# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#8

Question The water level in a reservoir rises and falls during a four-hour period of heavy rainfall. The height, h cm, of water above its normal level, t hours after it starts to rain, can be modelled by the equation , a.   Find the rate of change of the height of water, in cm per hour, 3 hours […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#7

Question The diagram shows the right-angled corner AFE of a building and four sections of fencing running  parallel to the walls of the building. Each of the sections of fencing AB and DE has length x metres and each of the sections of wall AF  and FE has length y metres. The total length of the four sections of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#6

Question A circle with centre C has .  a.   Express this equation in the form b.   Show that the circle touches the y-axis and crosses the x-axis in two distinct points. c.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the circle and the line satisfy  the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#5

Question A curve and the line AB are sketched below. The curves has the equation  and the points A(-1,9) and B(2,12) lie on the curve. a.   Find the equation of the normal to the curve at the point A, giving your answer in the form  . b.                         i.       Find .                   ii.       Hence find the area of the shaded region […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#4

Question The point A has coordinates (-2,5) and the point B has coordinates (8,-6). a.   Find and equation for the straight line AB, giving your answer in the form , where p, q and r are integers. b.   The point C has coordinates (k,k+1). Given that the angle ACB is a right angle, find the two  possible values […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#2

Question A curve has the equation . The curve has a stationary point at the point M where . a.  Find the coordinates of the other stationary point of the curve. b.  Find the value of  at the point M, and hence determine, with a reason, whether M is a  minimum point or a maximum point. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#1

Question a.  Express  in the form , where m and n are integers.  b. Solve the equation giving your answer in its simplest form. Solution a.   We are given; 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 […]