Hits: 156

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 156 Question i.       Show that   ii.       Hence, showing all necessary working, solve the equation For . Solution i.   We are given the expression;   We have the algebraic identity; We have the trigonometric identity;               Since ; We can write; Therefore; ii.   We are required […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 349 Question The diagram shows an arc BC of a circle with centre A and radius 5 cm. The length of the arc BC is  4 cm. The point D is such that the line BD is perpendicular to BA and DC is parallel to BA.      i.       Find angle BAC in radians.    […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 372 Question The diagram shows a triangle ABC in which BC = 20 cm and angle ABC = 90o. The perpendicular  from B to AC meets AC at D and AD = 9 cm. Angle BCA = .     i.      By expressing the length of BD in terms of in each of the triangles […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 263 Question The functions f and g are defined by  for  ,  for      i.      Solve the equation .   ii.     Sketch the graph of . Solution i.   We are given;  for  for We are required to solve equation ; To solve this equation for , we can substitute . Hence, Since given […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 632 Question The diagram shows a triangle OAB in which angle ABO is a right angle, angle AOB =  radians  and AB = 5 cm. The arc BC is part of a circle with centre A and meets OA at C. The arc CD is part  of a circle with centre O and meets […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 208 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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#6

Hits: 865 Question The diagram shows a sector POQ of a circle of radius 10 cm and centre O. Angle POQ is 2.2  radians. QR is an arc of a circle with centre P and POR is a straight line.     i.       Show that the length of PQ is 17.8 cm, correct to 3 significant […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#5

Hits: 229 Question a.   Express the equation  as a quadratic equation in  and hence solve the equation for . b.   The diagram shows part of the graph of , where  and  are constants and . Find the value of  and the value of . Solution a.     We are required to solve this quadratic equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#4

Hits: 260 Question A straight line cuts the positive x-axis at A and the positive y-axis at B(0, 2). Angle radians, where O is the origin.      i.       Find the exact value of the x-coordinate of A.    ii.       Find the equation of the perpendicular bisector of AB, giving your answer in the form y […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#7

Hits: 447 Question a.                         i.       Express  in the form , where  and are constants to be  found.       ii.       Hence, or otherwise, and showing all necessary working, solve the equation  For .   b.     The diagram shows the graphs of  and  for . The  graphs intersect at the points A […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#5

Hits: 1035 Question The diagram shows a triangle OAB in which angle OAB = 90o and OA = 5 cm. The  arc AC is part of a circle with centre O. The arc has length 6 cm and it meets OB at  C. Find the area of the shaded region. Solution It is evident from […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#10

Hits: 745 Question     i.       Solve the equation  for .    ii.       Sketch, on the same diagram, the graphs of  and for  .   iii.       Use your answers to parts (i) and (ii) to find the set of values of x for   for which . Solution      i.   We have the equation; We know that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#6

Hits: 2226 Question The diagram shows points A and B on a circle with centre O and radius r. The  tangents to the circle at A and B meet at T. The shaded region is bounded by the  minor arc AB and the lines AT and BT. Angle AOB is  radians.      i.       In the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#4

Hits: 773 Question The function f, is such that   for . It is given that  and .                             i.       Find the values of the constants a and b.                           ii.       Find the set of values of k for which the equation f(x) = k has no  solution. Solution i.   We are given the function […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#6

Hits: 1499 Question The diagram shows a circle with centre O and radius r cm. The points A and B lie on  the circle and AT is a tangent to the circle. Angle radians and OBT is a  straight line.      i.       Express the area of the shaded region in terms of r and . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#4

Hits: 617 Question i.Prove the identity    ii.Hence solve the equation  for . Solution i.       We have the trigonometric identity;         ii. We have the equation;   From (i) we know that left hand side of given equation can be written as;      Therefore;         […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 89 Question     i.       Use the factor theorem to show that (2x+3) is a factor of    ii.       Show that the equation  can be expressed as   iii.       Solve the equation For . Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 89   Question The diagram shows the curve with equation for values of x such that . Find the x-coordinate of the stationary point M, giving your answer correct to 3  significant figures. Solution We are required to find the x-coordinate of stationary point M. A stationary point on the curve is the point […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 139   Question The diagram shows the curve with equation  for . At  the points P and Q on the curve, the gradient of the curve is 3.      i.    Find an expression for .    ii.     By first expressing  in the form , where R > 0 and ,  find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 118 Question The diagram shows the curve  for . The region R is  bounded by the curve, the axes and the line .      i.       Use the trapezium rule with two intervals to find an approximation to the area of  R, giving your answer correct to 3 significant figures.    ii.       The […]