# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#10

Question The diagram shows the curve  defined for x>0. The curve has a minimum point at A and  crosses the x-axis at B and C. It is given that  and that the curve passes through the  point . i.       Find the x-coordinate of A. ii.       Find . iii.       Find the x-coordinates of B and C. iv.       Find, showing all necessary working, the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#9

Question The point A(2,2) lies on the curve .                     i.       Find the equation of the tangent to the curve at A. The normal to the curve at A intersects the curve again at B.                   ii.       Find the coordinates of B. The tangents at A and B intersect each other at C.                  iii.        Find the coordinates of C. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#8

Question The functions f and g are defined for  by i.       Show that  and obtain an unsimplified expression for . ii.       Find an expression for  and determine the domain of . iii.       Solve the equation . Solution      i.   We are given the functions; We can rewrite these as; First we find . Next we find .    ii.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#7

Question The function f is defined for  by .                     i.       Find  and . The first, second and third terms of a geometric progression are respectively ,   and .                   ii.       Find the value of the constant k. Solution      i.   We are given the function; Therefore; Rule for differentiation of  is: Therefore; Second derivative is the derivative of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#6

Question Relative to an origin , the position vectors of points A and B are given by and i.       Use a scalar product to find angle OAB. ii.       Find the area of triangle OAB. Solution      i.   It is evident that angle OAB is between  and . We are given that; and Next, we need scalar/dot product of  and . However, first we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#4

Question In the diagram, AB=AC=8 cm and angle  radians. The circular arc BC has centre A, the  circular arc CD has centre B and ABD is a straight line.                     i.       Show that angle  radians.                   ii.       Find the perimeter of the shaded region. Solution      i.   It is evident from the diagram that; Therefore; We are given that ABD is a straight line. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#3

Question The diagram shows a water container in the form of an inverted pyramid, which is such that when  the height of the water level is h cm the surface of the water is a square of side  cm.      i.       Express the volume of water in the container in terms of h. [The volume of a pyramid having […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#2

Question In the expansion of , the coefficient of x is 5. Find the value of the constant a. 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 ; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#1

Question Find the set of values of k for which the equation  has distinct real roots. Solution We are given the equation; Standard form of quadratic equation is; Expression for discriminant of a quadratic equation is; If   ; Quadratic equation has two distinct real roots. If   ; Quadratic equation has no real roots. If   ; Quadratic equation has one […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#5

Question The diagram shows the graphs of  and  for . The graphs intersect at  points A and B. i.       Find by calculation the x-coordinate of A. ii.       Find by calculation the coordinates of B. Solution      i.   We are required to find the x-coordinate of point A which is point of intersection of the two given  curves. If two lines (or […]