Macetes: conheça alguns macetes de matemática e seja aprovado

1404

Matemática maceteada

Redigido pelo professor Julio Cesar

Durante o meu ensino fundamental e, sobretudo, no ensino médio, assim como grande parte dos alunos, eu tinha muita dificuldade em matemática. Sinceramente, não existe uma causa específica para justificar essa deficiência que os alunos apresentam, mas posso citar alguns fatos que colaboram para isso: carga horária reduzida, falta de interesse dos alunos, professores com pouca especialização, etc.

Após terminar o meu ensino médio e me matricular em um curso preparatório aqui no Rio de Janeiro, a fim de concorrer ao meu primeiro cargo público, notei, logo na primeira aula de matemática, algo que nunca mais esqueci: a matemática ensinada nos cursos preparatórios é diferente da matemática ensinada na escola.

Parece estranho o que acabei de dizer, uma vez que a matemática é uma matéria que está no campo das exatas, mas vou te explicar o porquê dessa minha afirmação. Na escola, normalmente, os professores entravam em sala e, simplesmente, guiavam-se pela metodologia de ensino dos livros didáticos, a qual era desinteressante para os alunos, pois priorizava conceitos, definições, teoremas e axiomas.

Já nos cursos preparatórios, os professores de matemática priorizam a aplicação prática das incontáveis definições que a matemática nos contempla. Assim, o aluno tende a conseguir uma melhor assimilação do conteúdo ensinado, pois a metodologia de ensino é mais agradável, ou seja, mais interessante.

A aplicação prática supracitada tem um nome: macete. Os macetes ensinados pelos professores de matemática são muito úteis nas provas de concursos públicos, pois o aluno reduz consideravelmente o tempo na resolução das questões e, consequentemente, com menos desgaste, consegue obter um melhor desempenho.

Vou te mostrar um exemplo prático dessa diferença entre a matemática guiada pelos livros didáticos nas escolas e a matemática ensinada nos cursos preparatórios: a matemática maceteada. Veja a questão abaixo cobrada no concurso para Aspirante da Polícia Militar de São Paulo pela banca VUNESP:

(VUNESP) – Os valores das parcelas mensais estabelecidas em contrato para pagamento do valor total de compra de um imóvel constituem uma PA crescente de 5 termos. Sabendo que a1 + a3 = 60 mil reais, e que a1 + a5 = 100 mil reais, pode-se afirmar que o valor total de compra desse imóvel foi, em milhares de reais, igual a:

a) 220

b) 250

c) 270

d) 280

e) 230

1ª solução: Resolução através da definição de uma Progressão Aritmética, aplicando-se duas fórmulas: 

Temos os seguintes dados: 

a1 + a3 = 60 — a1 + a1 + 2.r = 60 — 2a1 + 2.r = 60

a1 + a5 = 100 — a1 + a1 + 4.r = 100 — 2a1 + 4.r = 100

Temos um sistema de equações. Veja: 

(I) 2a1 + 2.r = 60

(II) 2a1 + 4.r = 100

Subtraindo-se os termos semelhantes das equações II e I, encontramos a razão. Veja:

(2a1 – 2a1) + (4.r – 2.r) = 100 – 60

0 + 2.r = 40

2.r = 40

r = 40/2

r = 20

Agora, substituindo este valor em uma das equações, encontramos o a1. Veja:

2a1 + 2.r = 60

2a1 + 2.20 = 60

2a1 + 40 = 60

2a1 = 60 – 40

2a1 = 20

a1 = 20/2

a1 = 10

Daí, conseguimos achar o a5 para aplicar a fórmula da soma de uma PA.

a5 = a1 + 4.r

a5 = 10 + 4.20

a5 = 10 + 80

a5 = 90

A fórmula da soma é ‘Sn = (a1 + an) / 2] x n’. Assim, temos:

S5 = [(10 + 90) / 2] x 5

S5 = [100 / 2] x 5

S5 = 50 x 5

S5 = 250

Gabarito: Letra B 

2ª solução: Resolução através de macete

Macete da soma: [primeiro + último] x metade da quantidade

Basta aproveitar a equação ‘a1 + a5 = 100’.

