Macetes: conheça alguns macetes de matemática e seja aprovado

Por
Carolina Michelin
-
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.

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