Calculation in Section III
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The absence of a calculator in the GAMSAT requires you to adjust your approach to calculations. Rather than targeting absolute answers with a high number of significant figures, you will need to develop methods that enable rapid estimation.
Rounding numbers to indicate the minimum and maximum expected answer values is a good way to make numerical calculations manageable.
If only one answer option sits within the estimated range then this answer must be correct.
Estimating the calculation shown above may be necessary to answer a GAMSAT question. Here, the first thing to notice is that This simplifies the calculation significantly:
Now make the calculation of as simple as possible:
Minimum:
Maximum:
The solution should sit between and with the factor of 10 included: answer D is the only feasible answer.
If there were more answers still in scope, you would need to consider a more accurate estimate, and the associated time cost, or a different approach.
Learn the basic square and cube roots and use them to estimate the value of unknown surds.
In the table below, the most useful surds to memorise are highlighted.
An example of using this recall practically is estimating the value of
The solution of will be slightly less than but much greater than Therefore, the result would be approximately 3.8.
You will need to be comfortable rearranging algebraic equations quickly. If you can do this without much mental effort, you can focus on the reasoning.
In questions where you are comparing the output from two or more different inputs, look for ways to cancel out duplicated terms of the equation rather than solving each scenario completely.
In the example above, we are interested in moles, so rearrange to make the subject.
Ignore any of the figures for or the question states that they will be the same at both temperatures and therefore can combine to form a proportionality constant
This tells us is inversely proportional to Doubling halves
The only numeracy required is very simple:
Therefore:
So, the number of moles decreases by:
Answer D is correct.
Question walkthrough
Working with complex formulae
Analyse an advanced formula using calculation skills to determine the correct answer
ACER states that students should have familiarity with physics up to Year 12 level and biology and chemistry up to first-year university level. By association, the inclusion of mathematical competencies associated with the sciences at this level is to be expected in Section III.
Some of the calculation skills required to maximise your score for Section III are illustrated below.
These are six log rules most strongly linked to the sciences at the level required for GAMSAT.
Logarithms apply heavily in questions related to pH, where the “p” notation means a negative base-10 logarithm, so that:
A change in changes pH by 1 unit.
When applying these rules, the natural log is the same as where The natural logarithm is the inverse of the exponential function:
Except for the change of base rule, log laws can only be applied if there’s no change in the log’s base in the expression.
Logs can be converted to exponential form if required:
You could be expected to apply the rules of indices in calculations.
![SIX ESSENTIAL LAWS OF INDICES FOR GAMSAT: Exponent of 0: x^0 = 1; Negative exponent: x^-n = 1/x^n; Product: x^n × x^m = x^(n + m); Quotient: x^n ÷ x^m = x^(n - m); Power: (x^n)^m = x^(n*m); Radical: x^(m/n) = √[n]{x^m}](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3NDAyLCJwdXIiOiJibG9iX2lkIn19--b5c0f546351f88c94b6a5bba8960ee8f55a6a3d4/GM_S3_SK_008_light.png)
![SIX ESSENTIAL LAWS OF INDICES FOR GAMSAT: Exponent of 0: x^0 = 1; Negative exponent: x^-n = 1/x^n; Product: x^n × x^m = x^(n + m); Quotient: x^n ÷ x^m = x^(n - m); Power: (x^n)^m = x^(n*m); Radical: x^(m/n) = √[n]{x^m}](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3NDAzLCJwdXIiOiJibG9iX2lkIn19--8527b18ac0fea25995b8cb2e9071aa6e3851aacb/GM_S3_SK_008_dark.png)
Index laws can only be applied when there is no change to the base of the exponent in the expression.
Exponents can be converted into logarithmic form as required:
Many scientific figures will be displayed in standard form to 3 s.f.
Numbers on tables and axes in graphs can often be written in the standard form with the unit. For example, pollution levels as
Prefixes are used to write fractions and multiples of units in compact form.
Except for kilo, uppercase prefixes multiply by a factor greater than 1, whereas lowercase prefixes multiply by a factor less than 1.
Pythagoras and trigonometry, as applied to right-angle triangles, have applications in physics through the resolution of perpendicular forces.
Given the lack of a calculator, the nature of questions involving trigonometry may:
- Give values to input for a specific term (e.g. )
- Require the use of exact values (e.g. from the triangle for )
- Leave answers in a form containing the trigonometric function
Not all calculations relating to right-angle triangles require trigonometry. Where only lengths are required, Pythagoras can be applied.
