Matemática A · year 10 · Geometria

Geometria analítica no espaço (planos coordenados, superfície esférica, esfera)

27 exercises from national exams, newest first.

Exercise 4.2

1st phase 2026Open answer

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Shared statement

Exercise 4.2 — 4.2. Resolva este item sem recorrer à calculadora. Determine uma equação da superfície esférica de centro no ponto A e que passa no ponto F .

Source: IAVE/EduQA — exam 635, 1st phase, 2026

Exercise 8.2

2nd phase 2026Open answer

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Shared statement

Exercise 8.2 — 8.2. Resolva este item sem recorrer à calculadora. Determine o volume do cubo [ABCDEFGH] .

Source: IAVE/EduQA — exam 635, 2nd phase, 2026

Exercise 1.1

Special sitting 2026Multiple choice

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Exercise 1.1 — 1.1. Qual das equações seguintes define a superfície esférica? (A) x y z 2 1 3 3 9 2 2 2 b ^ ^ l h h (B) x y z 4 73 2 2 2 (C) x y z 2 1 3 3 4 73 2 2 2 b ^ ^ l h h (D) x y z 9 2 2 2

Source: IAVE/EduQA — exam 635, Special sitting, 2026

Exercise 10.2

1st phase 2025Open answer

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Exercise 10.2 — 10.2. Resolva este item sem recorrer à calculadora. Determine as coordenadas do ponto C .

Source: IAVE/EduQA — exam 635, 1st phase, 2025

Exercise 6.2

Special sitting 2025Open answer

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Shared statement

Exercise 6.2 — 6.2. Resolva este item sem recorrer à calculadora. Determine o volume do prisma [ABCDEFGH] .

Source: IAVE/EduQA — exam 635, Special sitting, 2025

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Exercise 1.2

2nd phase 2024Open answer

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Shared statement

Exercise 1.2 — 1.2. Resolva este item sem recorrer à calculadora. Determine a equação cartesiana reduzida da superfície esférica que contém todos os vértices do cubo [ABCDEFGH ] .

Source: IAVE/EduQA — exam 635, 2nd phase, 2024

Exercise 5.2

Special sitting 2024Open answer

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Shared statement

Exercise 5.2 — 5.2. Resolva este item sem recorrer à calculadora. Determine as coordenadas do ponto V .

Source: IAVE/EduQA — exam 635, Special sitting, 2024

Exercise 6.2

1st phase 2023Open answer

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Shared statement

Exercise 6.2 — 6.2. Resolva este item sem recorrer à calculadora. Determine as coordenadas do ponto C .

Source: IAVE/EduQA — exam 635, 1st phase, 2023

Exercise 8.1

2nd phase 2023Multiple choice

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Exercise 8.1 — 8.1. Qual das seguintes equações define a superfície esférica de diâmetro [AG] ? (A) x y z 8 4 13 1 16 441 2 2 2 ^ a ^ h k h (B) x y z 8 4 13 1 4 441 2 2 2 ^ a ^ h k h (C) x y z 4 16 441 2 2 2 ^ h (D) x y z 4 4 441 2 2…

Source: IAVE/EduQA — exam 635, 2nd phase, 2023

Exercise 8.2

2nd phase 2023Open answer

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Shared statement

Exercise 8.2 — 8.2. Resolva este item sem recorrer à calculadora. Determine as coordenadas do vértice F do prisma.

Source: IAVE/EduQA — exam 635, 2nd phase, 2023

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Exercise 5.2

Special sitting 2023Open answer

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Shared statement

Exercise 5.2 — 5.2. Resolva este item sem recorrer à calculadora. Determine o volume do prisma [OABCDE] .

Source: IAVE/EduQA — exam 635, Special sitting, 2023

Exercise 6.2

1st phase 2022Open answer

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Shared statement

Exercise 6.2 — 6.2. Resolva este item sem recorrer à calculadora. Determine o volume do cone.

Source: IAVE/EduQA — exam 635, 1st phase, 2022

Exercise 5.2

2nd phase 2022Open answer

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Shared statement

Exercise 5.2 — 5.2. Resolva este item sem recorrer à calculadora. Sabe-se que o vértice E do cubo pertence à reta definida pela equação , , , , , , , x y z k k 0 0 3 1 1 1 R ! ^ ^ ^ h h h Determine as coordenadas do vértice E .

