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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

Hits: 3588 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 […]

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

Hits: 667 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 […]

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

Hits: 575 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 […]

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

Hits: 1148   Question The diagram shows part of the curve  and the normal to the curve at the point P(2, 3).  This normal meets the x-axis at Q.      i.       Find the equation of the normal at P.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are required to find the equation of […]

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

Hits: 685   Question Points A and B lie on the curve . Point A has coordinates (4,7) and B is the  stationary point of the curve. The equation of a line L is , where m is a constant.                             i.       In the case where L passes through the mid-point of AB, find the value of m.                           ii.       Find the set of […]

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

Hits: 654   Question A function f is defined by  for .      i.       Find an expression for  and find the point of intersection of the graphs of  and  .    ii.       Sketch, on the same diagram, the graphs of  and , making clear the  relationship between the graphs. Solution i.   We have; We write it as; To find the inverse of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 715   Question The points A(1,1) and B(5,9) lie on the curve .      i.       Show that the equation of the perpendicular bisector of AB is 2y = 13 − x. The perpendicular bisector of AB meets the curve at C and D.    ii.       Find, by calculation, the distance CD, giving your answer in the form  , […]

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

Hits: 571   Question A curve has equation . Find the equation of the tangent to the curve at the  point (4,0). Solution To find the equation of the line either we need coordinates of the two points on the line (Two-Point  form of Equation of Line) or coordinates of one point on the line and slope of […]

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

Hits: 642   Question A(-1,1) and P(a,b) are two points, where a and b are constants. The gradient of AP is 2. (i)        Find an expression for b in terms of a. (ii)      B(10,-1) is a third point such that AP = AB. Calculate the coordinates of the possible positions          […]

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

Hits: 632   Question The line 3y+x=25 is a normal to the curve y= x2 – 5x + k. Find the value of the constant k. Solution If a line  is normal to the curve , then product of their slopes  and  at that point (where line is normal to the curve) is; Therefore, by finding slopes of both the […]

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

Hits: 482   Question Find the coordinates of the points of intersection of the curve  with the curve . Solution If two lines (or a line and a curve) intersect each other at a point then that point lies on both lines i.e.  coordinates of that point have same values on both lines (or on the line and the […]

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

Hits: 655   Question The equation of a curve is  .       i.       Find the coordinates of the stationary point of the curve.    ii.       Find an expression for  and hence, or otherwise, determine the nature of the                                 stationary point.   iii.       Find the values of x […]

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

Hits: 603   Question A curve has equation .      i.       Find the equation of the tangent to the curve at the point where the curve crosses the x-axis.     ii.       A point moves along the curve in such a way that the x-coordinate is increasing at a constant  rate of 0.04 units per second. Find the rate of change […]

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

Hits: 651   Question The point A has coordinates (-2,6).  The equation of the perpendicular bisector of the line AB is 2y=3x+5.      i.       Find the equation of AB.    ii.       Find the coordinates of B. Solution      i.   We are required to find the equation of line AB. To find the equation of the line either 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#10

Hits: 485   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 […]

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

Hits: 492   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 […]

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

Hits: 527   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 . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#10

Hits: 818 Question The diagram shows part of the curve .      i.       Find the equation of the normal to the curve at the point where x=1 in the form ,  where m and c are constants. The shaded region is bounded by the curve, the coordinate axes and the line x=1.    ii.       Find, showing all necessary working, the volume obtained […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#5

Hits: 837   Question The equation of a curve is .      i.       Sketch the graph of  for , stating the coordinates of the point of  intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of  and  respectively.    ii.       Find the length of PQ correct to 1 decimal place. The line through […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 462   Question A curve is such that  , where a is a positive constant. The point A(a2, 3) lies on the  curve. Find, in terms of a,      i.       the equation of the tangent to the curve at A, simplifying your answer,    ii.       the equation of the curve.  It is now given that B(16,8) also lies on the curve. […]