# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#11

Question The diagram shows the curve  and points A(1,0) and B(5,2) lying on the curve. i.       Find the equation of the line AB, giving your answer in the form y=mx+c.    ii.       Find, showing all necessary working, the equation of the tangent to the curve which is parallel to AB.   iii.       Find the perpendicular distance between the line AB and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#10

Question A curve has equation y=f(x) and it is given that , where a and b are positive  constants. i.       Find, in terms of a and b, the non-zero value of x for which the curve has a stationary point and  determine, showing all necessary working, the nature of the stationary point.    ii.       It is now given that the curve has […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#9

Question Relative to an origin O, the position vectors of points A, B and C are given by and A fourth point, D, is such that the magnitudes ,  and  are the first, second and third  terms respectively of a geometric progression.  i.       Find the magnitudes ,  and . ii.       Given that D is a point lying on the line […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#8

Question The diagram shows parts of the graphs of  and  intersecting at points A and  B.      i.       Find by calculation the x-coordinates of A and B.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are required to find the x-coordinates of points A and B which are intersection points of a line  and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#7

Question The diagram shows a rectangle ABCD in which AB = 5 units and BC = 3 units. Point P lies on DC  and AP is an arc of a circle with centre B. Point Q lies on DC and AQ is an arc of a circle with centre  D.      i.       Show that angle ABP = 0.6435 radians, correct […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#6

Question The functions f and g are defined by   for   for      i.       Find an expression for .    ii.       Solve the equation . Solution i.   We are given the function; We write it as; To find the inverse of a given function  we need to write it in terms of  rather than in terms of . As demonstrated in (i), […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#5

Question      i.       Show that the equation  may be expressed as     ii.       Hence solve the equation   for . Solution i.   We are given the equation; We have the trigonometric identity; From this we can substitute  in above equation; ii.   We are required to solve the equation   for . From (i) we know that given equation can be written as; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#4

Question The function f is such that  for , where k is a constant. Find the  largest value of k for which f is a decreasing function. Solution To test whether a function  is increasing or decreasing at a particular point , we  take derivative of a function at that point. If  , the function  is increasing. If  , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#3

Question      i.       Find the term independent of x in the expansion of .    ii.       Find the value of a for which there is no term independent of x in the expansion of Solution i.   Expression for the general term in the Binomial expansion of  is: For the given case: Hence; Since we are looking for the coefficient […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#2

Question Find the set of values of a for which the curve  and the straight line  meet at two  distinct points. Solution We need to find the equation that satisfies the x-coordinates of the points of intersection of given  curve and line. If two lines (or a line and a curve) intersect each other at a point then that point […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#1

Question An arithmetic progression has first term −12 and common difference 6. The sum of the first n terms  exceeds 3000. Calculate the least possible value of n. Solution We can compile following data from the given information for Arithmetic Progression (A.P) ; Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is: Therefore for the […]