Source: IAVE/EduQA — exam 635, 2nd phase, 2022

Exercise 1.2

1st phase 2021Open answer

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Shared statement

Exercise 1.2 — 1.2. Determine, sem recorrer à calculadora, a equação reduzida da superfície esférica de centro no ponto B e que passa no ponto D

Source: IAVE/EduQA — exam 635, 1st phase, 2021

Exercise 1.1

2nd phase 2021Multiple choice

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Shared statement

Exercise 1.1 — 1.1. Qual das condições seguintes define a superfície esférica de centro no ponto R e que passa no ponto Q? (A) x y z 5 5 3 59 2 2 2 ^ ^ ^ h h h (B) x y z 5 5 3 41 2 2 2 ^ ^ ^ h h h (C) x y z 5 5 3 41 2 2 2 ^ ^ ^ h h h…

Source: IAVE/EduQA — exam 635, 2nd phase, 2021

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Exercise 1.2

Special sitting 2021Open answer

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Shared statement

Source: IAVE/EduQA — exam 635, Special sitting, 2021

Exercise 5.1

1st phase 2020Open answer

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Shared statement

Source: IAVE/EduQA — exam 635, 1st phase, 2020

Exercise 1.2

2nd phase 2020Open answer

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Shared statement

Exercise 1.2 — 1.2. Determine a equação reduzida da superfície esférica que passa nos oito vértices do cubo.

Source: IAVE/EduQA — exam 635, 2nd phase, 2020

Exercise 4.1

2nd phase 2018Open answer

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Exercise 4.1 — 4.1. Seja P o ponto da superfície esférica de abcissa 1, ordenada 3 e cota negativa. Seja r a reta de equação vetorial , , , , , , x y z k 1 0 3 4 1 2 = − + − ^ ^ ^ h h h, k R d Determine uma equação do plano que passa…

Source: IAVE/EduQA — exam 635, 2nd phase, 2018

Exercise 2.1

Special sitting 2018Open answer

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Exercise 2.1 — 2.1. Seja u OP 2 = − e seja Q P u = + Determine as coordenadas do ponto Q e refira, no contexto do problema, o significado de PQ 6 @

Source: IAVE/EduQA — exam 635, Special sitting, 2018

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Exercise Part II · 2.1

1st phase 2017Open answer

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Exercise Part II · 2.1 — 2.1. Seja Tl o simétrico do ponto T , relativamente à origem do referencial. Escreva uma equação da superfície esférica de diâmetro TTl 6 @ x Figura 2

Source: IAVE/EduQA — exam 635, 1st phase, 2017

Exercise Part II · 5.1

Special sitting 2017Open answer

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Exercise Part II · 5.1 — 5.1. Determine a área da secção produzida no cilindro pelo plano de equação x 1 = Figura 3 A O B x y

Source: IAVE/EduQA — exam 635, Special sitting, 2017

Exercise Part II · 3.1

1st phase 2016Open answer

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Exercise Part II · 3.1 — 3.1. Escreva uma condição que defina a superfície esférica de centro no ponto A e que é tangente ao plano xOy Fi 3 x y O

Source: IAVE/EduQA — exam 635, 1st phase, 2016

Exercise Part II · 3.2

1st phase 2016Open answer

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Shared statement

Source: IAVE/EduQA — exam 635, 1st phase, 2016

Exercise Part II · 5.2

1st phase 2015Open answer

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Exercise Part II · 5.2 — 5.2. Determine uma equação cartesiana que defina a superfície esférica da qual o segmento de reta AB 5 ? é um diâmetro.

Source: IAVE/EduQA — exam 635, 1st phase, 2015

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Exercise Part II · 6.1

2nd phase 2015Open answer

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Shared statement

Exercise Part II · 6.1 — 6.1. Determine as coordenadas do ponto V

Source: IAVE/EduQA — exam 635, 2nd phase, 2015

Exercise Part II · 2.3

Special sitting 2015Open answer

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Exercise Part II · 2.3 — 2.3. Determine uma equação da superfície esférica de centro na origem do referencial, que é tangente ao plano b Na resolução deste item, tenha em conta que o raio relativo ao ponto de tangência é perpendicular ao plano b

Source: IAVE/EduQA — exam 635, Special sitting, 2015

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