# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#7

Question The parametric equations of a curve are for .  The curve crosses the x-axis at points B and D and the stationary points are A and C, as shown in the diagram. i.       Show that .    ii.       Find the values of t at A and C, giving each answer correct to 3 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#6

Question i.       Find the quotient and remainder when is divided by .    ii.       It is given that, when is divided by , the remainder is ZERO. Find the values of the constants  and .   iii.       When  and have these values, show that there is exactly one real value of satisfying the  equation And […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#5

Question      i.       Find    ii.       Find the exact value of Solution      i.   We are required find; We know that;  Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:        ii.   We are required to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#4

Question      i.       By sketching a suitable pair of graphs, show that the equation has exactly one real root .    ii.       Verify by calculation that 4.5 < < 5.0. iii.       Use the iterative formula to find correct to 2 decimal places. Give the result  of each iteration to 4 decimal places. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#3

Question      i.       Express in the form , where  and , Give the  value of correct to 2 decimal places.    ii.       Hence solve the equation for .   iii.       Determine the least value of  as  varies. Solution      i.   We are given the expression; We are required to write it in the form; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#2

Question The equation of a curve is Find the coordinates of the points on the curve at which the gradient is −4. Solution We are given equation of the curve as; We need expression for gradient of the curve. Gradient (slope) of the curve is the derivative of equation of the curve. Hence […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#1

Question Use logarithms to solve the equation 5x+3 = 7x−1 giving the answer correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;