Mathematics is an integral part of physics. No theory in physics is accepted as true without a mathematical equation to support it. This means that you will be doing a lot of mathematics when studying physics. Here are the mathematical requirements to study physics in Singapore.
In arithmetic, you must be able to do the following:
- Know the meaning of mathematical expressions given in decimal and standard form and use them in calculations.
- Compute arithmetic means, powers (including square roots and reciprocals), exponentials, logarithms, sines, cosines and tangents (and their inverse functions). For example: What is the square root of 50625 and the value of 1/2000?
- Calculate the approximate value of complex numerical expressions and use them to check the magnitude of calculations. For example: What is the approximate value of p2?
In algebra, you must be able to do the following:
- Change the subject of equations. The equations may include square roots, exponentials, and negative and positive indices.
- Solve algebraic equations. The equations may be linear, linear simultaneous or quadratic and may also involve inverse and inverse square relationships.
- Convert physical quantities into mathematical equations using the correct units of measurement and ensuring the dimensional consistency of the equations.
- Create mathematical models of physical situations by formulating simple algebraic equations, and identify the shortcomings of such models.
- Have a good grasp of the logarithmic forms of expressions like ab, a/b and xn and be able to use them in relation to quantities that have values of several orders of magnitude.
- Solve equations involving logarithmic and exponential functions
- Be familiar with the use of mathematical symbols like «, », ?, /, ?, ( = x ), ?, ?x, ?x, ? in algebra.
3. Geometry and Trigonometry
In geometry and trigonometry, you must be able to do the following:
- Calculate the area of triangles (right-angled and isosceles), area and circumference of circles, and area and volume of rectangular blocks, spheres and cylinders.
- Understand and use Pythagoras’ theorem, similarity between triangles, and the sum of an angle of a triangle.
- Calculate the values of sine, cosine and tangent for different angles.
- Understand the difference between degrees and radians and know how to convert degrees to radians and vice versa.
In vectors, you must be able to do the following:
- Calculate the resultant vector of two coplanar vectors.
- Obtain the right expression for the components of a vector in perpendicular direction.
In graphs, you must be able to the following:
- Interpret the meaning of the information provided by different types of graphs.
- Plot graphs using the appropriate variables and scales.
- Determine the slope, intercept and intersection of linear graphs.
- Find, by inspection, the line of best fit for a set of data points that are presented graphically.
- Know the standard linear form y = mx + c.
- Plot a graph of simple expressions like 1/x, x2, 1/x2, sinx and cosx.
- Draw the slope of a tangent to a curve in order to obtain the gradient.
- Test exponential and power law variations using logarithmic plots.
If you still feel uncomfortable in your application of these mathematical formulae, joining a physics tuition will help you improve in this area. The extra practice and time spent on the applications will help you get more comfortable with these concepts, which is especially essential in examinations where you have to perform under stress.