“Mathematics is worth studying because she’s got her mind in order,” said Lomonosov. And in fact, anyone can study it, no matter whether you’re preparing for your final exams or just decided to repeat the basics. From this article you will learn about the main sections of mathematics, with an emphasis on basic arithmetic necessary for junior high school students and all repeaters.
Part 1: How to do well with math in school
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Don’t miss out on lessons. If you miss a lesson, you will have to disassemble the material yourself or ask for help from one of your classmates. Of course, the teacher will explain something new better and more accessible.
Don’t be late. It’s better to come in advance, not just before the bell. Lay out the supplies and prepare for class.
Disease is the only valid reason to skip class. If you miss a lesson, be sure to ask your classmates about the topic and homework.
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Work with your teacher. If the teacher explains an example on the blackboard, write everything down carefully in the notebook.
Make sure that all entries are made clearly and clearly. Not only write down the example, but also write down everything the teacher says to help you learn new material.
Perform all the tasks that the teacher has given you. Be active: answer the questions.
If the teacher decides something on the board, participate. Do you know the answer to the question? Raise your hand and answer Something you don’t understand?
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Do your homework the same day it is done while your knowledge is still fresh. Sometimes it doesn’t work out, but most importantly, never come to class unprepared.
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If you need help, work out of class. At recess, go to the teacher and ask about extra lessons.
Join a group of schoolchildren, students on your own. There are usually children of all levels in these groups. If you are a Triple-A student, join a stronger group of kids, high achievers and good students. This will allow you to tighten up your level. Avoid groups with weaker students.
Part 2: Studying Mathematics at School
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Start with the arithmetic. The vast majority of schools in primary school teach arithmetic, which includes the basics of addition, subtraction, division and multiplication.
Work on examples. Solving many examples and problems again will allow you to learn the basics properly. Look for computer programs with many examples to solve. To increase the speed of the solution, set yourself a time limit.
Arithmetic examples can be found on the Internet, you can download the appropriate application to your phone.
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Go on to the basics of algebra. From this section you will learn the important basics.
Learn ordinary and decimal fractions. You will learn how to add, subtract, divide and multiply both decimal and plain fractions. As for the common fraction, you will also learn how to reduce them, learn what mixed numbers are. As for the decimal, you will learn all about digits and learn how to use fractions to solve problems.
Learn the proportions and percentages. These concepts help you compare different values.
Learn the basics of geometry. You will learn about all figures, both two- and three-dimensional. You will also learn about concepts such as area, perimeter, volume, surface area, parallels, perpendiculars and angles.
You will learn the basics of statistics. Graphs and different types of charts.
Learn to understand the basics of algebra. Learn to solve simple equations, draw their diagrams, solve inequalities, find areas of definition.
The transition to algebra. You will continue to study algebra, learn:
Solve equations and inequalities containing variables.
Problem solving. You will be surprised to learn how useful knowledge of algebra can be in everyday life. For example, algebra is needed when calculating interest rates in a bank or determining the duration of a necessary trip by car.
Working with degrees. Having started to solve equations with polynomials (containing both numbers and variables) you will need to deal with degrees, after that you can perform arithmetic operations with polynomials.
Finding squares and square roots. By studying this topic, you will know squares of numbers, and you will be able to solve equations with square roots.
An understanding of functions and charts. In algebra you will encounter graphical equations. You will learn how to find the slope of a line, how to plot functions, how to find intersection points on axes.
Solving systems of equations. Sometimes you are given two separate equations with variables x and have to find them for both equations. You will learn how to solve such systems of equations, including: graphing, replacement, addition, etc..
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Geometry. You will learn about properties of lines, segments, angles, different shapes.
You will learn the theorems and rules that will help you understand geometric concepts.
You will learn to find the area of a circle, to use the Pythagoras theorem, to learn how corners are connected with the lengths of sides of triangles.
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Continued algebra. You will learn more about previously mastered concepts and encounter new material like square equations and matrices.
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Trigonometry. You will learn such terms as: sinus, cosine, tangent, cotangent, etc. In the course of trigonometry you will learn many practical ways to find angles and lengths of sides. These skills are particularly useful for work in construction, architecture and engineering.
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Why is gre hard?
Mathematical analysis. It may sound scary, but it’s a very important and interesting section of mathematics.
You will learn about functions and their limits as well as logarithmic functions, is gre hard.
