# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#10

Question The diagram shows part of the curve . The curve intersects the x-axis at A. The normal to the curve at A intersects the y-axis at B. i.       Obtain expressions for  and ii.    Find the coordinates of B. iii. Find, showing all necessary working, the area of the shaded region. Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#9

Question Functions f and g are defined by;  for   for Where  is a constant.     i.      Find the value of for which the line is a tangent to the curve .   ii.     In the case where , find the set of values of for which .  iii.     In the case where , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#8

Question a)   Over a 21-day period an athlete prepares for a marathon by increasing the distance she runs each  day by 1.2 km. On the first day she runs 13 km. (i)          Find the distance she runs on the last day of the 21-day period. (ii)        Find the total distance […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#7

Question The diagram shows a three-dimensional shape OABCDEFG. The base OABC and the upper  surface DEFG are identical horizontal rectangles. The parallelograms OAED and CBFG both lie in  vertical planes. Points P and Q are the mid-points of OD and GF respectively. Unit vectors  and  are parallel to  and  respectively and the unit vector is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#6

Question a)   Given that x > 0, find the two smallest values of x, in radians, for which . Show  all necessary working. b)  The function is defined for . i.     Express f(x) in the form , where a and b are constants. ii.      Find the range of f. Solution a)     We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#5

Question The diagram shows a solid cone which has a slant height of 15 cm and a vertical height of h cm. i.Show that the volume, V cm3, of the cone is given by . [The volume of a cone of radius and vertical height  is .] ii.Given that can vary, find the value of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#4

Question The diagram shows a circle with centre O and radius cm. Points A and B lie on the circle and  angle radians. The tangents to the circle at A and B meet at T.     i.      Express the perimeter of the shaded region in terms of  and .   ii.      In the case where […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#3

Question A curve is such that  , where  is a constant. The points P(1, −1) and Q(4, 4) lie on the curve.  Find the equation of the curve. Solution We are given that; We can find equation of the curve from its derivative through integration; Therefore; Rule for integration of  is: If a point  lies […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#2

Question The point M is the mid-point of the line joining the points (3, 7) and (−1, 1). Find the equation of the  line through M which is parallel to the line .   Solution We are required to find the equation of the line which passes through the point M and is parallel  to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#1

Question The coefficient of  in the expansion of  is 3. Find the value of the constant a. Solution i.   First, we expand . Expression for the Binomial expansion of  is: In the given case: Hence;       Now can we find the coefficient of in the expansion of . We write only terms […]