Placement Test – Calculus I Deixe um comentário / Por adrianocesargois@gmail.com / maio 31, 2025 Placement Test – Calculus I Name WhatsApp 1. 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 2. 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 3. 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 4. 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 5. 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 6. 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 7. 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 8. 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 9. 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 $\sin\left(\dfrac{\pi}{6}\right)$? $\dfrac{\sqrt{3}}{2}$ $\dfrac{\sqrt{2}}{2}$ $\dfrac{1}{2}$ 1 I can't recall I've never learnt None Click submit to see your total hits! If you dont submit me, I can't see your results Time's up
