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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

Hits: 183 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 […]

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

Hits: 187 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      […]

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

Hits: 213 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 ;   […]

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

Hits: 197 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 […]

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

Hits: 302 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 […]

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

Hits: 221 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) […]

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

Hits: 145 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. […]

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

Hits: 259 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 […]

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

Hits: 104 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 […]