Fit for Studying Natural Sciences?

The atomic radius of an iron atom is around 0.0000000124 cm long. This is a very short length which can hardly be observed under a microscope. Scientists try to convert such small numerical values into a unit with which the numerical value is more suitable for handling. For this reason, atomic radii are usually expressed in picometers (pm). The factor for converting cm to pm is 10000000000. This means that the radius of an iron atom is 124 pm. The different orders of magnitude and the conversion factor are shown in the so-called prefixes of the SI units in order to convert to a wide variety of quantities (e.g. lengths or mass).

Solving quadratic equations is a necessary arithmetic operation that is defined as a minimum requirement. An example of this is the calculation of an exact concentration which is used to calculate a pH value based on the law of mass action. The pq formula (also known as the midnight formula) is required to solve quadratic equations:

The unit circle serves as a tool for deriving trigonometric functions (f(x) = sin(x) and f(x) = cos(x)). In this example, we have an angle of α = 45°. If we enter this in the unit circle, we can see that at α = 45° we get a value of sin(α) = 0.71. Accordingly, at α = 90°, we would have a value of sin(α) = 1. In experimental physics and physical chemistry in particular, oscillations are modeled with a sine or cosine function, which is why the basics of trigonometry are an essential minimum requirement.

Practical experience and laboratory practicals are an essential part of a science degree. This includes not only carrying out an experiment, but also measuring and analyzing data. For example, you want to determine the concentration of a standard solution during a titration and add a drop of caustic soda until a clear color change can be observed with an indicator. You carry out this experiment five times to obtain accurate data and obtain the following values for the volume added until the color change:

In the practical course, you would now determine the arithmetic mean, the variance and the standard deviation. How does this work? - Find out here.

Any derivation laws mean a total of 4 laws:

a) Potency rule
f(x) = x³ + x² + 2x² + 2
f'(x) = 3x² + 2x + 4x + 0 ⇒ f'(x) = 3x² + 6x
This means that the individual summands are derived independently, constants are dropped during derivation and factors are multiplied.

b) Product rule

With the product rule, the terms are considered individually and defined as functions g(x) and h(x).
f(x) = g(x) ∙ h(x)

Both functions are then derived independently of each other. The product rule can then be used to derive and summarize the function equation using the following rule:
f'(x) = g'(x) ∙h(x) + g(x) ∙ h'(x)

c) Quotient rule

The quotient rule is similar to the product rule and the denominator and numerator are labeled as g(x) and h(x). The following rule applies:
f(x) = g(x) / h(x)
f'(x) = g'(x) ∙ h(x) - g(x) ∙ h'(x) / h(x)²

d) Chain rule

The chain rule can be applied to a function f(x) = a(i(x) which consists of i(x) as the inner function and a(x) as the outer function. The derivative of a concatenation of functions is given by f'(x) =i'(x) ∙a'(ix).

In the test and in the recommended actions, you have the opportunity to check and practice your skills in deriving functions.