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Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#8

Hits: 4   Question The gradient, , at the point (x,y) on a curve is given by a.                        i.               Find                   ii.               The curve passes through the point . Verify that the curve has a minimum point at P. b.                       i.               Show that at the points on the curve where y is decreasing                   ii.               Solve the inequality Solution a.   We are given;                     i. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#7

Hits: 8   Question The diagram shows the sketch of a curve and the tangent to the curve at P. The curve has equation  and the point P(-2,24) lies on the curve. The tangent at P  crosses the x-axis at Q. a.                       i.               Find the equation of the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#6

Hits: 4   Question a.  A curve has equation .                     i.               Find the values of x where the curve crosses the x-axis, giving your answer in the form   , where m and n are integers.                   ii.               Sketch the curve, giving the value of the y-intercept. b. A line has equation  , where k is a constant.                     i.               Show that the x-coordinates of any points […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#5

Hits: 4   Question A circle with center C(5,-3) passes through the point A(-2,1). a.   Find the equation of the circle in the form b.   Given that AB is a diameter of the circle, find the coordinates of the point B. c.   Find an equation of the tangent to the circle at the point A, giving your answer […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#4

Hits: 1   Question The polynomial  is given by . a.                                i.       Use the Factor Theorem to show that  is a factor of .                          ii.      Express  as a product of three linear factors. b.                                i.       Use Remainder Theorem  to find the remainder when  is divided by .                          ii.       Express  in the form , where b and c are integers. Solution a.                               i. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#3

Hits: 2   Question a.                         i.       Express  in the form  , where p and q are rational numbers.                   ii.       Hence write down the minimum value of . a.   Describe the geometrical transformation which maps the graph of  onto the graph  of  . Solution a.                               i.   We have the expression; We use method of “completing square” to obtain the desired form. First we […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#2

Hits: 3   Question a.   Simplify . b.   Express  in the form  , where m and n are integers. Solution a.   b.   If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#1

Hits: 0   Question The line AB has equation . a.   The line AB is parallel to the line with equation .  Find the value of m. b.    The line AB intersects the line with equation  at the point B. Find the coordinates of B. c.    The point with coordinates  lies on the line AB. Find the value of […]