Como ‘a1 + a5’ representa a soma do primeiro e último termos, então basta multiplicar o valor dessa soma pela metade da quantidade de termos. Veja:

Soma = 100 x 2,5 = 250

Gabarito: Letra B

Tenho certeza que ficou evidente a diferença entre o que se ensina na escola (1ª solução) e o que se ensina em um curso preparatório (2ª solução). Existem inúmeros outros macetes que você pode aprender estudando para concursos aqui no Alfacon que é referência nacional em aprovações para os mais variados segmentos do serviço público no país.

Conversando com muitos alunos nas aulas presenciais e até mesmo pelas redes sociais, percebi que alguns já desistiram ou pensam em desistir de concorrer a vagas em concursos devido ao conteúdo programático de matemática. Calma! Isso não é necessário. Para ‘abrir a mente’ daqueles que ainda estão na dúvida, segue uma dica de um professor que também é concurseiro.

Ainda que você não se considere muito bom em matemática, pois ao longo da via nunca teve facilidade em aprender esta disciplina, acredite no potencial de seus professores nos cursos preparatórios. Eles vão te ensinar a “matemática para concursos”, começando do zero, passo a passo, sempre focados nas aplicações práticas (nos macetes) para que você possa conquistar o tão sonhado cargo público.

É isso, pessoal. Acreditem! A matemática ensinada nos cursos preparatórios é diferente da matemática ensinada na escola devido ao foco de ambos. Nesta, o foco é aprender matemática. Naqueles, o foco é a aprovação em um concurso público. Garanto que é possível ser aprovado em um concurso que apresenta matemática em seu conteúdo programático ainda que você não saiba absolutamente nada nesta disciplina, pois o nosso foco é a sua aprovação.

178 Comentário

  1. Hello! I’ve been reading your blog for some time now and
    finally got the courage to go ahead and give you a shout out from Atascocita Tx!
    Just wanted to mention keep up the good job!

  2. What’s up everyone, it’s my first go to see at this web site, and piece of writing is truly
    fruitful in support of me, keep up posting these types of articles.

    Stop by my blog – Florian

  3. We stumbled over here from a different website and thought
    I should check things out. I like what I see so now
    i am following you. Look forward to looking into your
    web page again.

  4. We would like to thank you just as before for the lovely ideas you offered Jeremy when preparing
    her own post-graduate research as well as, most importantly, pertaining to providing all
    the ideas in one blog post. If we had known of your website
    a year ago, we may have been kept from the pointless measures
    we were implementing. Thanks to you.

    Also visit my site: Vigor Max [l2ti.eu]

  5. I’d like to thank you for the efforts you’ve put in writing this site.

    I really hope to see the same high-grade blog posts by you later on as well.
    In fact, your creative writing abilities has inspired me to get my own, personal site now 😉

  6. Hey There. I found your blog using msn. This is an extremely well written article.
    I’ll be sure to bookmark it and come back to read more of
    your useful info. Thanks for the post. I will
    definitely comeback.

  7. Yesterday, while I was at work, my sister stole my iPad and tested
    to see if it can survive a 30 foot drop, just so she can be a youtube sensation. My apple ipad
    is now broken and she has 83 views. I know this is completely off topic but I had to share it with
    someone!

  8. Hiya, I am really glad I have found this information. Today bloggers publish just about gossips
    and net and this is really annoying. A good website with interesting content,
    this is what I need. Thank you for keeping this web-site, I
    will be visiting it. Do you do newsletters?
    Can’t find it.

    Look at my site; sylvbuster.free.fr

  9. You are so interesting! I don’t believe I’ve read anything like this before.

    So good to find somebody with unique thoughts on this subject matter.

    Seriously.. many thanks for starting this up. This site is something that’s needed
    on the web, someone with some originality!

    Here is my page :: Yoni Pur Tightening

  10. This is the right site for anyone who hopes to understand this
    topic. You understand a whole lot its almost
    tough to argue with you (not that I personally will need to?HaHa).
    You definitely put a new spin on a subject that’s been written about for ages.
    Great stuff, just excellent!

    Stop by my blog: Eagle CBD Reviews (http://librarius.main.jp)

  11. Thank you for the sensible critique. Me and my neighbor
    were just preparing to do some research on this.
    We got a grab a book from our area library but I think I learned more clear from this post.
    I’m very glad to see such great information being shared freely out there.

