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

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 its vertex […]

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

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 geometrically the […]

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

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 , the equation […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#6

Question The diagram below shows a rectangular sheet of metal 24 cm by 9 cm. A square of side x cm is cut from each corner and the metal is then folded along the broken lines to  make an open box with a rectangular base and height x cm. a.   Show that the volume,  cm3, of liquid the […]

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

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 the equation […]