Any differentiation or integration in GAMSAT is likely to be limited to polynomials.
Simple differentiation and integration are used to find rates of change, gradients and areas.
![DIFFERENTIATION AND INTEGRATION OF POLYNOMIALS. Differentiation: d/dx [x^n] = n × x^(n-1). Integration: ∫ x^n dx = 1/(n + 1) x^(n+1) + c, n ≠ -1.](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3MzIyLCJwdXIiOiJibG9iX2lkIn19--260683dd42612b2fb177b9c1ad7a7f7f7dd2ed7c/GM_S3_SK_012_light.png)
![DIFFERENTIATION AND INTEGRATION OF POLYNOMIALS. Differentiation: d/dx [x^n] = n × x^(n-1). Integration: ∫ x^n dx = 1/(n + 1) x^(n+1) + c, n ≠ -1.](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3MzIzLCJwdXIiOiJibG9iX2lkIn19--39dd770496c40d89014562d931a0a89832c4d675/GM_S3_SK_012_dark.png)
Medify does not consider formal calculus theory to be a core skill needed to succeed in Section III, but a basic level of knowledge will prove useful if your sitting happens to be the one where it comes up.
It is common to be given formulae within Section III of the GAMSAT.
It is highly likely you will encounter several formulae you have never seen before during your sitting. They can sometimes be relatively dense and intimidating, often containing multiple terms. This will test your ability to comprehend the formula and develop an understanding of what it reveals and how it can be applied.
More ‘typical’ formulae are sometimes included, but can also be assumed to be part of your baseline scientific literacy. There is no consistency of the application here, and we strongly recommend you become familiar with the core formulae in this article before sitting Section III.
Knowing these formulae in biology will help.
To succeed in the chemistry section of the exam, you should feel confident with these key formulas. This will allow you to apply reasoning effectively to typical chemistry questions, even those where the formula is not provided.
![FUNDAMENTAL FORMULAE IN CHEMISTRY: ΔG = ΔH – TΔS Gibbs free energy, ΔG = –RTln(K) Gibbs free energy, c = n/V Concentration, n = m/Mr Molar mass, pX = –log[X] Potential of X, PV = nRT Ideal gas law, k = Ae^(-Ea/RT) Arrhenius rate, PA = xA × ptot Partial pressure, ptot = pA + pB + ... Total pressure, Kc = [C]c[D]d/[A]a[B]b Equilibrium constant (concentration), Kp = [pC]c[pD]d/[pA]a[pB]b Equilibrium constant (pressure), E°cell = E°cath – E°an Cell potential © Medify](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3Mzk2LCJwdXIiOiJibG9iX2lkIn19--ce4afd81d2904454088e0bf207091b82668a6f57/GM_S3_SK_015_light.png)
![FUNDAMENTAL FORMULAE IN CHEMISTRY: ΔG = ΔH – TΔS Gibbs free energy, ΔG = –RTln(K) Gibbs free energy, c = n/V Concentration, n = m/Mr Molar mass, pX = –log[X] Potential of X, PV = nRT Ideal gas law, k = Ae^(-Ea/RT) Arrhenius rate, PA = xA × ptot Partial pressure, ptot = pA + pB + ... Total pressure, Kc = [C]c[D]d/[A]a[B]b Equilibrium constant (concentration), Kp = [pC]c[pD]d/[pA]a[pB]b Equilibrium constant (pressure), E°cell = E°cath – E°an Cell potential © Medify](/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTM3Mzk3LCJwdXIiOiJibG9iX2lkIn19--de0e436bd978f8a5ca39b8665d1b2df1615214fc/GM_S3_SK_015_dark.png)
These are covered in more detail in articles within Medify’s scientific literacy study notes.
Physics is more formula-heavy than biology and chemistry. You are more likely to encounter questions that incorporate your understanding of the concepts underlying the formulae than those requiring a numerical solution derived from an unprovided formula.
It is critical to remember that the equations of motion are only valid under constant acceleration.
The equations of motion are also known as the suvat equations:
- s = displacement
- u = initial Velocity
- v = final Velocity
- a = acceleration
- t = time
These equations are correct for constant mass and non-relativistic speeds.
