• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths Assignment - trigonometry, trend line, probability and calculus questions.

Extracts from this document...




Trigonometry can be used to solve problems instead of constructing a scale diagram.

A man leaves a point walking at 6kmh on a bearing of 80o. A cyclist leaves the same point at the same time on a bearing of 120o travelling at a speed of 17kmh. Calculate their distance apart after 4 hours using trigonometry.        (6)



Figure 01

As shown in the figure 01, let’s take ‘A’ as the starting point.

After 4hrs the man is at point M and cyclist at point C

Distance travelled by the man after 4hrs                


Distance travelled by the cyclist after 4hrs        


Now let’s consider the


Using the information in the question, the application of the Cosine rule would seem

...read more.



a)  Using Excel verify this is true.


b)  Add the appropriate trend line.


c)  Display the equation of this trend line.




(a).As you can see in the graph the given data of pressure Vs altitude shows an exponential variation.

(b).The appropriate trend line is shown in dotted lines on the graph.

(c). Trend line equation is given by




Probability can be used so that companies can decide on reasonable waiting times.

The waiting times for a bus are normally distributed with a standard deviation of 0.3 minutes. 80% of people waiting for a bus have to wait no more than 5 minutes. Calculate the mean average waiting time for one of these buses.        (3)


Table 01: Cumulative probability for Z values






According to the above table

...read more.



Angular displacement

 is given by function of

 by following equation


(a).Then Angular velocity

, is given by



Angular velocity of the disc after 1.5s


(b).Then Angular acceleration

, is given by



Angular acceleration of the disc after 1.5s



(c).When angular velocity becomes zero for the first time whereimage00.png







A gas expands according to the law pv constant. When the volume is 2m3 the pressure is 240kPa. Calculate the work done as the gas expands from 1m3 to 4m3 given that work

done  v2p dv



Note:  1


 ln x



Gas expands according to the law of

Where k is constant

When  image00.png


When gas expands work done is given by








...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Numerical integration can be described as set of algorithms for calculating the numerical value ...

    Simpson's rule is different to the trapezium rule in that it fits a parabola between successive triples of points, whereas the trapezium rule fits a straight line between successive pairs of points. As a result the number of strips must not be even.

  2. Exponential decay:The objective of this experiment is to get the trend line of heart ...

    Base heart rate Heart rate after t mins(after running 5 mins) Time(min) 1 2 3 0.5 1 1.5 2.0 2.5 3.0 3.5 Name Abby 84 84 80 130 150 150 150 130 120 140 Alex 90 78 90 180 180 150 150 140 140 140 Ben 78 90 110 130

  1. Numerical Method (Maths Investigation)

    Hence it can't find the required roots here using both methods. COMPARISON MADE WITH ALL THREE METHODS After doing all three methods, i.e. Change of Sign Method, Newton-Raphson Method and Rearrangement Method, with each different examples showing how it works.

  2. Arctic Research (Maths Coursework)

    km/h because in the arctic, from my research, the average wind speeds are mostly 30 km/h. Simple Scenario This is a sketch of all journeys the researchers would need to make to visit every observation site and return to base camp.

  1. Portfolio - Stopping Distances

    increases exponentially. Since it is a quadratic we can develop a model to fit a data using the equation also known as, however, there is another model that would fit the data is by using a power function. First I will develop a quadratic model.

  2. Functions Coursework - A2 Maths

    x f(x) 1.8790 -0.002926 1.8791 -0.002166 1.8792 -0.001407 1.8793 -0.000647 1.8794 0.0001121 1.8795 0.0008718 1.8796 0.0016316 1.8797 0.0023915 1.8798 0.0031516 1.8799 0.0039117 1.8800 0.0046720 The root therefore lies in the interval [1.8793,1.8794]. The next table show values of f(x) at values of x from 1.8793 to 1.8794, with intervals of 0.00001.

  1. Sars Math Portfolio ...

    I went and inserted the values for day 0 and day 28 and developed the model shown above. There are no modifications to this function because it mirrors the results almost exactly (as shown in the graph below) so I did not to modify it to create a better fit.

  2. The open box problem

    This graph is also symmetrical. Now that I tested have 3 different squares I will now draw a table to show the volumes and values of x for the squares together to find a pattern. Dimensions Maximum Volume X (that allows volume to be its maximum)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work