How can I brush up on my mathematical basics?

Mathematics basics / basic knowledge

What basics in mathematics should one definitely be able to do? What basic knowledge is important in math? You will be given an answer to this in the next few sections. An important note about this: a teacher in school will understand mathematics fundamentals as something different than a professor with a doctorate.

The absolute basics in mathematics are of course covered in elementary school. For this reason, let's first take a look at important basics from elementary school. First learn the addition and subtraction in the number range of 10 and 20. Then you should practice multiplication and division:

If the numbers are a little larger, written procedures are useful.

It makes sense for both students and adults to know some important units and be able to deal with them. Initially, these would be time units such as seconds, minutes and hours. Everyone should also know lengths (distances). With these units of length, centimeters, meters and kilometers are extremely important. When it comes to weights, grams, kilograms and tons are on the agenda. These are very important fundamentals of math, as well as dealing with money:

Important rules of mathematics are also basic knowledge in mathematics. These are, for example, the point before line rule or rounding rules. These topics and a few other important areas are included in the next small list:

Basic knowledge of mathematics in secondary schools and high schools

Absolute basic knowledge of math is taught in elementary school. But please don't get it wrong: This is only basic knowledge. Of course, other relevant topics are dealt with in the following grades. Laws in mathematics and units for lengths, areas, weights and volumes are important.

In the secondary school and high school, further math basics are dealt with. This also includes the prime numbers, the gcd (greater common divisor) and the lcm (smallest common multiple). The basics of powers, the coordinate system and of course fractions are highly relevant. Learn them!

From the sixth grade in mathematics, equations and inequalities are calculated. Fractions and brackets can also appear in the equations. Three other big topics belong to the basic knowledge of mathematics: Percentage calculation, interest calculation and the rule of three. Also take a look at the basics of probability theory (6th grade).

It continues with important topics in mathematics. This basic knowledge of mathematics is only imparted to a limited extent in the Hauptschule, while the subjects are dealt with more extensively in the Realschule and Gymnasium. Here is a mix of different topics:

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Mathematics fundamentals secondary level

In the last sections we introduced you to important basics in mathematics and linked the relevant topics. To do this, you should know two things:

  1. These were just a few topics from the basics. The list could be extended as much as you like. In doing so, however, we would massively go beyond the scope. For this reason, we have again broken down by grade level to create another overview up to grade 9.
  2. If this is not enough for you and you find it insufficient, there is another remedy. In the mathematics overview you will not only find the basics but also other topics related to higher mathematics.

Here is the list of topics sorted by grade level, there is also content for the secondary level.

Math divided by grade level:

One more tip at the end: do tasks! Only those who solve exercises themselves will be fit in the various topics of mathematics.