# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#8

Question The diagram shows the curve with equation The curve crosses the x-axis at the point P and has a minimum point M.      i. Find the gradient of the curve at the point P.    ii. Find the exact coordinates of the point M. Solution      i.   We are required to find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#7

Question The parametric equations of a curve are      i.       Find  and use division to show that  can be written in the form , where a and b are  constants to be found.    ii.       The straight line x − 2y + 9 = 0 is the normal to the curve at the point P. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#6

Question The diagram shows the curve  for . The shaded region is bounded by the  curve and the lines , and y = 0.      i.       Use the trapezium rule with two intervals to find an approximation to the area of the shaded  region, giving your answer correct to 3 significant figures.     ii.       Find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#5

Question i.       Express  in the form , where  and , giving the  value of  correct to 2 decimal places.    ii.       Hence solve the equation for . Solution      i.   We are given the expression; We are required to write it in the form; If  and are positive, then; can be written in the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#4

Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Determine the value of correct to 2 decimal places, giving the result of each iteration to 4  decimal places.    ii.       Determine the exact value of . Solution      i.   If we can write the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#3

Question Given that find the value of the constant a correct to 3 significant figures. Solution     We are given that; Rule for integration of , or ; Taking logarithm of both sides;  for any

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#2

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#1

Question Given that 5x = 34y, use logarithms to show that y = mx and find the value of the  constant m correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule; We compare this equation with; Therefore;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#1

Question Solve the equation ln(3x + 1) – ln(x + 2) = 1, giving your answer in terms of e. Solution We are given; Division Rule; We can write it as; Taking anti-logarithm of both sides; For any ;