Mathematics is a subject that studies concepts such as quantity, structure, change and space. It is a discipline with strict logic and high accuracy, which is widely used in natural science, engineering technology, social science and other fields. The basic knowledge of mathematics includes mathematical symbols, algorithms, functions, equations and so on.

Mathematical Common Sense: How to Solve Equations?

Solving equations is an important skill in mathematics, which can be used to solve various practical problems. Here's how to solve a linear equation with one variable.

First, we need to change the equation into a standard form: ax+b=c, where a, b and c are known numbers and x is unknown.

Then, we subtract b from both sides of the equation at the same time to get ax = c-b.

Then, we divide both sides of the equation by a at the same time and get x = (c-b)/a.

Finally, let's check whether the solution is correct and substitute x into the original equation. If this equation holds, this solution is correct.

Math Common Sense: How to Calculate the Area of a Circle?

The circle is a basic figure in mathematics, and it has many special properties. Here's how to calculate the area of a circle.

First of all, we need to know the formula of circle area: S=πr2, where S represents the area of the circle, R represents the radius of the circle, and π is a constant, which is about 3. 14.

Then, we substitute the radius r of the circle into the formula to calculate the area of the circle.

For example, if the radius of a circle is 5cm, then the area of the circle is S = π R2 = 3.14× 52 = 78.5cm.

Mathematical common sense: how to calculate the area of triangle?

Triangle is a basic figure in mathematics, and it has many special properties. Here is how to calculate the area of a triangle.

First of all, we need to know the area formula of triangle: S= 1/2× base length× height, where s represents the area of triangle, and both base length and height are known numbers.

Then, we substitute the length and height of the triangle base into the formula to calculate the area of the triangle.

For example, if the base length of a triangle is 10cm and the height is 6cm, the area of the triangle is S= 1/2× 10×6=30cm2.

Mathematical common sense: how to calculate the average?

The average value is the central value of a set of data, which can be used to describe the overall characteristics of this set of data. Here's how to calculate the average.

First, we need to add a set of data and get their sum.

Then, we divide the sum by the number of data to get the average.

For example, a set of data is 2, 4, 6, 8, 10, their sum is 30, and the number of data is 5, so the average is 30/5=6.

Common sense of mathematics: how to calculate percentage?

Percentage is a method of expressing proportional relationship, which can be used to describe the size of one value relative to another. Here's how the percentage is calculated.

First, we need to divide one value by another to get their ratio.

Then, we multiply the ratio by 100 to get the percentage.

For example, if a company has an annual profit of 6,543,800,000 yuan and total assets of 6,543,800,000 yuan, the annual profit rate is 654.38+000/654.38+000× 654.38+000% = 654.38+00%.

Mathematical common sense: how to calculate the cube root?

Cubic root is a special root of a number, which can be used to calculate the cube of a number. Here's how to calculate the cube root.

First, we need to know the symbol of the cube root:? .

Then, we express the cube root of a number as? X, where x is this number.

Then, we can use a calculator or hand calculation to find the cube root of this number.

For example, if we want to calculate the cube root of 125, then? 125=5。

Mathematics Common Sense: How to Calculate Logarithms?

Logarithm is a special exponent of a number, which can be used to calculate the power of a number. Here's how to calculate logarithm.

First, we need to know the sign of logarithm: log.

Then, we express the logarithm of a number as logx, where x is the number.

Then, we can use a calculator or hand calculation to find the logarithm of this number.

For example, if we want to calculate the logarithm of 100, then log 100=2.

Mathematical common sense: how to calculate the root of cubic equation?

Cubic equation is a kind of high-order equation, and its solution is complicated. Here's how to calculate the roots of cubic equations.

First, we need to change the cubic equation into the standard form: ax3+bx2+cx+d=0, where A, B, C and D are all known numbers.

Then Newton iteration method and Lagrange interpolation polynomial can be used to find the root of cubic equation.

For example, the cubic equation x3-6x2+ 1 1x-6=0, and its three roots are 1, 2 and 3 respectively.

Mathematical common sense: how to calculate the determinant of a matrix?

Matrix is a common mathematical tool, which can be used to represent linear equations and transformations. Here's how to calculate the determinant of a matrix.

First, we need to arrange the elements of the matrix into a square in a certain order.

Then, the determinant of the matrix can be obtained by Gaussian elimination method and cofactor expansion method.

For example, a 2×2 matrix is {{a, b}, {c, d}}, and its determinant is ad-bc.

Math Common Sense: How to Calculate Probability?

Probability is a method to describe the possibility of random events and can be used to predict the results of actual events. Here is the calculation method of probability.

First of all, we should know the symbol of probability: p.

Then, we divide the number of times an event occurs by the total number of times to get its probability.

For example, a coin has one face and one back, and we want to know the probability that it faces up, so p (face up) = 1/2.

Mathematical common sense: how to calculate the derivative?

Derivative is a method to describe the rate of change of function, which can be used to study the properties of function. Here's how to calculate the derivative.

First, we need to know the sign of the derivative: f'.

Then, we express a function as f(x), where x is the independent variable.

Then, we can use derivative formula, derivative table and so on.