Mathematics 7357: Numerical methods Topical Past Paper Questions

Figure 2 below shows a 1.5 metre length of pipe. Figure 2 The symmetrical cross-section of the pipe is shown below, in Figure 3, where x and y are measured in centimetres. Figure 3 Use the trapezium rule, with the values shown in the table below, to find the best estimate for the…

The function f is defined by $$ \mathrm{f}(x)=\arccos x\mathrm{f o r}0\leq x\leq a $$ The curve with equation $y = f(x)$ is shown below. (a) State the value of $a$ [1 mark] (b)(i) On the diagram above, sketch the curve with equation $$ y=\cos x\text{f o r}0\leq x\leq\frac{\pi}{2}…

The diagram shows a sector of a circle OAB. (a) The point C lies on OB such that AC is perpendicular to OB. Angle AOB is $ \theta $ radians. Given the area of the triangle OAC is half the area of the sector OAB, show that $$ \theta=\sin2\theta $$ $ \theta = \sin 2\theta $ [4 mark…