Hits: 54

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 26 Question Relative to an origin O, the position vectors of points A, B and X are given by and i.Find and show that AXB is a straight line. The position vector of point C is given by . ii.Show that CX is perpendicular to AX. iii.Find the area of triangle ABC. Solution i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 24 Question The first, second and third terms of a geometric progression are ,  and  respectively. (i)       Show that  satisfies the equation 7k2 − 48k + 36 = 0. (i)       Find, showing all necessary working, the exact values of the common ratio corresponding to  each of the possible values of k. (ii) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 24 Question A function  is defined for  and is such that .     i.      Find the set of values of  for which f is decreasing.   ii.      It is now given that . Find . Solution      i.   We are given derivative of the function as; We are also given that it is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 44 Question     i.      Show that the equation  can be expressed as Where   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; Let ;      ii.   We are required to solve the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 41 Question A line has equation  and a curve has equation , where k is a constant. i.Find the set of values of  for which the line and curve meet at two distinct points. i.For each of two particular values of , the line is a tangent to the curve. Show that these two […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 15 Question The dimensions of a cuboid are x cm, 2x cm and 4x cm, as shown in the diagram. i.Show that the surface area S cm2 and the volume V cm3 are connected by the relation  ii.When the volume of the cuboid is 1000 cm3 the surface area is increasing at 2 cm2 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 26 Question The diagram shows a semicircle ACB with centre O and radius . Arc OC is part of a circle with  centre A. (i)Express angle CAO in radians in terms of . (ii)Find the area of the shaded region in terms of ,  and , simplifying your answer. Solution (i)   We are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 8 Question The equation of a curve is . The curve has no stationary points in the interval  . Find the least possible value of and the greatest possible value of . Solution We are given; We are given that curve has no stationary point. A stationary point on the curve is the point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 12 Question The function g is defined by  for . By first completing the square, find an  expression for and state the domain of . Solution We are given that; We use method of “completing square” to obtain the desired form. We complete the square for the  terms which involve . We have the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#1

Hits: 37 Question (i)          Expand  in ascending powers of y as far as the term in y2. (ii)       In the expansion of  the coefficient of x2 is 48. Find the value of the positive  constant . Solution i.   We are required to expand . Expression for the Binomial expansion of  is: In […]

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

Hits: 72 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 […]

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

Hits: 41 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 […]

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

Hits: 25 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 […]

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

Hits: 21 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 […]

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

Hits: 37 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)   […]

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

Hits: 35 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 […]

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

Hits: 19 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 […]

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

Hits: 24 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 […]