Questions and Worked Solutions for Edexcel Pure Maths Paper 2 Sample.
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Edexcel Pure Maths Paper 2 Sample Past Paper (page 59)
Student B gives θ = –26.6° as one of the answers to cos θ = 2 sin θ.
(b) (i) Explain why this answer is incorrect.
(ii) Explain how this incorrect answer arose.
(a) find an expression for gf(x), simplifying your answer.
(b) Show that there is only one real value of x for which gf (x) = fg(x)
According to the model,
(a) find the mass of the radioactive substance six months after it was first observed,
(b) show that dm/dt = km, where k is a constant to be found.
A student attempts to substitute x = 1 into both sides of this equation to find an
approximate value for √3.
(b) State, giving a reason, if the expansion is valid for this value of x.
Given that the equation f(x) = k, where k is a constant, has two distinct roots,
(c) state the set of possible values for k.
(b) Hence find the smallest positive solution of the equation
3sin^{2}(2θ – 30°) + sin (2θ – 30°) + 8 = 9 cos^{2}(2θ – 30°)
giving your answer to 2 decimal places.
H = a - 10 cos (80t)° + 3 sin (80t)°
where a is a constant.
Figure 3 shows the graph of H against t for two complete cycles of the wheel.
Given that the initial height of the passenger above the ground is 1 metre,
(b) (i) find a complete equation for the model,
(ii) hence find the maximum height of the passenger above the ground.
(c) Find the time taken, to the nearest second, for the passenger to reach the maximum
height on the second cycle.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
It is decided that, to increase profits, the speed of the wheel is to be increased.
(d) How would you adapt the equation of the model to reflect this increase in speed?
Given that r can vary,
(b) find the dimensions of a can that has minimum surface area.
(c) With reference to the shape of the can, suggest a reason why the company may choose not to manufacture a can with minimum surface area.
The point P with coordinates (4, 15) lies on C.
The line l is the tangent to C at the point P.
The region R, shown shaded in Figure 4, is bounded by the curve C, the line l and the y-axis.
Show that the area of R is 24, making your method clear.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
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