Exams
Each question has a declared source (book · section · exercise number) and a deep step-by-step with the why behind each operation.
The ledger consists of these books: OpenStax (College Algebra 2e, Algebra & Trig 2e, Calculus Vol 1/2/3, Introductory Statistics — all CC-BY 4.0), Notes on Diffy Qs (Lebl, CC-BY-SA), Active Calculus (Boelkins, CC-BY-NC-SA). We only adapt the PT-BR translation and numeric context (PETR4 instead of Apple).
Term — bronze border = year 1, silver = year 2, gold = year 3
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
Exam version Term 1 · Version 1 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 2 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 3 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 4 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 5 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 6 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 7 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 8 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 9 — Functions, linear, quadratic, exp/log ✓ Term 1 · Version 10 — Functions, linear, quadratic, exp/log ✓
Prova de fechamento do Trim 1 (1.º ano). Domínio de funções, gráficos, afim, quadrática, exponencial e logarítmica.
Term 1 · version 1 · 15 questions · 0 solutions revealed
Q1 aplicacao
Determine o domínio da função
f ( x ) = x + 1 x 2 − 9 f(x) = \dfrac{x+1}{x^2 - 9} f ( x ) = x 2 − 9 x + 1 .
source: OpenStax College Algebra 2e · §3.2 Domain and Range, ex. 17 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-02-funcoes licao-01-conjuntos-intervalos
Q2 aplicacao
Encontre a equação da reta que passa por
( 2 , − 3 ) (2, -3) ( 2 , − 3 ) e tem inclinação
m = 4 m = 4 m = 4 .
source: OpenStax College Algebra 2e · §4.1 Linear Functions, ex. 28 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-03-afim
Q3 aplicacao
Encontre o vértice e os zeros (raízes) de
f ( x ) = 2 x 2 − 8 x + 6 f(x) = 2x^2 - 8x + 6 f ( x ) = 2 x 2 − 8 x + 6 .
source: OpenStax College Algebra 2e · §5.1 Quadratic Functions, ex. 35 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-04-quadratica
Q4 compreensao
Sejam
f ( x ) = x 2 + 1 f(x) = x^2 + 1 f ( x ) = x 2 + 1 e
g ( x ) = 2 x − 3 g(x) = 2x - 3 g ( x ) = 2 x − 3 . Calcule
( f ∘ g ) ( x ) (f \circ g)(x) ( f ∘ g ) ( x ) e
( g ∘ f ) ( x ) (g \circ f)(x) ( g ∘ f ) ( x ) .
source: OpenStax College Algebra 2e · §3.4 Composition of Functions, ex. 22 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-05-composicao-inversa
Q5 aplicacao
Resolva
3 2 x − 1 = 27 3^{2x-1} = 27 3 2 x − 1 = 27 .
source: OpenStax College Algebra 2e · §6.6 Exponential and Logarithmic Equations, ex. 41 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-06-exponencial
Q6 compreensao
Resolva
log 2 ( x + 3 ) + log 2 ( x − 3 ) = 4 \log_2(x+3) + \log_2(x-3) = 4 log 2 ( x + 3 ) + log 2 ( x − 3 ) = 4 .
source: OpenStax College Algebra 2e · §6.6 Logarithmic Equations, ex. 56 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-07-logaritmo
Q7 modelagem
Uma cultura de bactérias começa com 200 indivíduos e dobra a cada 3 horas. Quantos haverá após 12 horas?
source: OpenStax College Algebra 2e · §6.7 Exponential and Logarithmic Models, ex. 12 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-08-crescimento
Q8 compreensao
Determine se
f ( x ) = x 3 f(x) = x^3 f ( x ) = x 3 é par, ímpar ou nenhum dos dois.
source: OpenStax College Algebra 2e · §3.3 Even and Odd Functions, ex. 8 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-02-funcoes
Q9 aplicacao
Resolva a inequação
∣ 2 x − 1 ∣ < 5 |2x - 1| < 5 ∣2 x − 1∣ < 5 .
source: OpenStax College Algebra 2e · §2.7 Absolute Value Inequalities, ex. 14 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-01-conjuntos-intervalos
Q10 aplicacao
Encontre o ponto de interseção das retas
y = 2 x + 3 y = 2x + 3 y = 2 x + 3 e
y = − x + 6 y = -x + 6 y = − x + 6 .
source: OpenStax College Algebra 2e · §9.1 Systems of Linear Equations, ex. 6 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-03-afim
Q11 compreensao
Soma e produto das raízes de
x 2 − 7 x + 12 = 0 x^2 - 7x + 12 = 0 x 2 − 7 x + 12 = 0 .
source: OpenStax College Algebra 2e · §5.1 Quadratics — Vieta's, ex. 41 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-04-quadratica
Q12 aplicacao
Se
f ( x ) = 2 x + 1 f(x) = 2x + 1 f ( x ) = 2 x + 1 , encontre
f − 1 ( x ) f^{-1}(x) f − 1 ( x ) .
source: OpenStax College Algebra 2e · §3.7 Inverse Functions, ex. 9 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-05-composicao-inversa
Q13 aplicacao
Calcule
log 2 32 \log_2 32 log 2 32 .
source: OpenStax College Algebra 2e · §6.3 Logarithmic Functions, ex. 13 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-07-logaritmo
Q14 aplicacao
Calcule a taxa média de variação de
f ( x ) = x 2 + 1 f(x) = x^2 + 1 f ( x ) = x 2 + 1 no intervalo
[ 1 , 4 ] [1, 4] [ 1 , 4 ] .
source: OpenStax College Algebra 2e · §3.3 Average Rate of Change, ex. 11 (adaptado) · CC-BY 4.0 Reveal step-by-step licao-09-taxa-variacao
Q15 modelagem
Modelagem: depreciação de um carro segue
V ( t ) = 50000 ⋅ ( 0 , 85 ) t V(t) = 50000 \cdot (0,85)^t V ( t ) = 50000 ⋅ ( 0 , 85 ) t (R\$, t em anos). Valor após 5 anos.
source: OpenStax College Algebra 2e · §6.7 Exponential Decay, ex. 22 (adaptado para BR) · CC-BY 4.0 Reveal step-by-step licao-08-crescimento
How it works Choose the term and version. Set aside the indicated time and solve it in your notebook. Check each question: click on Reveal step-by-step . Note the points where you got it wrong and revisit the corresponding lesson (lesson-ID badges below each question). Curious about the source? Click the book name and go straight to the original chapter. Versions marked as "in curation" do not yet have questions loaded. Version 1 of each term is always ready. Want to help curate more versions? Every additional PR is welcome on GitHub.