Hits: 1724

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#11

Hits: 1724 Question Triangle ABC has vertices at A(−2,−1), B(4,6) and C(6,−3). i.       Show that triangle ABC is isosceles and find the exact area of this triangle. ii.    The point D is the point on AB such that CD is perpendicular to AB. Calculate the x-coordinate of  D. Solution      i.   An isosceles triangle is a triangle with (at least) two […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#10

Hits: 1089 Question The function f is such that  for . The function g is such that  for      , where a, b and q are constants. The function fg is such that  for . i.       Find the values of a and b. ii.       Find the greatest possible value of q. It is now given that . iii.       Find the range of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#9

Hits: 510 Question The position vectors of points A, B and C relative to an origin O are given by and where p is a constant. i.       Find the value of p for which the lengths of AB and CB are equal. ii.       For the case where p=1, use a scalar product to find angle ABC. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#8

Hits: 592 Question i.       Show that  can be written as a quadratic equation in  and hence solve the equation  for .    ii.       Find the solutions to the equation  for . Solution i.   We have the expression; We know that ; therefore, We have the trigonometric identity; It can be rearranged to; Therefore; To solve this equation for , we can substitute […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#7

Hits: 1448 Question The point P(x,y) is moving along the curve  in such a way that the rate of change  of y is constant. Find the values of x at the points at which the rate of change of x is equal to half the rate of change of y. Solution We are required to find values of x […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#6

Hits: 1991 Question The diagram shows triangle ABC where AB=5cm, AC=4cm and BC=3cm. Three circles with centres  at A, B and C have radii 3 cm, 2 cm and 1 cm respectively. The circles touch each other at  points E, F and G, lying on AB, AC and BC respectively. Find the area of the shaded region EFG. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#5

Hits: 517 Question A curve has equation . Find the values of x at which the curve has a stationary  point and determine the nature of each stationary point, justifying your answers. Solution Coordinates of stationary point on the curve  can be found from the derivative of equation of the  curve by equating it with ZERO. This results in […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#4

Hits: 2352 Question The 1st, 3rd and 13th terms of an arithmetic progression are also the 1st, 2nd and 3rd terms  respectively of a geometric progression. The first term of each progression is 3. Find the common  difference of the arithmetic progression and the common ratio of the geometric progression. Solution From the given information, we can compile following data […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#3

Hits: 694 Question A curve is such that  and passes through the point P(1,9). The gradient of the curve at P is 2. i.       Find the value of the constant k. ii.       Find the equation of the curve. Solution i.   We are given that; Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#2

Hits: 558 Question The diagram shows part of the curve  and the point P(2,3) lying on the curve. Find,  showing all necessary working, the volume obtained when the shaded region is rotated through  360o about the x-axis. Solution Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the x-axis is; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#1

Hits: 550 Question Find the coefficient of  in the expansion of .   Solution We are given expression as; Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the terms with  i.e. : we can  equate; Now we can find the term with; Substituting ; Hence the coefficient of the term containing […]