MATHEMATICS TEST - COURT OFFICER OF TJ SP (DECEMBER 2024)

RESOLUTION OF THE MATHEMATICS TEST, OF THE HIGHER LEVEL COMPETITION, FOR COURT OFFICER OF THE TJ SP, WHICH TOOK PLACE ON DECEMBER 15, 2024
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Question 83 (Percentage and 1st degree equation)
A capital of R$ 35,000.00 was divided into two parts, with the largest part invested in investment A, with an interest rate of 7% per year, and the smallest part in investment B, with an interest rate of 8% per year.
After one year, the total return on these two investments was R$ 2,580.00 and, if instead of investing the smallest part in investment B, investment C, whose interest rate was not pre-fixed, had been chosen, the total return on the investments would have been R$ 2,801.00.
In this one-year period, the interest rate effectively paid by investors who chose investment C was equal to:
Question 84 (System of first-degree equations and Simple rule of three)
Regarding the pie chart shown below, it is known that sector A has a central angle measurement corresponding to a quarter of the central angle measurement of sector B, and that sector C has a central angle measurement 180º greater than the central angle measurement of sector A.
With this information, it is correct to state that if the sum of the number of elements belonging to sectors B and C is 220, then it is certain that the number of elements belonging to sector C is equal to:
Question 85 (Simple and weighted arithmetic mean)
In a public examination with two phases, the weight of the grade corresponding to the evaluation in the second phase is twice the weight of the grade corresponding to the evaluation in the first phase.
In each of these phases, the assessment score can range from zero to 100 points, and the final score is the weighted arithmetic mean of the scores for these phases.
A candidate scored 45 points in the first phase assessment, and if the final score had been calculated using the simple arithmetic mean, the simple arithmetic mean would have been 3 points lower than the score actually calculated using the weighted arithmetic mean.
The score that this candidate scored in the second phase assessment is between:
Question 86 (Ratio, Proportion and Area Calculation)
A rectangular sheet of paper will be divided into two regions by a segment with one end coinciding with a vertex of the sheet and the other end at point E, which is on the side of the sheet, as shown in the figure below.
Knowing that point E divides the side of the sheet into two parts, so that the ratio between the measurements of these parts is equal to 4/5, the ratio between the area of ​​region 2 and the area of ​​region 1 is equal to:
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[@viniciustorres1567]

Perfeitamente, professor! Muito obrigado pela correção! Vou compartilhar com os colegas

[@diegosb7200]

Parabéns, Professor Joaquim!
Levei um pau nessa prova na parte de matemática, RLM chutei duas pq o tempo estava acabando!!!

[@CanaldoProfessorJoaquim]

Olá Diego,
A prova de matemática, até que não estava difícil.
Apenas aquela última questão, que não concordei, pois falta informação no texto, para a tomada de decisão.
Penso que deveria ser anulada.
Mas enfim, a Vunesp, dificilmente irá anular, já que tem resposta né.

[@diegosb7200]

Em casa, eu consegui fazer só a do gráfico de pizza e a juros.
A de média eu não estava conseguindo montar a equação e a última eu tbm não consegui

[@CanaldoProfessorJoaquim]

@@diegosb7200 mas agora, depois de ter visto a minha resolução, vc conseguiu entender, ou ficou alguma dúvida?

[@viniciusribeiro3451]

Professor, poderia por gentileza, fazer um recurso para nós alunos impetrar contra a banca, creio que o Sr. tem mais aptidão e chance de fazer um recurso que pode prosperar.

[@otaldepeewee3596]

De grátis???? não né fofa.