[ DOST 11 ] DOST SCHOLARSHIP EXAM REVIEWER XI

Mathematics

Instructions:

Please answer each question to the best of your ability. Each question is multiple choice, and only one answer per question is correct. Select the most appropriate answer from the options provided. There are 20 questions in total.

When you have completed all questions, click the "Submit" button at the bottom of the page to see your score. Good luck!

1. What is the derivative of \( f(x) = 3x^2 + 4x - 5 \)?

A) \(3x + 4\)
B) \(6x + 4\)
C) \(3x^2 + 4\)
D) \(6x - 4\)

2. Find the limit as \( x \to 2 \) of \( f(x) = \frac{x^2 - 4}{x - 2} \).

A) 0
B) 4
C) 2
D) 1

3. If \( f(x) = x^3 \), what is the second derivative, \( f''(x) \)?

A) \(6x^2\)
B) \(x\)
C) \(6x\)
D) \(3x\)

4. What is the integral of \( f(x) = 3x^2 \) with respect to \( x \)?

A) \(x^3 + C\)
B) \(3x + C\)
C) \(9x + C\)
D) \(2x^3 + C\)

5. If \( f(x) = e^x \), what is \( f'(x) \)?

A) \(e^x\)
B) \(xe^x\)
C) \(2e^x\)
D) \(0\)

6. What is the derivative of \( f(x) = \sin(x) \)?

A) \( \cos(x) + x\)
B) \( \cos(x) \)
C) \( -\sin(x) \)
D) \( \tan(x) \)

7. Evaluate \( \int_0^1 3x \, dx \).

A) \(1.5\)
B) \(3\)
C) \(0.5\)
D) \(2\)

8. Which of the following is the Taylor series expansion of \( e^x \) around \( x = 0 \)?

A) \(1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots\)
B) \(1 + x + \frac{x^2}{3!} + \dots\)
C) \(x + \frac{x^2}{2!} + \dots\)
D) \(1 + x - \frac{x^2}{2!} + \dots\)

9. If \( f(x) = \ln(x) \), what is \( f'(x) \)?

A) \(2x\)
B) \(e^x\)
C) \(\frac{1}{x}\)
D) \( \ln(x)\)

10. What is the integral of \( f(x) = 1/x \) with respect to \( x \)?

A) \(x\)
B) \(x + C\)
C) \(\ln|x| + C\)
D) \(\ln(x)\)

11. What is the derivative of \( f(x) = \tan(x) \)?

A) \( \sec^2(x) \)
B) \( \cos(x) \)
C) \( \sin(x) \)
D) \( \sec(x) \)

12. Evaluate \( \int x^3 \, dx \).

A) \( \frac{x^3}{3} + C \)
B) \( \frac{x^4}{3} + C \)
C) \( \frac{x^4}{4} + C \)
D) \( x^3 + C \)

13. What is the limit as \( x \to 0 \) of \( \frac{\sin(x)}{x} \)?

A) 1
B) 0
C) \( \infty \)
D) -1

14. If \( f(x) = x^2 + 3x + 1 \), what is \( f'(1) \)?

A) 5
B) 3
C) 4
D) 6

15. Find the area under the curve \( f(x) = x^2 \) from \( x = 0 \) to \( x = 2 \).

A) 6
B) 2
C) \( \frac{8}{3} \)
D) \( \frac{10}{3} \)

16. What is the derivative of \( f(x) = \ln(x^2) \)?

A) \( \frac{2}{x} \)
B) \( \ln(2x) \)
C) \( \frac{1}{x^2} \)
D) \( \ln(x) \)

17. Which of the following functions is continuous at \( x = 2 \)?

A) \( f(x) = x^2 - 4x + 4 \)
B) \( f(x) = \frac{1}{x-2} \)
C) \( f(x) = \tan(\frac{\pi x}{2}) \)
D) \( f(x) = \frac{x}{x - 2} \)

18. What is the integral of \( f(x) = 5e^x \) with respect to \( x \)?

A) \( 5e^x + C \)
B) \( e^x + C \)
C) \( 5xe^x + C \)
D) \( \frac{e^x}{5} + C \)

19. Evaluate \( \lim_{x \to \infty} \frac{3x + 2}{x + 1} \).

A) 0
B) 3
C) 1
D) 2

20. If \( f(x) = x \cdot e^x \), what is \( f'(x) \)?

A) \( x \cdot e^{x-1} \)
B) \( e^x (x + 1) \)
C) \( x \cdot e^x - 1 \)
D) \( e^x \)

Result

If you want to improve your score, there are more practice tests available here.