    Here is my site Caridad

  12. Hi! This post couldn’t be written any better!
    Reading this post reminds me of my good old room mate! He
    always kept talking about this. I will forward this
    write-up to him. Pretty sure he will have a good read.
    Thank you for sharing!

  13. I have to thank you for the efforts you have
    put in writing this website. I really hope to see the same high-grade blog posts from you in the
    future as well. In truth, your creative writing abilities has inspired me to
    get my own blog now 😉

    Have a look at my web blog :: Yoni Pur Review

  14. Hello there, just became alert to your blog through Google, and found
    that it’s really informative. I’m gonna watch out for brussels.
    I will appreciate if you continue this in future. A lot of people will be benefited from your writing.
    Cheers!

    Visit my website :: Ketorol Reviews

  15. I have been browsing online more than three hours today, yet I never found any interesting article like yours.
    It is pretty worth enough for me. In my view,
    if all website owners and bloggers made good content as you did,
    the internet will be much more useful than ever before.

  16. I am really impressed with your writing skills and also with the layout
    on your blog. Is this a paid theme or did you modify it yourself?
    Anyway keep up the nice quality writing, it is rare to see a great blog like this one today.

    Also visit my webpage Merissa

  17. Just want to say your article is as astonishing. The clarity
    on your publish is simply excellent and that i could think you’re a professional on this subject.
    Well together with your permission let me to take hold
    of your RSS feed to stay updated with forthcoming post. Thanks a
    million and please keep up the rewarding work.

    Here is my site :: Wawza Gummies Review

  18. It’s a pity you don’t have a donate button! I’d without a doubt donate to this fantastic blog!
    I guess for now i’ll settle for book-marking and
    adding your RSS feed to my Google account. I look forward to fresh
    updates and will talk about this website with my Facebook group.

    Chat soon!

    My website – Luiresse Skin Review

  19. hello there and thank you for your information ?
    I have certainly picked up something new from right here.
    I did however expertise some technical points using this web site,
    as I experienced to reload the web site lots of times previous to I could get it to load correctly.

    I had been wondering if your web hosting is OK? Not that I am complaining, but slow loading instances times will
    often affect your placement in google and can damage
    your high quality score if advertising and marketing with Adwords.

    Anyway I am adding this RSS to my email and can look out for
    much more of your respective intriguing content. Make sure you update this again very soon..

    my web page :: Nature Fused Cream Review

  20. What i do not understood is in reality how you are not really a lot more
    well-appreciated than you might be right now. You’re so intelligent.
    You recognize thus considerably in terms of this matter, made me in my opinion imagine it from numerous varied
    angles. Its like women and men don’t seem to be involved unless it’s one thing to do with Girl gaga!
    Your personal stuffs outstanding. All the time handle it up!

    My web-site Neo Bio Health Keto

  21. I seldom comment, but i did some searching and wound up here Macetes: conheça alguns macetes de matemática e seja aprovado.

    And I actually do have some questions for you if it’s allright.

    Is it just me or does it look like some of the remarks appear as if they
    are coming from brain dead folks? 😛 And,
    if you are posting on other social sites, I would like to
    follow everything new you have to post. Would you list of every
    one of all your communal sites like your linkedin profile, Facebook page
    or twitter feed?

    my homepage; Synaptic IQ Core Focus

  22. Wow, marvelous blog layout! How long have you been blogging for?
    you make blogging look easy. The overall look of your site is magnificent, let
    alone the content!

  23. Hi, I do believe this is an excellent web site. I stumbledupon it 😉 I will revisit yet again since I
    saved as a favorite it. Money and freedom is the best way to change, may you be rich and continue
    to help other people.

  24. I was suggested this web site by my cousin. I’m not sure whether
    this post is written by him as nobody else know such detailed
    about my problem. You’re wonderful! Thanks!

  25. This is very attention-grabbing, You’re a very professional blogger.
    I’ve joined your feed and look ahead to looking for extra
    of your magnificent post. Additionally, I have shared your website in my social networks!

    my site – Niva CBD Gummies Review; Vickie,

  26. Howdy just wanted to give you a quick heads up.

    The words in your post seem to be running off the screen in Internet explorer.

    I’m not sure if this is a formatting issue or something to do with web browser compatibility but I figured I’d post
    to let you know. The design and style look great though! Hope you get the issue fixed soon.
    Many thanks

    Also visit my website – Maximum Recall

  27. Thanks for the good writeup. It actually was once a
    amusement account it. Look complex to far introduced agreeable from you!

