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#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#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 | (P1-9709/12) | Q#10

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 the normal […]

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

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 values 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

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 a given […]

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

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 , where p and […]

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

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 the line […]

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

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 of P. […]

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

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 line and […]

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

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 curve). Therefore, […]

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

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 at which […]

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

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 of 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#2

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 need coordinates […]

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#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 | May-Jun | (P1-9709/11) | Q#10

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 when this […]

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

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 P and […]

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 […]

Coordinate Geometry (CIE-P1-2017) Archives — O/A Level Solutions