You will learn how to find derivatives. The first derivative contains information about a tangent angle. For example, thanks to the derivative, you can determine how often something changes in a nonlinear situation. The second derivative lets you know whether a function increases or decreases within a certain range.
From the Integral section you will learn to find the area separated by the curve and the volume.
The school course of mathanalysis usually ends with differential equations.
Part 3: Basics of Mathematics– work on the addition
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Start with a “+1”. By adding to number 1 you get the next number in order. For example, 2 + 1 = 3.
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Understand what zero is. Zero is “nothing”, and by adding zero you get the same number.
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Learn to double. Doubling is multiplication by two or adding it to your own. For example, 3 + 3 = 6.
Use a grade 2 math gamesand you can master the addition more quickly. In the example below, you can clearly see what happens when you fold 3 and 5, 2 and 1. Try to “add 2” yourself.
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The fold is after 10. Learn to stack 3 or more numbers.
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Add more numbers. Examine the digits of units, tens, hundreds, etc.
First add the numbers in the right column. 8 + 4 = 12, which means we have 1 tens and 2 units. Write 2 in a column of units.
Write 1 column of tens.
Add up the numbers in the tens column.
Part 4: Basics of Mathematics – Subtraction methods
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Start with “back to one.” By subtracting from number 1 you just get the previous number. For example, 4 – 1 = 3.
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Study the subtraction after doubling. For example, we get 5 + 5 with 10. Write the opposite and get 10 – 5 = 5.
If 5 + 5 = 10, then 10 – 5 = 5.
If 2 + 2 = 4, then 4 – 2 = 2.
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Remember that. For example:
3 + 1 = 4
1 + 3 = 4
4 – 1 = 3
4 – 3 = 1
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Find the missing numbers. For example, _ + 1 = 6 (answer – 5).
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Remember the subtraction to 20.
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Practice subtracting unambiguous numbers from two-digit numbers without doing anything. Subtract the numbers in the first column(s) and simply move down the number from the second column(s).
Try to spread the numbers by digits.
32 = 3 tens and 2 units.
64 = 6 tens and 4 units.
96 = _ tens and _ units.
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Practice subtracting with exercise.
You have to subtract 42 to 37. You can’t subtract 2 – 7 in the first column!
We lend 10 in a column of tens and put it in the first column. Now instead of 4 tens we have 3, but instead of 2 units we have 12.
First, we subtract in the first column: 12 – 7 = 5. Then we go to the second column (tens): 3 – 3 = 0, 0 should not be written. Answer: 5.
Part 5: Fundamentals of Mathematics — Methods of Multiplication
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Start with 1 and 0. When you multiply a number by 1, we get that number. When we multiply the number by 0, we get 0.
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Remember the multiplication table.
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Resolve examples by multiplying unambiguous numbers.
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Multiply two-digit numbers by single digits.
Multiply the number from the bottom right to the top right.
Multiply the bottom right number by the top left number.
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Multiply two double digit numbers.
Multiply the bottom right number by the top right number and then the top right number.
Move the second row by one digit to the left.
Multiply the number from the bottom left to the top right, and therefore the number from the top left.
Fold it up in a column.
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Multiplication with repositioning of columns.
Multiply 34 x 6. Start by multiplying the first column (4 x 6), but you cannot put 24 in the first column.
We leave 4 in the first column. 2 we transfer in the second column (tens).
We multiply 6 x 3, we receive 18. We add the transferred 2, it will be 20.
Part 6: Basics of Mathematics – Division
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Splitting is the opposite of multiplication. If 4 x 4 = 16, then 16 / 4 = 4.
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Write down an example.
Split the number to the left of the division sign, dividable, but the first number of the divider. Since 6 / 2 = 3, we write 3 above the dividing sign.
Multiply the number above the divider sign by the divider. Write the result under the first number under the dividing sign. 3 x 2 = 6, then we write 6 down.
We subtract the 2 recorded numbers. 6 – 6 = 0. We can leave it at 0.
Write down the second number under the division sign.
Divide the number written at the bottom by a divider. In our case 8 / 2 = 4. Write 4 above the dividing sign.
Multiply the number from the top right by the divider and write the number down. 4 x 2 = 8.
Subtract the numbers. The last subtraction gives 0, so the example is solved. 68 / 2 = 34.
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Consider the residue. Some numbers are not shared entirely and the remainder, the last number.