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Placement Test – Calculus I

Name

What is the factorization of the polynomial $x^2-1$?

$(x-1)(x-1)$

$(x-1)(x+1)$

$(x+1)(x+1)$

$x(x-1)$

I can't recall

I've never learnt

None

What are the roots of the equation $x^2-5x+6=0$?

2 and 3

2 and -3

1 and 2

1 and 3

I can't recall

I've never learnt

None

Solve the inequality $3x - 5 < 2x + 4$:

$S=\{ x \in \mathbb{R} : x < -9\}$

$S=\{ x \in \mathbb{R} : x < 9\}$

$S=\{ x \in \mathbb{R} : x > 9\}$

$S=\{ x \in \mathbb{R} : x > -9\}$

I can't recall

I've never learnt

None

Solve the inequality $x^2 - 4x - 5 > 0$:

$S = (-\infty, -1) \cup (5, +\infty)$

$S = (-1, 5)$

$S = (-\infty, -1) \cap (5, +\infty)$

$S = \mathbb{R} \setminus \{-1, 5\}$

I can't recall

I've never learnt

None

Solve the equation $|2x - 7| = 3$:

$S=\{3, 5\}$

$S=\{1, 2\}$

$S=\{2, 5\}$

$S=\{2, 3\}$

I can't recall

I've never learnt

None

Simplify the expression $\dfrac{(x^2 y^{-3})^2 \cdot x^{-4} y^5}{x y^2}$:

$x^{-1} y^{-3}$

$x^{-3} y^{-3}$

$x^{-2} y^{-1}$

$x^{-1} y^{-2}$

I can't recall

I've never learnt

None

Simplify the expression $\dfrac{\sqrt{50} \cdot \sqrt{18}}{\sqrt{2}}$

$\sqrt{450}$

$15$

$30$

$45$

I can't recall

I've never learnt

None

What is the factorization of the polynomial $x^2+x-2=0$?

$(x+2)(x-3)$

$(x-2)(x+3)$

$(x-1)(x-2)$

$(x-1)(x+2)$

I can't recall

I've never learnt

None

Solve the equation $4(x - 2) = 2(x + 3) + 2x$:

$x = 5$

$x = 2$

$x = 4$

$x = 3$

I can't recall

I've never learnt

None

10.

Solve the equation $2x^2 - 3x - 5 = 0$:

$x = -1 \text{ or } x = 2{,}5$

$x = -1 \text{ or } x = 3$

$x = 1 \text{ or } x = 3$

$x = -2{,}5 \text{ or } x = 1$

I can't recall

I've never learnt

None

11.

Consider the function $f(x) = 2x - 5$. Determine the value of $f(3)$:

$f(3) = 6$

$f(3) = 1$

$f(3) = -1$

$f(3) = -11$

I can't recall

I've never learnt

None

12.

Consider the function $f(x) = -3x + 2$. For which value of $x$ do we have $f(x) = -10$?

$x = -4$

$x = -2$

$x = 4$

$x = 2$

I can't recall

I've never learnt

None

13.

Determine the domain of the function $f(x) = \dfrac{1}{x - 2}$:

$D = \mathbb{R} \setminus \{0\}$

$D = \mathbb{R}$

$D = \mathbb{R} \setminus \{2\}$

$D = \mathbb{R} \setminus \{-2\}$

I can't recall

I've never learnt

None

14.

Determine the domain of the function $f(x) = \sqrt{x - 3}$:

$D = \{x \in \mathbb{R} \mid x > 3\}$

$D = \{x \in \mathbb{R} \mid x < 3\}$

$D = \{x \in \mathbb{R} \mid x \geq 3\}$

$D = \{x \in \mathbb{R} \mid x \leq 3\}$

I can't recall

I've never learnt

None

15.

Determine the domain of the function $f(x) = \dfrac{1}{\sqrt{x - 1}}$:

$D = \{x \in \mathbb{R} \mid x \geq 1\}$

$D = \{x \in \mathbb{R} \mid x > 1\}$

$D = \{x \in \mathbb{R} \mid x < 1\}$

$D = \mathbb{R}$

I can't recall

I've never learnt

None

16.

Factor the polynomial $x^2 - 5x + 6$:

$(x - 2)(x - 3)$

$(x + 2)(x + 3)$

$(x - 6)(x + 1)$

$(x - 1)(x - 6)$

I can't recall

I've never learnt

None

17.

Factor the polynomial $x^3 - 6x^2 + 11x - 6$, knowing that $x = 1$ is a root:

$(x - 1)(x^2 - 3x + 2)$

$(x + 1)(x^2 - 5x + 6)$

$(x - 1)(x^2 + 5x + 6)$

$(x - 1)(x^2 - 5x + 6)$

I can't recall

I've never learnt

None

18.

Factor the polynomial $x^4 - 3x^3 + 2x^2$, knowing that $x = 1$ and $x = 2$ are roots:

$x^2(x - 1)(x - 2)$

$x(x - 1)(x - 2)(x + 1)$

$x(x^2 - 3x + 2)$

$x^2(x + 1)(x - 2)$

I can't recall

I've never learnt

None

19.

Given the points $A(1, 2)$ and $B(3, 6)$, the equation of the line passing through $A$ and $B$ is:

$y = 2x$

$y = x + 1$

$y = 2x + 1$

$y = 4x - 2$

I can't recall

I've never learnt

None

20.

