Precalculus courses combine algebra and trigonometry to prepare students for studying calculus. Of course, precalculus is a bit easier to study than calculus, but often students have problems with it as well. For such cases, they can get precalculus homework help from professional experts. Such experts can assist with anything starting from irrational numbers to quadratic equations.
How to solve problems correctly
If you are just starting to master the skill of solving problems, you need to adhere to a certain algorithm.
Carefully read the conditions
It is better to do it out loud and several times. After you have read the problem, make sure that you understand what should be calculated. Try not to be nervous if you miss something. Try to figure out what you haven’t paid attention to. If the conditions mention realities unknown to you, check the textbook for explanations.
Make a description of the task
In solving some problems, the presentation of data in the form of a diagram, graph, or picture will help. The brighter the image is, the easier it will be to comprehend. A visual record will allow you not only to quickly understand the conditions of the problem but also help to see the connection between them. Often a solution plan arises at this stage.
You should clearly understand the meanings of verbal formulas and know what mathematical actions correspond to them.
Choose a solution
A clearly written condition should push you to find a solution. If this does not happen, try to illustrate the problem with the help of surrounding objects. If this method did not work, try to come up with another. Repeating the same method over and over is ineffective.
All, even the most complex, precalculus problems are reduced to the principle “from two known we get the unknown.” But to find this pair of numbers, it is often required to perform several actions, that is, to decompose the task into several simpler ones.
Once you have found an action plan, write down the solution in detail. It should reflect the entire sequence of actions – so you can remember the principle and use it in the future.
The answer must be complete and accurate. This is not just a formality: when considering the answer, you get used to taking the results of your work seriously. And most importantly, the logic of the solution should be clear from the description.
One of the most common mistakes is that, in the answer, you present not the data that was originally asked for. If such a problem arises, you need to return to the first point.
Fix the result
Do not think that after completing the task once, you will immediately learn to solve problems. The result obtained must be fixed. To do this, think about the solved problem a little more: look for another solution or think how the answer will change when one or another parameter in the condition is changed.
It is important that you have a clear algorithm of reasoning and actions in each of the options.
What will help you solve problems
In conclusion, let’s talk about how to make the process of solving problems easier and more interesting:
- In order to solve problems, you need to be able to count. You should learn the multiplication table, master examples with fractions, and simple equations.
- So that solving problems do not turn into a routine for you, show your imagination. Change the text of the assignment in accordance with your interests.
- A student with developed logic learns to solve problems faster. We advise you to dilute precalculus tasks purely with logical ones. Tricky tasks will relieve you of stereotyped thinking, and tasks with a large amount of unnecessary data will teach you to highlight the main thing from a large number of conditions.
After you have solved enough problems of one type, come up with the problem yourself. This will allow you not only to consolidate the material but also to show creativity.
3 hardest math problems that remain unsolved
Over the centuries, the best minds of mankind have solved one mathematical problem after another, but there are several that have not succumbed to anyone so far. Some funds and companies are ready to pay big money for finding an algorithm for their solution.
Little progress in solving this problem was outlined not so long ago. However, the famous American mathematician Terence Tao only came closest to it but still did not find an answer. The Collatz conjecture is the foundation of such a mathematical discipline as Dynamical Systems, which, in turn, is important for many other applied sciences, such as chemistry and biology.
The binary Goldbach conjecture
The problem was formulated by Christian Goldbach in his correspondence with another great mathematician, Leonhard Euler, in 1742. Christian himself posed the question in a somewhat simpler way. In 2013, the mathematician Harald Helfgott found the final solution to this option. However, the consequence of this statement proposed by Euler, which was called the “binary Goldbach conjecture,” still defies anyone.
Twin prime conjecture
As always in mathematics, if the problem is not solved, it is approached from the other end. For example, in 2013, it was proved that the number of primes differing by 70 million is infinite. At the same time, with a difference of less than a month, the value of the difference was improved to 59 470 640, and then to 4 982 086. At the moment, there are theoretical justifications for the infinity of pairs of primes with a difference of 12 and 6; however, only a difference of 246 was proved. Like other problems of this kind, the twin prime conjecture is especially important for cryptography.
If you follow our advice, you can quickly solve any precalculus problem. Good luck!