# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#11

Question The diagram shows part of the curve and the minimum point M. i.Find the expressions for and ii.Find the coordinates of M. The shaded region is bounded by the curve, the y-axis and the line through M parallel to the x-axis. iii.Find, showing all necessary working, the area of the shaded region. Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#10

Question a.In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five  terms. The first term is . i.Show that the common difference of the progression is . ii.Given that the tenth term is 36 more than the fourth term, find the value of . b.The […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#9

Question The curve C1 has equation y = x2− 4x + 7. The curve C2 has equation y2 = 4x + k, where k is a constant. The tangent to C1 at the point where x = 3 is also the tangent to C2 at the point P. Find the  value of k and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#8

Question The position vectors of points A and B, relative to an origin O, are given by and Where  is a constant. i.Find the value of  for which the angle AOB=90o. ii.Find the values of  for which the lengths of OA and OB are equal. The point C is such that . iii.In the case […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#7

Question The functions f and g are defined by , , i.Obtain expressions for and , stating the value of x for which is not defined. ii.Solve the equation Solution i. We are given;  for  for We have; We write them as; To find the inverse of a given function we need to write it […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#6

Question The equation of a curve is and the equation of a line is . i.State the smallest and largest values of y for both the curve and the line for . ii.Sketch, on the same diagram, the graphs of and for . iii.State the number of solutions of the equation for . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#5

Question The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the  circumference and angle AOC = radians. The perimeter of sector BOC is twice the perimeter of  sector AOC. Find the value of correct to 2 significant figures. Solution We are required to find the value […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#4

Question Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants. A curve is such that . The point P (2,9) lies on the curve.     i.       Show that a2 +b2 has a constant value for all values of x.    […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#3

Question A curve is such that . The point P (2,9) lies on the curve. i.  A point moves on the curve in such a way that the x-coordinate is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the y-coordinate when the point is at P. ii.  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#2

Question Two points A and B have coordinates (1, 3) and (9, −1), respectively. The perpendicular bisector of  AB intersects the y-axis at the point C. Find the coordinates of C. Solution Coordinates of point C which is y-intercept of the perpendicular bisector of AB. The point at which curve (or line) intercepts y-axis, the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#1

Question Find the coefficient of x in the expansion of .   Solution We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: […]