Hits: 66

# 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

Hits: 66 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 […]

# 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

Hits: 60 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 […]

# 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

Hits: 68 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.     […]

# 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

Hits: 68 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 […]

# 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

Hits: 58 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 […]

# 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

Hits: 43 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

Hits: 55   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 […]

# 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

Hits: 60 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

Hits: 102   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 ;