Section 3

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There’s no specific mathematics section in Section 3: Reasoning in Biological and Physical Sciences of the GAMSAT, so why should we learn it?

Mathematics is the language of analysis used by science.

With Section 3, a student would need to have a good understanding of first year biology and chemistry as well as year 12 level physics in order to succeed. All these subjects involved a certain level of maths. So without a strong understanding of concepts such as algebraic manipulation, the student will severely limit their capacity to interpret and manipulate the data provided in Section 3 stems.

Mental mathematical manipulation is a very important skill to hone for the GAMSAT, as:

- There is no calculators allowed
- Online exam format does not allow for physical annotations on exam paper
- ACER provides students with only 2 blank sheets of paper for calculation

Please note that the blank sheets of paper are for 75 questions for Section 3. This means that students must be selective as to which stems they choose to make notes on and calculations to perform.

While there is no explicit information in the GAMSAT syllabus as to what level of mathematics is recommended to sit the exam, Fraser’s GAMSAT has analysed over a decade of exam content in order to identify the required mathematics level to efficiently navigate Section 3.

The table above summarises the required level of mathematics required for confidence in the sciences expressed in terms of the relevant high-school subject in each Australian state.

Please note that the exam will not require a candidate to utilise the entire scope of mathematics taught across these subjects, but GAMSAT maths will never exceed the syllabus of the subjects listed in the table above.

Having mentioned this knowledge recommendation for GAMSAT maths, it is now important to discuss the context of GAMSAT maths questions. In the case of Section 3 biology questions, stems relating to Population Health and Experimental Biology are heavily reliant on numbers.

Chemistry in Section 3 also tends to rely heavily on candidates’ maths skills. Your ability to translate algebraic equations into graphs is crucial in comparing and extrapolating information from various provided data. This is substantiated by ACER’s frequent use of logarithmic expressions and logarithmic scales, as these types of GAMSAT maths questions frequently catch out weaker candidates. Furthermore, topics such as Equilibrium, Acid-Base and Kinetics may also require algebraic manipulation and meticulous calculations.

In terms of GAMSAT physics, virtually every single stem you encounter in the GAMSAT is necessarily going to require mathematics. In a previous article in this series, Fraser’s GAMSAT answered the question of “how to prepare for the physics exam” with a recommendation of starting with a review of the relevant level of GAMSAT maths. We will discuss the specific maths skills required for the GAMSAT later in this piece, however if you are interested consider reading our article on GAMSAT Physics!

The breadth of knowledge that Fraser’s recommends for GAMSAT maths questions is incredibly broad. No single GAMSAT exam will examine the entire scope of the above mentioned maths topics, however this exam can and will draw on any concepts from within this syllabus.

These are the following mathematical concepts that students should gain a full, mental understanding of in order to succeed in the GAMSAT:

Approximation and estimation are arguably the most important maths skill you can learn for the GAMSAT. Both in the GAMSAT, and in the real world of medical training, this is the skill-set which will be most useful. In essence, this type of GAMSAT maths is focused on understanding which aspects of an equation are contributing the most to the equation solution. It involves asking yourself questions such as, “if I was to change a particular number in this formula, how would the answer change?”

Approximation and Estimation can be broken down into three sub-skills as follows:

1) Combinations

2) Rounding Numbers

3) Cancellations

Students should understand how to selectively remove elements of a formula. This will allow them to better understand what impact various combinations of variables have on the outcome of the equations.

Students should understand how to round decimals to the nearest whole number to simplify the calculation process. When rounding values, it is important to keep track of the margin and direction of error within the estimation. This is especially important when there are multiple successive calculations with successive number rounding required.

Students should be able to identify common variables and cancel them out to simplify the equation. This not only applies to numbers with values and pronumerals, but also common units. For example, Newton-Metres divided by metres would result in a value with units of Newtons.

Ignoring constants and isolating variables is another important skill we would like to emphasise in this article. Consider the following equation, what is the relationship between v_{1} and v_{2}?

An overwhelming equation no doubt. But after some thought, we can hold other variables constant since the question only asks for the variables v_{1} and v_{2}.

And derive an inverse relationship between v_{1} and v_{2}.

Unit manipulation is a common type of physics and chemistry question that has been extensively employed by ACER in the past. It is important to understand how each unit type is derived to ensure success on Section 3 as the topic is created for all of the major physics, and chemistry GAMSAT syllabus topics.

For example, if a stem discusses torque, it can be concluded that the relevant units are Newton-Metres. This is due to the fact that torque is calculated via a multiplication of force, and lever length. However this can be further broken down into Mass-Acceleration-Length units for purposes of simplification or cancellation, as is dictated by Newton’s Second Law. It is important to know how units are created for all of the major physics, and chemistry GAMSAT syllabus topics.

Ensure to watch out for alternative units.

For example, the length is not always in meters, sometimes it is in millimetres or centimetres. The standard units for torque, however, are previously mentioned to be Newton-**meters**, therefore it is critical for a candidate to consider which units they are operating with, and which units are required for the mathematical manipulation that are required to perform.

To develop the skill of mathematical graphical analysis, the first step is to recognise the shape of common functions. Take note of the shapes of the graphs in the image above. Notice the plateau of the logarithmic curve, the upward slope of an exponential curve, and the decay of a reciprocal graph.

These are common graphs which have been embedded in past biology, chemistry and physics GAMSAT questions. Knowing the shapes of each family of function is the foundation of relating equations to graphs. This is useful when comparing the behaviour of two different chemistry or physics reactions, as well as extrapolating their possible future progress.

The aspect of GAMSAT maths that requires the most consistent and deliberate practice is algebraic manipulation. It is critical to recognise the rules governing equations - specifically techniques which allow an individual to isolate, and calculate the value of unknown variables.

The above examples are a small sample of the techniques relevant to GAMSAT maths analysis - however this subject also includes more complex manipulations involving elements such as logarithms. Logarithms are incredibly common in chemistry calculations, and are most notably present in the Henderson Hasselbalch Equation, which is a mainstay of GAMSAT Section 3 Chemistry questions.

As mentioned in the previous sections, logarithm and exponential laws are the two sets of GAMSAT maths laws that the GAMSAT exam will punish you for neglecting. Logarithms and exponentials are ever present in Section 3 of the GAMSAT.

For example, biology stems describing exponential processes will often employ logarithms to convert a curved graph into a linear graph. Chemistry acid-base calculations such as pH, pKa, and Henderson Hasselbalch Equation all depend on a strong understanding of the technicalities of logarithms. GAMSAT Section 3 Physics employs exponential power and logarithms in calculations associated with half-life calculation stems, such as those referring to the Arrhenius equation .

It is practically impossible to derive the logarithm and exponential laws from first principles in the time-pressured environment of the GAMSAT exam. This means that the best way to practise this aspect of GAMSAT maths is by solving and reviewing as many logarithm and exponential questions as possible.

GAMSAT maths trigonometry is a branch of mathematics which deals with the relationships between angles and side-lengths in triangles. This discipline of mathematics is seen predominantly in physics, especially questions concerning projectile motion.

Memorisation of the specific trigonometric values is of limited value, (as they will usually be provided in the stem), it ** is** nevertheless useful to understand ‘how’ and ‘why’ the values are derived and calculated. It is also certainly valuable to make the use of mnemonics such as SOHCAHTOA when studying GAMSAT maths trigonometry.

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