## SAQ 5

Are the reptiles a proper clade?

### Answer

No, because despite the reptiles being derived from a common ancestor, two descendent groups – the birds and the mam

This unit is from our archive. It is an adapted extract from the *Science* (S365) module that is no longer in presentation. If you wish to study formally at The Open University, you may wish to explore the courses we offer in this Curriculum Area

This unit is concerned with *macroevo*

*In essence, the argument about intermediate forms runs as follows. If whales evolved from a terrestrial ancestor through the accumulation of small differences over time, we should expect to find the fossils of a number of ‘missing links’, i.e. creatures with a mixture of terrestrial and aquatic characteristics. In fact, we might expect to find a succession of such animals, each a little bit more whale-like and a little bit less well adapted to life on land than its predecessor.*

*To m*

The structural formulae of organic molecules can be divided into the carbon-hydrogen framework or skeleton, and the functional group(s). In the first approximation, the functional groups are the sites where reaction occurs, the framework remaining unreactive.

This approximation works best when the framework consists of saturated carbon atoms.

*Author(s):*

*Some students contend with physical difficulties in reading. Here is one:*

*
*

*And here is another being offered advice by a friend:*

*
Author(s): *

*2.12 How likely are particular results? *

*In real experiments, as opposed to hypothetical ones, it is very rare that scientists make a sufficiently large number of measurements to obtain a smooth continuous distribution like that shown in Figure 7d. However, it is often convenient to assume a particular mathematical form for typically distributed measurements, and the form that is usually*

*2.11 Using a calculator for statistical calculations *

*
Table 3 shows all the values for each step in the process of calculating a standard deviation, so that you can see what the operations encapsulated by Equation 7 actually entail, but you will probably be relieved to hear that it is not usually necessary to carry out such detailed calculations. Scientific and graphics calculators (or computer sp*

*Scientists collect many different types of information, but sets of data may be very loosely classified into two different types. In the first type, so-called ‘repeated measurement’, an individual quantity is measured a number of times. An astronomer wanting to determine the light output of a star would take many measurements on a number of different nights to even out the effects of the various possible fluctuations in the atmosphere that are a cause of stars ‘twinkling’. In the seco*

*The probabilities described in Section 2.3 and Section 2.4 related to the outcomes of a single process, such as repeatedly tossing one coin. Now suppose you were to toss three separate coins simultaneously. What is the prob*

*1.4 How precise are the measurements? *

*Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room.*

*Author(s):*

*2.1 The four rules of arithmetic *

*You are now going to use the four operation keys (on the bottom right-hand side of the TI-84 keyboard): , Author(s): *

*Example 3*

*Author(s):*

*Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.*

*Activity 1 Carl Jung's school days*

*Read*

*In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by*

*From this, one can justify the performance of ordinary algebraic operations on expressions of the form a + ib*

*Scientific notation can be very useful when estimating the answers to calculations involving very large and/or small decimal numbers.*

*Example 9*

*A lottery winner won £7851 000. He put the money straight into a deposit account which earns 7.5% interest per annum (i.e. each year). If he wanted to*

**1** The new home owners from Example 4 above want to price grass seed, as well as the turf (transport only). The best buy seems to be loose seed, which says ‘1 kilo covers 80 m^{2}’. They wonder what length the side of an 80 m^{2Author(s): The Open University}

**1** Evaluate the following:

*(a) 6*^{2}*(b) 0.5*^{2}*(c) 1.5*^{2}

## Answer<

Author(s):

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Copyright 2009 University of Nottingham

## Answer<

Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (^{−}2, 3) or (^{−}2, ^{−}3). Just as a number line can be extended to deal with negative numbers, the *x*-axis and *y*-axis can be extended to deal with negative coordinates.

**1** The frequency diagram below shows the numbers of people in different age groups in a sample of the UK population.

(a) What is the width of each age group?

(b) Which age group conta

This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

This unit is an adapted extract from the course *Mathematical methods and models* (MST209