# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#3

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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#3

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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will hold for ; SOLVING INEQUALITY: ALGEBRAICALLY […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#10

Question a.   On the axes below sketch the graphs of                                     i.       y = x (4 – x)                                    ii.       y = x2 (7 – x) showing clearly the coordinates of the points where the curves cross the coordinate axes. b.   Show that the x-coordinates of the points of intersection of y = x (4 – x) and y = […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#4

Question a)   Show that x2 + 6x + 11 can be written as (x + p)2 + q, where p and q are integers to be found. b)  In the space at the top of page 7, sketch the curve with equation y = x2 + 6x +11, showing clearly  any intersections with the coordinate axes. c)   Find […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#3

Question Find the set of values of x for which a.   b.   c.   both  and Solution a.   We are given; b.   We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are  & […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#10

Question f(x) = x2 + 4kx + (3+11k), where k is a constant. a)   Express f(x) in the form (x + p)2 + q, where p and q are constants to be found in terms of k.  Given that the equation f(x) = 0 has no real roots, b)  find the set of possible values of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#7

Question a. i.Express  in the form  , where p and q are integers. ii.Use your result from part (a)(i) to explain why the equation  has no real roots. b.The quadratic equation  has real roots. i.Show that . ii.Hence find the possible values of k.   Solution a. i. We have the expression; We use method of “completing square” to obtain the desired form. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#7

Question A circle with centre C has . a.   Find:                            i.       the coordinates of C;                          ii.       the radius of the circle b.   Explain why the circle lies entirely below the x-axis. c.   The point P with coordinates  lies outside the circle.                            i.       Show that .                          ii.       Hence show that                        iii.       Find the possible values of k. Solution a.   We are given […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#5

Question a.   Express  in the form  , where p and q are integers. b.                        i.       Sketch the graph of  , stating the coordinates of the minimum point  and the point where the graph crosses the y-axis.                   ii.       Write down an equation of the tangent to the graph of  at its vertex. c.   […]