# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#1

Question A curve passes through the point (4, −6) and has an equation for which . Find the equation of the curve. Solution We are required to find the equation of the curve from the given derivative. We can find equation of the curve from its derivative through integration; We are given; Therefore; Rule for […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#7

Question The diagram shows part of the curve defined by the parametric equations The curve has a minimum point at M and crosses the x-axis at the point P.     i.       Find the gradient of the curve at P.    ii.       Find the coordinates of the point M.   iii.       The value of the gradient […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#6

Question      i.       Show that    ii.       Hence find the exact value of .   iii.       Find Solution      i.   We are given;   provided that   provided that   provided that      ii.     provided that Therefore; Hence; Therefore; Hence;   iii.   We are required to find; As demonstrated […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#5

Question It is given that a is a positive constant such that i.       Show that    ii.       Use the equation in part (i) to show by calculation that 1.0 < a < 1.5.   iii.       Use an iterative formula based on the equation in part (i) to find the value of a correct […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#4

Question The polynomial p(x) is defined by     i.       Use the factor theorem to show that (x+3) is a factor of p(x).    ii.       Factorise p(x) completely.   iii.       Hence, given that find the value of 2u and, using logarithms, find the value of u correct to 3 significant figures. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#3

Question      i.       Use the trapezium rule with four intervals to find an approximation to giving your answer correct to 3 significant figures.    ii.       Hence find an approximation to Solution i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#2

Question A curve has equation . Find the equation of the tangent to the curve at the point for which . Solution      i.   We are given that curve with equation  and we are required to find the equation of the  tangent to the curve at origin . To find the equation of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (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 with […]