How do I learn in grade 9

Mathematics, 9th grade

In the 9th grade you will also learn a lot of exciting things from various mathematical areas such as geometry, functions and stochastics.

geometry

In geometry you will mainly deal with calculations on different bodies, circles and polygons.

body

Now that you've learned how to calculate the volume and surface area of ​​bodies like prisms and cylinders, you are ready to go pyramid, Bullet and cone on the plan. The Cavalieri and the Euler's polyhedron substitute discussed in class.

Circles

You already know that the circle number Pi ($ \ pi $) has an important function for calculations on circles. For example, you can determine the area and perimeter. Are also helpful Circumferential angle set and the Center point angle set. Not just the whole circle, but also parts like Section of a circle, arc and segment of a circle can be calculated. There are, for example, tasks such as dividing a cake or packing a pizza slice.

Polygons

If you have mainly calculated with triangles and squares up to now, you may now learn a lot Pentagons and also the Heron's formula.

Numbers, arithmetic and quantities

In this sub-area of ​​mathematics, you face some new topics: powers, roots, and logarithms.

Powers and power laws

Potencies are numbers with a superscript exponent, such as $ 3 ^ {6} $ or $ 10 ^ {2} $. The exponent can also be negative or rational. The Power laws are used for correct arithmetic with powers. For example, one thing says that when you multiply the powers, the exponents are added.

Logarithms and logarithmic laws

The inversion of exponentiation is called Logarithm. The logarithm helps you find an unknown exponent. There are special logarithms such as the Logarithm naturalis $ \ log_e = \ ln $. And here too you need Logarithmic Lawsto be able to calculate correctly.

Roots and Root Laws

Also root are very useful for computing powers. In this way an unknown basis can be determined. The second root of a number is most commonly used in schools, namely the square root $ \ sqrt [2] {x} $. With the help of Root Laws do you know how to calculate well with roots.

Terms and equations

In addition to the linear and quadratic equations you are familiar with, there are both Power and root equations as well as Exponential and logarithm equations added. Also important are the so-called trigonometric Equations, so the Equations with sine, cosine and tangent. These applications are important for angles in a triangle, for example.

Functions

Just as there are linear and quadratic functions, there are also Power and root functions as Exponential and logarithmic functions. Here it is important that you know the various laws of calculation well. Perhaps this year you will also learn how to derive functions. This then takes place in so-called Curve discussions, in which you examine various properties of functions, play a role.

Probability Theory and Stochastics

Depending on what you learned in the last school year, different new content will be added. Data evaluation using various parameters and Data representation for example with Box plots you probably already know. In multi-level random experiments, there are those with or without Return and which with or without heed the sequence. Important terms are also Laplace experiment and Bernoulli experiment.