Among the values below, what is the exact value of $\sin\left(\dfrac{\pi}{6}\right)$?

$\dfrac{\sqrt{3}}{2}$

$\dfrac{\sqrt{2}}{2}$

$\dfrac{1}{2}$

I can't recall

I've never learnt

None

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Teste de Nivelamento - Cálculo I

Nome

WhatsApp (Insira com o DD, exemplo: 17996737240)

Qual a fatoração do polinômio $x^2-1$?

$(x-1)(x-1)$

$(x-1)(x+1)$

$(x+1)(x+1)$

$x(x-1)$

None

Quais são as raízes da equação $x^2-5x+6=0$?

2 e 3

2 e -3

1 e 2

1 e 3

None

Resolva a inequação $3x - 5 < 2x + 4$:

$S=\{ x \in \mathbb{R} : x < -9\}$

$S=\{ x \in \mathbb{R} : x < 9\}$

$S=\{ x \in \mathbb{R} : x > 9\}$

$S=\{ x \in \mathbb{R} : x > -9\}$

None

Resolva a inequação $x^2 - 4x - 5 > 0$:

$S = (-\infty, -1) \cup (5, +\infty)$

$S = (-1, 5)$

$S = (-\infty, -1) \cap (5, +\infty)$

$S = \mathbb{R} \setminus \{-1, 5\}$

None

Resolva a equação $|2x - 7| = 3$:

$S=\{3, 5\}$

$S=\{1, 2\}$

$S=\{2, 5\}$

$S=\{2, 3\}$

None

Simplifique a expressão $\dfrac{(x^2 y^{-3})^2 \cdot x^{-4} y^5}{x y^2}$:

$x^{-1} y^{-3}$

$x^{-3} y^{-3}$

$x^{-2} y^{-1}$

$x^{-1} y^{-2}$

None

Simplifique a expressão $\dfrac{\sqrt{50} \cdot \sqrt{18}}{\sqrt{2}}$

$\sqrt{450}$

$15$

$30$

$45$

None

Qual a fatoração do polinômio $x^2+x-2=0$?

$(x+2)(x-3)$

$(x-2)(x+3)$

$(x-1)(x-2)$

$(x-1)(x+2)$

None

Resolva a equação $4(x - 2) = 2(x + 3) + 2x$:

$x = 5$

$x = 2$

$x = 4$

$x = 3$

None

10.

Resolva a equação $2x^2 - 3x - 5 = 0$:

$x = -1 \text{ ou } x = 2{,}5$

$x = -1 \text{ ou } x = 3$

$x = 1 \text{ ou } x = 3$

$x = -2{,}5 \text{ ou } x = 1$

None

11.

Considere a função $f(x) = 2x - 5$. Determine o valor de $f(3)$:

$f(3) = 6$

$f(3) = 1$

$f(3) = -1$

$f(3) = -11$

None

12.

Considere a função $f(x) = -3x + 2$. Para qual valor de $x$ temos $f(x) = -10$?

$x = -4$

$x = -2$

$x = 4$

$x = 2$

None

13.

Determine o domínio da função $f(x) = \dfrac{1}{x - 2}$:

$D = \mathbb{R} \setminus \{0\}$

$D = \mathbb{R}$

$D = \mathbb{R} \setminus \{2\}$

$D = \mathbb{R} \setminus \{-2\}$

None

14.

Determine o domínio da função $f(x) = \sqrt{x - 3}$:

$D = \{x \in \mathbb{R} \mid x > 3\}$

$D = \{x \in \mathbb{R} \mid x < 3\}$

$D = \{x \in \mathbb{R} \mid x \geq 3\}$

$D = \{x \in \mathbb{R} \mid x \leq 3\}$

None

15.

Determine o domínio da função $f(x) = \dfrac{1}{\sqrt{x - 1}}$:

$D = \{x \in \mathbb{R} \mid x \geq 1\}$

$D = \{x \in \mathbb{R} \mid x > 1\}$

$D = \{x \in \mathbb{R} \mid x < 1\}$

$D = \mathbb{R}$

None

16.

Fatore o polinômio $x^2 - 5x + 6$:

$(x - 2)(x - 3)$

$(x + 2)(x + 3)$

$(x - 6)(x + 1)$

$(x - 1)(x - 6)$

None

17.

Fatore o polinômio $x^3 - 6x^2 + 11x - 6$, sabendo que $x = 1$ é raiz:

$(x - 1)(x^2 - 3x + 2)$

$(x + 1)(x^2 - 5x + 6)$

$(x - 1)(x^2 + 5x + 6)$

$(x - 1)(x^2 - 5x + 6)$

None

18.

Fatore o polinômio $x^4 - 3x^3 + 2x^2$, sabendo que $x = 1$ e $x = 2$ são raízes:

$x^2(x - 1)(x - 2)$

$x(x - 1)(x - 2)(x + 1)$

$x(x^2 - 3x + 2)$

$x^2(x + 1)(x - 2)$

None

19.

Dado os pontos $A(1, 2)$ e $B(3, 6)$, a equação da reta que passa por $A$ e $B$ é:

$y = 2x$

$y = x + 1$

$y = 2x + 1$

$y = 4x - 2$

None

20.

Dentre os valores abaixo, qual é o valor exato de $\sin\left(\dfrac{\pi}{6}\right)$?

$\dfrac{\sqrt{3}}{2}$

$\dfrac{\sqrt{2}}{2}$

$\dfrac{1}{2}$

None

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