Subjects algebra and physics

Practice Exam

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Practice Exam


1. **Practice Exam Creation:** Here is a practice exam with algebra and physics questions. 2. **Question 1 (Algebra):** Solve for $x$ in equation $$2x^2 - 5x + 2 = 0$$. 3. **Solution 1:** Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a=2$, $b=-5$, $c=2$. $$x = \frac{5 \pm \sqrt{(-5)^2 - 4 \cdot 2 \cdot 2}}{2 \cdot 2} = \frac{5 \pm \sqrt{25 - 16}}{4} = \frac{5 \pm 3}{4}$$ So, $x = \frac{5 + 3}{4} = 2$ or $x = \frac{5 - 3}{4} = \frac{1}{2}$. 4. **Question 2 (Physics):** Calculate the final velocity of an object accelerating at $3$ m/s$^2$ for $4$ seconds starting from rest. 5. **Solution 2:** Use formula $v = u + at$ where initial velocity $u=0$, acceleration $a=3$, time $t=4$. $$v = 0 + 3 \times 4 = 12 \text{ m/s}$$. 6. **Answer Key:** - Q1: $x = 2$ or $x = \frac{1}{2}$ - Q2: Final velocity $v = 12$ m/s