Hits: 749

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 749 Question i.       The diagram shows the line  and the curve , which intersect at the points A and B. Find a.   the x-coordinates of A and B, b.   the equation of the tangent to the curve at B, c.   the acute angle, in degrees correct to 1 decimal place, between this tangent and the line . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 248 Question The diagram shows a rectangle . The point  is  and  is . The diagonal  is parallel to the x-axis.     i.       Explain why the y-coordinate of  is 6. The x-coordinate of  is .    ii.       Express the gradients of  and  in terms of .   iii.       Calculate the x-coordinates of  and .   iv.       Calculate the area of the rectangle . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 255 Question A curve is such that , where k is a constant.     i.       Given that the tangents to the curve at the points where  and  are perpendicular, find the value of .    ii.       Given also that the curve passes through the point (4, 9), find the equation of the curve. Solution      i.   If two lines […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#11

Hits: 1602 Question The diagram shows the curve  for . The curve has a maximum point at A and a minimum point on the x-axis at B. The normal to the curve at C (2, 2) meets the normal to the curve at B at the point D. i.       Find the coordinates of A and B.    ii.       Find the equation of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#8

Hits: 1213 Question The diagram shows points A, B and C lying on the line . The point A lies on the y-axis and AB = BC. The line from D(10, −3) to B is perpendicular to AC. Calculate the coordinates of B and C. Solution      i.   First we find the coordinates of point B. We recognize […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#2

Hits: 764 Question Find the set of values of  for which the line  intersects the curve  at two distinct points. 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 […]