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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#7

Hits: 928 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 | (P1-9709/12) | Q#4

Hits: 575   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#5

Hits: 518   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: 365   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 | (P1-9709/12) | Q#4

Hits: 445   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 | Feb-Mar | (P1-9709/12) | Q#4

Hits: 338   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: 487   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 2016 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 327   Question The diagram shows a major arc AB of a circle with centre O and radius 6 cm. Points C and D on OA  and OB respectively are such that the line AB is a tangent at E to the arc CED of a smaller  circle also with centre O. Angle COD = 1.8 radians. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 457 Question The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. The part DAB is a segment of a circle with centre O and radius 10 cm. Angle BOD is 1.2 radians.     i.       Show that the radius of the semicircle is 5.646 cm, correct to 3 decimal places.    ii.       Find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 348 Question In the diagram OCA and ODB are radii of a circle with centre O and radius  cm. Angle  adians. CD and AB are arcs of circles with centre O and radii  cm and  cm respectively. The  perimeter of the shaded region ABDC is 4.4r cm.      i.       Find the value of .    ii.       It is given that the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#6

Hits: 352 Question The diagram shows triangle ABC where AB=5cm, AC=4cm and BC=3cm. Three circles with centres  at A, B and C have radii 3 cm, 2 cm and 1 cm respectively. The circles touch each other at  points E, F and G, lying on AB, AC and BC respectively. Find the area of the shaded region EFG. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#6

Hits: 386 Question The diagram shows a circle with radius r cm and centre O. The line PT is the tangent to the circle at  P and angle  radians. The line OT meets the circle at Q.      i.       Express the perimeter of the shaded region PQT in terms of r and .   ii.       In the case where  and , find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#7

Hits: 485 Question In the diagram, AOB is a quarter circle with centre O and radius r. The point C lies on the arc AB  and the point D lies on OB. The line CD is parallel to AO and angle  radians.      i.       Express the perimeter of the shaded region in terms of r,  and .    ii.       For […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#9

Hits: 566 Question a.     Figure 1 In Fig. 1, OAB is a sector of a circle with centre O and radius r. AX is the tangent at A to the arc AB and angle .      i.       Show that angle .    ii.       Find the area of the shaded segment in terms of r and .   b.     […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 284 Question The diagram shows a metal plate OABCDEF consisting of 3 sectors, each with centre O. The radius of sector COD is 2r and angle COD is  radians. The radius of each of the sectors BOA and FOE is  r, and AOED and CBOF are straight lines. i. Show that the area of the metal plate is . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 336 Question The diagram shows a metal plate OABC, consisting of a right-angled triangle OAB and a sector  OBC of a circle with centre O. Angle AOB = 0.6 radians, OA = 6 cm and OA is perpendicular to OC.       i.       Show that the length of OB is 7.270 cm, correct to 3 decimal places.    ii.       Find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 631 Question The diagram shows a circle with centre A and radius r. Diameters CAD and BAE are perpendicular  to each other. A larger circle has centre B and passes through C and D.      i.       Show that the radius of the larger circle is .    ii.       Find the area of the shaded region in terms of . Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#11

Hits: 564 Question In the diagram, OAB is a sector of a circle with centre O and radius r. The point C on OB is such  that angle ACO is a right angle. Angle AOB is  radians and is such that AC divides the sector into  two regions of equal area.     i.       Show that   It […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#2

Hits: 875   Question In the diagram, AYB is a semicircle with AB as diameter and OAXB is a sector of a circle with centre  O and radius r. Angle AOB = 2 radians. Find an expression, in terms of r and , for the  area of the shaded region. Solution It is evident from the diagram that; First we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#5

Hits: 440  Question A piece of wire of length 24 cm is bent to form the perimeter of a sector of a circle of radius r cm.      i.       Show that the area of the sector, A cm2, is given by .    ii.       Express A in the form , where a and b are constants.   iii.       Given that r can […]