Edexcel A-Level Maths October 2021 - Question Walkthroughs
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Pure Paper 2, 2021, Q1In an arithmetic series
• the first term is 16 • the 21st term is 24 (a) Find the common difference of the series. (b) Hence find the sum of the first 500 terms of the series. |
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Pure Paper 2, 2021, Q2The functions f and g are defined by f (x) = 7 – 2x^2, g (x) = 3x / (5x – 1)
(a) State the range of f b) Find gf (1.8) (c) Find g^–1(x) |
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Pure Paper 2, 2021, Q3Using the laws of logarithms, solve the equation log3 (12y + 5) – log3 (1 – 3y) = 2
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Pure Paper 2, 2021, Q4Given that θ is small and measured in radians, use the small angle approximations to show that 4 sin θ/2 + 3 cos2 θ = a + bθ + cθ^2 where a, b and c are integers to be found.
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Pure Paper 2, 2021, Q5The curve C has equation y = 5x^4 – 24x^3 + 42x^2 – 32x + 11
(a) Find (i) dy/dx (ii) dy^2/d^2x (b) (i) Verify that C has a stationary point at x = 1 (ii) Show that this stationary point is a point of inflection, giving reasons for your answer. |
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Pure Paper 2, 2021, Q6The shape OABCDEFO shown in Figure 1 is a design for a logo.
In the design • OAB is a sector of a circle centre O and radius r • sector OFE is congruent to sector OAB • ODC is a sector of a circle centre O and radius 2r • AOF is a straight line Given that the size of angle COD is θ radians, (a) write down, in terms of θ, the size of angle AOB b) Show that the area of the logo is 1/2 r^2 (3θ + π) (c) Find the perimeter |
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Pure Paper 2, 2021, Q7Figure 2 shows a sketch of part of the curve C with equation y = x^3 – 10x^2 + 27x – 23
The point P(5, –13) lies on C The line l is the tangent to C at P (a) Use differentiation to find the equation of l, giving your answer in the form y = mx + c where m and c are integers to be found. (b) Hence verify that l meets C again on the y-axis. The finite region R, shown shaded in Figure 2, is bounded by the curve C and the line l. (c) Use algebraic integration to find the exact area of R. |
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Pure Paper 2, 2021, Q8The curve C has equation px^3 + qxy + 3y^2 = 26 where p and q are constants.
(a) Show that dy/dx = apx^2 +bqy / qx + cy where a, b and c are integers to be found. Given that • the point P (–1, – 4) lies on C • the normal to C at P has equation 19x + 26y + 123 = 0 (b) find the value of p and the value of q. |
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Pure Paper 2, 2021, Q9Show that Σ(3/4)^n cos(180n) = 9/28
We will show that the sum from n=2 to infinity of 3/4 to the power of n multiplied by cos(180n) equals 9/28. |
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Pure Paper 2, 2021, Q10The time, T seconds, that a pendulum takes to complete one swing is modelled by the formula T = al^b where l metres is the length of the pendulum and a and b are constants.
(a) Show that this relationship can be written in the form log10 T = b log10 l + log10 a A student carried out an experiment to find the values of the constants a and b. The student recorded the value of T for different values of l. |
Figure 3 shows the linear relationship between log10 l and log10 T for the student’s data. The straight line passes through the points (– 0.7, 0) and (0.21, 0.45) Using this information,
(b) find a complete equation for the model in the form T = al^b giving the value of a and the value of b, each to 3 significant figures.
(c) With reference to the model, interpret the value of the constant a.
(b) find a complete equation for the model in the form T = al^b giving the value of a and the value of b, each to 3 significant figures.
(c) With reference to the model, interpret the value of the constant a.