    By the way, how could we be in contact?

  28. Thanks a lot for being my mentor on this area. My partner and i enjoyed
    your current article a lot and most of all appreciated how you really
    handled the aspect I widely known as controversial.

    You’re always really kind to readers really like me and
    aid me in my lifestyle. Thank you.

    Feel free to surf to my web page; Infinuity CBD Review

  29. Greetings! I’ve been reading your web site for a long time now and finally got the courage to go
    ahead and give you a shout out from New Caney Texas!
    Just wanted to mention keep up the excellent job!

  30. A lot of thanks for your own effort on this site.
    My mother really likes participating in internet research and it’s really easy to understand
    why. A number of us hear all regarding the compelling way you present precious tactics via your
    website and as well foster response from others on that concern while our favorite
    princess is without question becoming educated a whole lot.
    Take advantage of the rest of the new year. You are conducting a dazzling job.

    My webpage: Derma Ella Advanced Skin Care Reviews

  31. An outstanding share! I’ve just forwarded this onto a colleague who was doing a little homework on this.
    And he in fact ordered me lunch due to the fact that I found it for him…
    lol. So let me reword this…. Thank YOU for the meal!!
    But yeah, thanx for spending some time to talk about this topic here on your internet site.

    Here is my page :: Molten Keto Garcinia

  32. Howdy would you mind letting me know which webhost you’re utilizing?
    I’ve loaded your blog in 3 completely different internet browsers
    and I must say this blog loads a lot faster then most.
    Can you recommend a good web hosting provider at a honest
    price? Thanks a lot, I appreciate it!

  33. you are in reality a excellent webmaster. The site loading speed is incredible.
    It kind of feels that you are doing any unique trick. In addition, The contents
    are masterpiece. you have performed a great process
    on this matter!

    My web blog: Modern Belle

  34. Nice post. I was checking constantly this blog and I’m
    impressed! Very helpful info specifically the last part 🙂 I care for such information much.
    I was seeking this certain info for a long time.
    Thank you and good luck.

    My website … Kieran

  35. I really love your website.. Pleasant colors & theme. Did you make this
    site yourself? Please reply back as I’m hoping to create my own site
    and would like to find out where you got this from or exactly what the theme is named.
    Thanks!

    Check out my web-site … Ilok Air

  36. I like the valuable information you provide in your articles.
    I’ll bookmark your weblog and check again here regularly.
    I’m quite sure I’ll learn a lot of new stuff right here!
    Best of luck for the next!

    Check out my website; ecuamir.com

  37. I drop a comment when I like a article on a blog
    or I have something to add to the discussion. It is triggered by the passion displayed in the post I read.

    And after this post Macetes: conheça alguns macetes de matemática e seja aprovado.
    I was excited enough to post a leave a responsea response ;
    ) I actually do have a couple of questions for you if it’s allright.
    Could it be just me or do some of these responses look
    like coming from brain dead folks? 😛 And, if you are posting
    on other online social sites, I would like to keep up
    with everything new you have to post. Could you make a list all of your social pages
    like your twitter feed, Facebook page or linkedin profile?

    Look into my blog; Dermal Pearle Reviews

  38. Nice blog here! Also your website loads up very fast!
    What web host are you using? Can I get your affiliate
    link to your host? I wish my website loaded up as fast as yours lol

    Here is my homepage: Vigalix

  39. Thank you for your site post. Jones and I are actually saving to
    buy a new e-book on this topic and your blog post has made all of us to save
    the money. Your notions really answered all our inquiries.
    In fact, above what we had thought of ahead of the time we came across your excellent blog.
    I actually no longer have doubts plus a troubled mind because you have attended to the needs above.
    Thanks

    Here is my site – Reneaux Cream

  40. First off I would like to say great blog!
    I had a quick question in which I’d like to ask
    if you do not mind. I was curious to find out how you center yourself and clear your mind prior to writing.

    I have had difficulty clearing my thoughts in getting my thoughts out there.

    I do enjoy writing however it just seems like the first 10 to 15 minutes are generally
    lost simply just trying to figure out how to begin. Any suggestions or hints?
    Thanks!

    Here is my blog post – MegaXL Advantage

Deixe uma resposta

Please enter your comment!
Please enter your name here