# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#4

Question a.   The function f is defined for all values of  by  .                            i.       Find the remainder when  is divided by .                          ii.       Given that  and  , write down two linear factors of .                        iii.       Hence express  as the product of three linear factors. b.   The curve with equation  is sketched below.                            i.       The curve intersects the y-axis at the point . Find the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#6

Question A rectangular garden is to have width x metres and length  metres. a.  The perimeter of the garden needs to be greater than 30 metres. Show that; b.  The area of the garden needs to be less than 96 square metres. Show that; c.  Solve the inequality .  d.   Hence determine the possible values of the width of […]

# 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#5

Question a.   Simplify . b.   Express  in the form  , where  is an integer. c.   Express  in the form  , where  and  are an integers. Solution a.    We have algebraic formula; For the given case; b.   Since ; Comparing with  gives us; c.   To express  in the form  , we need to rationalize the denominator. If we need a rational number […]

# 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 […]

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

Question A curve has equation   . a.   Find . b.   The point  on the curve has coordinates .                            i.       Show that the gradient of the curve at  is 5.                          ii.       Hence find an equation of the normal to the curve at P, expressing your answer in the form ax + by = c , where a, b and c are integers. […]

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

Question The point  has coordinates  and the point  has coordinates . a.                 i.    Find the gradient of .           ii.    Hence, or otherwise, show that the line  has equation . b.   The line with equation   intersects the line  at the point . Find the coordinates of . Solution a.   i.   Expression […]