Hits: 5130

# 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#7

Hits: 5130 Question The diagram shows a rectangle ABCD in which AB = 5 units and BC = 3 units. Point P lies on DC  and AP is an arc of a circle with centre B. Point Q lies on DC and AQ is an arc of a circle with centre  D.      i.       Show that angle ABP = […]

# 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#5

Hits: 870 Question      i.       Show that the equation  may be expressed as     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; ii.   We are required to solve the equation   for . From (i) we know that given equation can be […]

# 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#6

Hits: 1722   Question a.   The function f, defined by   for , is such that  and .                             i.       Find the values of the constants a and b.                           ii.       Evaluate . b.   The function g is defined by  for for . The range of g is given by  . Find the values of the constants c and d. Solution a.   i.   We […]

# 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#5

Hits: 1209   Question      i.       Show that the equation  can be expressed as    ii.       Hence solve the equation  for . Solution      i.   We are given equation as; Utilising , we can write the given equation as; We have the trigonometric identity; It can be arranged to get; Substituting in the above equation obtained.    ii. […]

# 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#4

Hits: 6306   Question The diagram shows a semicircle with centre O and radius 6 cm. The radius OC is perpendicular to  the diameter AB. The point D lies on AB, and DC is an arc of a circle with centre B.      i.       Calculate the length of the arc DC.    ii.       Find the value of giving your answer […]

# 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#7

Hits: 3727   Question a.   The diagram shows part of the graph of y=a+b sin x. Find the values of the constants a and b. b.                         i.       Show that the equation may be expressed as .       ii.       Hence solve the equation for . Solution a.   We are given graph of the equation; y=a+b sin […]

# 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#5

Hits: 3949   Question The diagram shows an isosceles triangle ABC in which AC = 16 cm and AB = BC = 10 cm. The circular arcs BE and BD have centres at A and C respectively, where D and E lie on AC.      i.       Show that angle BAC = 0.6435 radians, correct to 4 decimal places.    […]

# 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#7

Hits: 3711   Question The diagram shows two circles with centres A and B having radii 8 cm and 10 cm respectively. The  two circles intersect at C and D where CAD is a straight line and AB is perpendicular to CD. (i)          Find angle ABC in radians. (ii)        Find the area of the shaded region. Solution (i)   It is evident from […]

# 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#5

Hits: 714   Question (i)          Show that the equation  may be expressed as . (ii)        Hence solve the equation  for 0o < < 180o. Solution (i)   We are given that; Utilizing ; (ii)   We are required to solve the equation  for 0o < < 180o. From (i) we know that given equation can be written as; Now we have two options. Using […]

# 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#10

Hits: 1837   Question The function f is defined by , for .     i.       Solve the equation , giving your answer correct to 1 decimal place.    ii.       Find an expression for  and find the domain of .   iii.       Sketch, on the same diagram, the graphs of y=f(x) and . Solution      i.   We are given the function as; We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#4

Hits: 6036   Question The diagram shows a circle with radius r cm and centre O. Points A and B lie on the circle and  ABCD is a rectangle. Angle AOB = 2 radians and  cm.     i.       Express the perimeter of the shaded region in terms of r and .    ii.       In the case where  and , find the area 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#3

Hits: 1673   Question      i.       Prove the identity .    ii.       Hence solve the equation  ,for . Solution      i.   Utilizing ; We have the trigonometric identity; We can write from this identity; Therefore; We have algebraic identity; Therefore;    ii.   We are required to solve the equation  ,for . From (i) we have found that given equation can […]

# 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#4

Hits: 2758   Question In the diagram, AB=AC=8 cm and angle  radians. The circular arc BC has centre A, the  circular arc CD has centre B and ABD is a straight line.                     i.       Show that angle  radians.                   ii.       Find the perimeter of the shaded region. Solution      i.   It is evident from the diagram that; Therefore; We are given that ABD is a […]

# 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#8

Hits: 3421   Question In the diagram, OAXB is a sector of a circle with centre O and radius 10 cm. The length of the chord  AB is 12 cm. The line OX passes through M, the mid-point of AB, and OX is perpendicular to  AB. The shaded region is bounded by the chord AB and by the […]

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

Hits: 1662   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 2017 | May-Jun | (P1-9709/11) | Q#3

Hits: 1181   Question i.       Prove the identity      ii.       Hence solve the equation  for .   Solution      i.   We have the trigonometric identity; We can write from this identity; Therefore;    ii.   We have the equation; From (i) we know that left hand side of given equation can be written as; Therefore; Using calculator […]

# 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

Hits: 1463 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 […]