# 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#8

Question      i.       Given that   and find in terms of .    ii.       Solve the equation giving all solutions in the interval 0◦ ≤ x ≤ 360◦. Solution      i.   We are given; We are given that ; therefore;    ii.   We are required to solve  giving all solutions in the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#7

Question The equation of a curve is        i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from an implicit equation, […]

# 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 | Oct-Nov | (P2-9709/22) | Q#4

Question The diagram shows the part of the curve  for .      i.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       The line y=x intersects the curve at point P. Use the iterative formula to determine the x-coordinate of […]

# 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#3

Question The polynomial  is denoted by p(x). i.       Find the quotient when p(x) is divided by  .  ii.       Hence solve the equation  p(x)=0. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to solve; When a polynomial, , is divided by a non-constant divisor, , […]

# 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#2

Question The curve with equation has one stationary point  in the interval . Find the exact  x-coordinate of this point. Solution We are required to find the x-coordinate of stationary point of the curve with equation; A stationary point on the curve is the point where gradient of the curve is equal to […]

# 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 | (P2-9709/22) | Q#1

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 […]