Hits: 133

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#1

Hits: 133   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 […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | January | Q#3

Hits: 20   Question Given that the equation , where k is a positive constant, has equal roots, find the value of k. Solution We are given; We can given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two distinct […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#5

Hits: 16   Question Solve the simultaneous equations Solution We are given simultaneous equations; Rearranging the first equation we get expression for ; Substituting this for  in the second equation; We have the algebraic formula; Therefore; For a quadratic equation , the expression for solution is; For the above equation; Now we have two options. By substituting one-by-one these values of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#7

Hits: 26   Question Solve each of the following inequalities: a.   b.   Solution a.   We are given; b.   We are given; First we find the critical values for this inequality. Therefore; Now we have two options. Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If  (‘a’ is positive) then parabola opens upwards  and […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#2

Hits: 27   Question a.   Express  in the form . b.   A curve has equation  .  Using your answer form part (a), or otherwise:                       i.       Find the coordinates of the vertex (minimum point) of the curve.                     ii.       Sketch the curve, indicating the value where the curve crosses the y-axis. c.   Describe […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#7

Hits: 32   Question a.   Simplify    b.   The quadratic equation  has real roots.                            i.       Show that                          ii.       Hence find the possible values of . Solution a.   We are given; b.                               i.   We are given that following quadratic equation has real roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#3

Hits: 63   Question A circle has equation .  a.   By completing  the square, express the equation in the form b.   Write down:                            i.       the coordinates of the center of the circle;                          ii.       the radius of the circle c.   The line with equation  intersects the circle at the points P and Q.                            i.       Show that the x-coordinates of P and Q satisfy […]