[ AFPSAT 26 ] Armed Forces of the Philippines Service Aptitude Test Reviewer XXVI

Armed Forces of the Philippines Service Aptitude Test Reviewer

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.

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 sin(x)cos(x)?

A) cos²(x) - sin²(x)
B) sin²(x) + cos²(x)
C) cos(2x)
D) cos(x)sin(x)

2. What is the solution to the system of equations: 2x + y = 10, 3x - y = 5?

A) (3, 4)
B) (5, 0)
C) (4, 2)
D) (2, 6)

3. If log(x) + log(y) = 3, what is the value of log(xy)?

A) 2
B) 3
C) 4
D) 1

4. What is the integral of (3x² + 4x) dx?

A) x³ + 2x² + C
B) x² + 2x + C
C) 3x³ + 4x² + C
D) 3x² + 4x + C

5. Find the eigenvalues of the matrix: [[1, 2], [3, 4]].

A) 5, -1
B) 5, -2
C) 3, 2
D) 4, 1

6. Find the value of x for the equation 2^(x + 1) = 32.

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

7. What is the value of the limit: lim (x → ∞) (1 + 1/x)²?

A) 1
B) 2
C) 0
D) ∞

8. Solve for x: 3(x + 2) = 18.

A) 6
B) 4
C) 5
D) 7

9. What is the value of sin(π/6)?

A) 1/2
B) √2/2
C) 1/2
D) √3/2

10. What is the derivative of tan(x)?

A) sec²(x)
B) sec²(x) + 1
C) cos(x)
D) sin(x)

11. Solve the inequality: 3x - 4 > 8.

A) x > 4
B) x > 5
C) x > 4
D) x > 6

12. If a series is defined as S = 1 + 2 + 3 + ... + n, what is the sum of the first n natural numbers?

A) n²
B) n(n + 1)
C) n(n + 1)/2
D) n²/2

13. What is the solution to the equation log₅(x) = 2?

A) 25
B) 5
C) 10
D) 20

14. What is the area of a circle with radius r?

A) 2πr
B) πr²
C) 2πr²
D) πr³

15. What is the result of the integral ∫(x³ + 4x²) dx?

A) x⁴/4 + 4x³/3 + C
B) x⁴/4 + 4x³/3 + C
C) x⁵/5 + 4x⁴/4 + C
D) x³ + 4x² + C

16. What is the solution to the quadratic equation x² - 5x + 6 = 0?

A) x = 1, 6
B) x = 2, 3
C) x = -2, -3
D) x = 4, 2

17. What is the matrix product of [[1, 2], [3, 4]] × [[5, 6], [7, 8]]?

A) [[19, 22], [43, 50]]
B) [[23, 26], [53, 60]]
C) [[15, 18], [33, 38]]
D) [[20, 22], [40, 44]]

18. What is the value of sin(2θ) if sin(θ) = 1/2 and cos(θ) = √3/2?

A) 1/2
B) √3/2
C) 1
D) 0

19. Find the inverse of the matrix: [[1, 2], [3, 4]].

A) [[-2, 1], [3/2, -1/2]]
B) [[-4, 2], [3, 1]]
C) [[-2, 1], [3/2, -1/2]]
D) [[-3, 1], [2/3, 1]]

20. Find the limit of the function lim(x → 0) (sin(x)/x).

A) 1
B) 0
C) ∞
D) Does not exist

21. What is the determinant of the matrix: [[2, 4], [3, 6]]?

A) 12
B) 0
C) 2
D) 6

22. What is the solution to the equation: log₂(x) = 5?

A) x = 32
B) x = 10
C) x = 16
D) x = 25

23. What is the equation of a line with slope 2 and passing through the point (3, 4)?

A) y = 2x - 2
B) y = 2x + 2
C) y = x + 2
D) y = x - 2

24. If the area of a triangle is 12 and the base is 6, what is the height?

A) 6
B) 4
C) 8
D) 3

25. What is the value of e^ln(5)?

A) 5
B) 1
C) e
D) 0

26. What is the integral of the function f(x) = x² + 3x with respect to x?

A) x³/3 + 3x² + C
B) x³ + 3x² + C
C) x³/3 + 3x²/2 + C
D) x³/3 + x² + C

27. A function f(x) is defined as f(x) = 2x² + 5x + 1. What is the derivative of f(x)?

A) 2x + 5
B) 4x + 5
C) 2x + 1
D) 4x + 1

28. A point (x, y) lies on the circle x² + y² = 25. What is the distance from the origin (0, 0) to the point (3, 4)?

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

29. The sum of the angles of a triangle is always equal to what value?

A) 180°
B) 360°
C) 90°
D) 120°

30. What is the solution to the system of equations: x + y = 7 and x - y = 3?

A) x = 4, y = 3
B) x = 5, y = 2
C) x = 3, y = 4
D) x = 6, y = 1

Result

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