    ii.   We are required to solve the equation  for . From (i) we know that; Substituting this in the given equation to solve; We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#5

Question The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3rd terms is 30. Find the sum to infinity. Solution From the given information, we can compile following data about Geometric Progression (G.P); Expression for the sum to infinity of the Geometric Progression (G.P) when  or […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#4

Question C is the mid-point of the line joining A(14,−7) to B(−6,3). The line through C perpendicular to AB  crosses the y-axis at D.      i.       Find the equation of the line CD, giving your answer in the form .     ii.       Find the distance AD. Solution i.   We are required to write equation of the line CD. To find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#3

Question In the diagram OCA and ODB are radii of a circle with centre O and radius  cm. Angle  adians. CD and AB are arcs of circles with centre O and radii  cm and  cm respectively. The  perimeter of the shaded region ABDC is 4.4r cm.      i.       Find the value of .    ii.       It is given that the area of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#2

Question Find the term independent of  in the expansion of . Solution Expression for the Binomial expansion of  is: In the given case: Hence;         The term independent of  in the expansion of is .

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#1

Question i.    Express  in the form , where a and b are constants. ii.   Hence, or otherwise, find the set of values of  for which . Solution i.   We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have the algebraic […]