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Math exam – What’s Underneath

• - Calculating with fractions, variables and polynomials
• - Solving linear and quadratic equations
• - Applying properties of linear and quadratic functions
• - Calculations of simple geometric figures
• - Solve simple word problems
• - Applying properties of trigonometric functions
• - Apply basic rules of differentiation and integration

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Math – More German Curriculum!

Right, I’ve gotten my hands on more valuable Maths websites, so without further ado, here they are:

Grundwissen/Übung Mathematik - A treasure trove of Math subjects sorted by classes. This is exactly the sort of thing that really gauges you on where you stand. I know that I personally find these quite hard once I start going through grade 9.

The website has both general information and briefing of a subject and exercises with solutions (step-by-step too!)

The Math Page has various useful information on the limit “infinity” as well as general Calculus. I tend to use the approach of visiting several websites on the same topic when I’m learning something new, it helps to see the topic with different eyes and helps me when one single source may fail. Karl’s Calculus is another page worth a visit.

Updates:

Bruchgleichung, or the calculation of fractions. Here are some more exercises.

Wurzelgleichung, equations with roots and radicals. This website goes step-by-step to show you the ways of solving.

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Getting Up To Level With Maths

The main problem with preparing for an entrance exam in maths is that your required learning may not be clearly stated by your university or college of choice. Don’t assume that your O-level Mathematics class will be enough, especially for a German university! I learned the hard way. This applies to other countries as well, where a knowledge of a very vast subject like Mathematics may be learned in different ways. It’s as simple as having a different curriculum and you wouldn’t notice it if you never cross-check.

Notation

The basic item which will also become most obvious to you is the different mathematical symbols used. Take the multiplication sign: It’s x or * in my English syllabus, but · in German. Yes, that dot in the middle.

Let’s look at the division sign. Fair enough, it’s ÷ in English, but it lacks the bar in German and simply looks like : (The two overhanding dots). You can also use the diagonal bar / in either, but that sort of thing is something you can figure out on your own.

German school systems may use different notation for answers or have additional parameters you need to state in your answer. For instance, a number may be part of a set of integers or real numbers. The phrase “element in a set of” is denoted by the symbol ∈. Besides knowing what the symbol stands for, you need to know how to use it.

For instance, a ∈ Z means that a certain variable “a” is an element of a set of integers.

Here’s another one: a ∈R {2;4}
That right there means that “a” is an element of a set of real numbers, but excluding 2 and 4.

By the by, the Z and the R are also mathematical notation! You’d need to know what a real number is, what an integer is. “-3″ – is that a real number? Is that an integer? Such things are very important when you’ll have an answer and need to check with your given definition in an exercise.

This information might all be very old stuff for you, but for someone like me it was all news and hieroglyphs when I first got into German mathematics.

Try the German Wikipedia entry on Mathematical notation, as well as this web page; it’s always handy to keep more than one reference. If you get your hands on a German textbook, it’s even better, they usually have a list of notation in the front.

Compare The Syllabus

It all goes down to comparing what you learned to what the equivalent class of the country of your choice learned. Did you know what German gymnasium children learned about limits and derivatives back in class 9? We never had it at all. I do believe you only began learning about it in A-levels, which is basically Grades 12 and 13.

Although you might be given a thorough list of subjects you will need, bear in mind that your methods of solving might be different; the German schools might explain everything more thoroughly. You’re liable to get the worst sums for your exams and without a way to solve them, but it’ll be a subject you studied in your school.

That’s what happened to me an Absolute Value Inequalities. We did them in school in a very limited way, so when the exam rolled about, I was caught unable to solve the sum.

The Internet is your biggest help here, especially if you’re unable to find German math books in your country.

My List of Subjects

This is more of a safe-keeping part of the post where I’m putting down all the points I covered in Maths so far. This is the sort of Maths that the German students learn and which I am covering in my self-study. Not all of it will actually come for my test, but introducing yourself to everything is a good way to cover your basics.

Trigonometry + Unit Circle + Trigonometric Functions
Algebra + Exponentials + Logarithms + Division of a polynomial + Finding the roots of an equation
Absolute Value Equations and Inequalities + Multiple Absolute Value Inequalities
Calculus + Differentiation (First differential, second differential, etc) + Integration + Sketching graphs of a differential of a function + Finding the area of a graph using integration
Graphs + Finding the equation of a graph + Sketching a graph of a function
Limits + Limits at infinity

And additional items I personally didn’t need for my exam, but which I have studied nevertheless:

Vectors
3-Dimentional graphs
Probability
Various shape problems
Matrices

Related Entries:

Math Using Internet’s Help

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Maths Using Internet’s Help

I’m preparing for my math entrance exam – a daunting task, since German mathematics is harder than English maths, in the sense that my GCSE O-level curriculum didn’t include a lot of what the German students are taught. This might very well be since they take a year or two longer to finish up with school, but their mathematic symbols are ones I’ve never seen used in school. They’re official math symbols, good and proper, just nothing I’m used to.

Below I’ve got my top two learning resources for the new material I just didn’t learn in High School – Calculus and in-depth Trigonometry. It was a nasty surprise, learning that German gymnasium students started with differential equations as early as Grade 9!

Learning Resources

Paul’s Online Math Notes - An invaluable resource for personal study! Paul put Algebra and Calculus material in a form I could understand much better. A must for those without prior knowledge of Calculus, for example.

PatrickJMT’s YouTube Channel - This saved me! I could finally understand Calculus through his videos. They have me a teacher who could explain in really simple terms and draw as he explained. Definitely use this in conjunction with Paul’s Notes. He has videos on Calculus and Trigonometry, both important parts of German maths education.

Others

Here are bits and bobs; pages that only cover one topic, but which do it well.

Nullstellen - This website gives a pretty good explanation of what a Nullstelle is. Auf Deutsch, naturally, but you should have no problem with a translator like Google.