Edexcel A-Level Maths, Pure Paper 1, June 2018
Question Walkthroughs
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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).
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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. |
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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. |
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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.
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Pure Paper 1, 2018, Q5Given that y = 3 sin theta / (2 sin theta + 2 cos theta) show that dy/dtheta = A / (1 + sin 2theta).
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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.
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Pure Paper 1, 2018, Q7Show that the integral of 2/(3x-k) with respect to x between k and 3k is independent of x.
Show that the integral of 2/(2x-k)^2 with respect to x is inversely proportional to k. |
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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).
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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)/(3y-x) |
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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. |
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Pure Paper 1, 2018, Q11Use binomial expansions to show that root (1+4x)/(1-x) = 1+5/2 x - 5/8 x.
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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. |