# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#6

Question a.   Find b.   Show that Solution a.     We are required to find; Rule for integration of , or ; b.     We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#5

Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M can be written in the form , where the value of a is to be  stated.    ii.       Find the exact value of the area of the region enclosed by the curve and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#5

Question The parametric equations of a curve are      i.       Find an expression for in terms of t.      i.       Find the equation of the normal to the curve at the point for which t = 0. Give your answer in  the form ax + by + c = 0, where a, b and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#5

Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M can be written in the form , where the value of a is to be  stated.    ii.       Find the exact value of the area of the region enclosed by the curve and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#2

Question Use logarithms to solve the equation 5x = 32x-1, giving your answer correct to 3 significant figures.  Solution We are given; Taking natural logarithm of both sides; Power Rule; Power Rule; Division Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#5

Question The variables x and y satisfy the equation y = A(b-x), where A and b are constants. The graph of    ln  y against x is a straight line passing through the points (1, 2.9) and (3.5, 1.4), as shown in the  diagram. Find the values of A and b, correct to 2 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#2

Question Use logarithms to solve the equation 5x = 32x-1, giving your answer correct to 3 significant figures.  Solution We are given; Taking natural logarithm of both sides; Power Rule; Power Rule; Division Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/23) | Q#2

Question The variables x and y satisfy the equation y = A(bx), where A and b are constants. The graph of      ln y  against x is a straight line passing through the points (0, 2.14) and (5, 4.49), as shown in the diagram. Find the values of A and b, correct to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#2

Question      i.       Given that 52x + 5x = 12, find the value of 5x.    ii.       Hence, using logarithms, solve the equation 52x + 5x = 12, giving the value of x correct to 3  significant figures. Solution i.   We are given; Let , then; Therefore; It is a quadratic […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/21) | Q#2

Question The variables x and y satisfy the equation y = A(bx), where A and b are constants. The graph of      ln y  against x is a straight line passing through the points (0, 2.14) and (5, 4.49), as shown in the diagram. Find the values of A and b, correct to […]