Edexcel ALevel Maths, Pure Paper 1, June 2018
Question Walkthroughs

Pure Paper 1, 2018,Q11. Given that theta is small and is measured in radians, use the small angle approximations to find an approximate value of (1  cos 4theta)/(2theta sin 3theta).


Pure Paper 1, 2018, Q22. A curve C has equation y = x^2  2x  24rootx, x>0.
ai. Find dy/dx ii. Find d2y/dx2 b. Verify that C has a stationary point when x = 4. c. Determine the nature of this stationary point, giving a reason for your answer. 

Pure Paper 1, 2018, Q33. Figure 1 shows a sector AOB of a circle with centre O and radisu r cm. The angle AOB is theta radians. The area of the sector AOB is 11cm^2.
Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r. 

Pure Paper 1, 2018, Q44. The curve with equation y =2 ln(8  x) meets the line y = x at a single point, x = alpha. Show that alpha is between 3 and 4.


Pure Paper 1, 2018, Q5Given that y = 3 sin theta / (2 sin theta + 2 cos theta) show that dy/dtheta = A / (1 + sin 2theta).


Pure Paper 1, 2018, Q6The circle C has centre A with coordinates (7, 5). The line l, with equation y = 2x + 1, is the tangent to C at the point P, as shown in the diagram. Show that an equation of the line PA is 2y + x = 17.


Pure Paper 1, 2018, Q7Show that the integral of 2/(3xk) with respect to x between k and 3k is independent of x.
Show that the integral of 2/(2xk)^2 with respect to x is inversely proportional to k. 

Pure Paper 1, 2018, Q8The depth of water, D metres, in a harbour on a particular day is modelled by the formula D = 5 + 2sin(30t).


Pure Paper 1, 2018, Q9Figure 4 shows a sketch of the curve with equation x^2  2xy +3y^2 = 50.
a. Show that dy/dx = (y  x)/(3yx) 

Pure Paper 1, 2018, Q10The height above ground, H metres, of a passenger on a roller coaster can be modelled by the differential equation dH/dt = Hcos(0.25t)/40 where t is the time, in seconds, from the start of the ride.
a. Show that H = 5e^0.1sin(0.25t) b. State the maximum height of the passenger above the ground. The passenger reaches the maximum height for the second time, T seconds after the start of the ride. c. Find the value of T. 

Pure Paper 1, 2018, Q11Use binomial expansions to show that root (1+4x)/(1x) = 1+5/2 x  5/8 x.


Pure Paper 1, 2018, Q12The value, £V, of a vintage car t years after it was first valued on 1st January 2001 is modelled by the equation V = Ap^t where A and p are constants.
Given that the value of the car was £32000 on 1st January 2005 and £50000 on 1st January 2012, ai. find p to 4 decimal places ii. show that A is approximately 24 800. 