Hits: 119

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#1

Hits: 119     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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#1

Hits: 161   Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let  and , then; 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 Let, . […]

Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#10

Hits: 84   Question a.   Find the values of the constants a and b. b.   In the space provided below, sketch the graph of , indicating clearly the coordinates of any intersections with the coordinate axes. c.   Find the value of the discriminant of . Explain how the sign of the discriminant relates  to your sketch in […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#2

Hits: 25   Question a.   Express  in the form , where  and  are integers. b.   Hence, or otherwise, show that the equation  has no real solutions. c.   Sketch the graph of , stating the coordinates of the minimum  point and the point where the graph crosses the y-axis. d.   Describe geometrically the transformation that maps the graph of  onto the graph of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#8

Hits: 80   Question The diagram shows the curve with equation  and the line  . The points  and  have coordinates  and  respectively. The curve touches the x-axis at  the origin  and crosses the x-axis at the point .  The line  cuts the curve at the point   where  and touches the curve at  where . a.   Find the area of the rectangle . b.                                i.  […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#4

Hits: 13   Question The quadratic equation , where  is a constant,  has equal roots.  a.   Show that . b.   Hence find the possible values of . Solution a.   For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two roots. If , the equation will have […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#3

Hits: 28   Question a.                                i.       Express  in the form , where   and  are integers.                          ii.       Hence, or otherwise, describe the coordinates of the minimum point of the curve with                       equation . b.   The line  has equation  and the curve  has the equation .                             i.       Show that the x-coordinates of the […]