# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#11

Question     i.      Express in the form of where a, b and c are constants. The function f is defined by  for .    ii.       State the largest value of the constant k for which f is a one-one function.  iii.     For this value of k find an expression for and state the domain of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#10

Question The diagram shows part of the curve  and the lines  and . The curve and the line  intersect at point A. i.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 3600 about the x-axis.    ii.       Find the equation of the normal to the curve at A, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#9

Question A curve has equation  and a line has equation , where  is a constant. i.Show that, for all values of k, the curve and the line meet. ii.State the value of k for which the line is a tangent to the curve and find the coordinates of the  point where the line touches the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#8

Question A curve passes through (0, 11) and has an equation for which , where a and b are  constants.      i.      Find the equation of the curve in terms of a and b.    ii.       It is now given that the curve has a stationary point at (2, 3). Find the values […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#7

Question i.       Show that   ii.       Hence, showing all necessary working, solve the equation For . Solution i.   We are given the expression;   We have the algebraic identity; We have the trigonometric identity;               Since ; We can write; Therefore; ii.   We are required to solve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#6

Question The diagram shows a solid figure OABCDEFG with a horizontal rectangular base OABC in which  OA = 8 units and AB = 6 units. The rectangle DEFG lies in a horizontal plane and is such that D is 7  units vertically above O and DE is parallel to OA. The sides DE and DG […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#5

Question In an arithmetic progression the first term is and the common difference is 3. The nth term is 94  and the sum of the first  terms is 1420. Find  and . Solution We can compile following data from the given information for Arithmetic Progression (A.P) ; First we consider the nth term which is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#4

Question Two points A and B have coordinates  and respectively. The line BC is perpendicular to  AB and intersects the x-axis at C.     i.       Find the equation of BC and the x-coordinate of C.    ii.       Find the distance AC, giving your answer correct to 3 decimal places. Solution i.   We are required […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#3

Question The diagram shows an arc BC of a circle with centre A and radius 5 cm. The length of the arc BC is  4 cm. The point D is such that the line BD is perpendicular to BA and DC is parallel to BA.      i.       Find angle BAC in radians.    ii.       Find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#2

Question The function f is defined by  for . Determine, showing all necessary working, whether f is an increasing function, a decreasing  function or neither. Solution We are given function;   We are required to find whether is an increasing function, decreasing function or neither. To test whether a function is increasing or decreasing at […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#1

Question Find the coefficient of  in the expansion of . Solution We are required to expand; We can write it in standard form; Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the coefficient of the term : we can equate; Finally substituting […]