Tahsili Mathematics 2 — Questions and Answers
Question 1: What is the integral of ∫ 2x dx?
- x² + C (Correct answer)
- 2x² + C
- x + C
- 2 + C
Correct answer: x² + C
Using the power rule for integration: ∫ 2x dx = 2 × (x²/2) + C = x² + C. The constant of integration C is always added for indefinite integrals.
Question 2: If log₂(x) = 5, what is the value of x?
- 10
- 25
- 32 (Correct answer)
- 64
Correct answer: 32
log₂(x) = 5 means 2⁵ = x. Therefore x = 32. The logarithm answers the question: 'To what power must the base be raised to get the number?'
Question 3: What is the equation of a circle with center (2, -3) and radius 5?
- (x-2)² + (y+3)² = 5
- (x-2)² + (y+3)² = 25 (Correct answer)
- (x+2)² + (y-3)² = 25
- (x-2)² + (y-3)² = 25
Correct answer: (x-2)² + (y+3)² = 25
Circle equation: (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius. Center (2,-3), radius 5: (x-2)² + (y-(-3))² = 5² → (x-2)² + (y+3)² = 25.
Question 4: What is the probability of getting at least one head when flipping a fair coin 3 times?
- 3/8
- 1/2
- 7/8 (Correct answer)
- 1/8
Correct answer: 7/8
P(at least 1 head) = 1 - P(no heads) = 1 - P(all tails) = 1 - (1/2)³ = 1 - 1/8 = 7/8. The complement approach is easier than counting all favorable outcomes.
Question 5: Simplify: (x² - 9)/(x + 3)
- x - 9
- x + 3
- x - 3 (Correct answer)
- x² - 3
Correct answer: x - 3
Factor the numerator as a difference of squares: x² - 9 = (x+3)(x-3). Then: (x+3)(x-3)/(x+3) = x - 3 (where x ≠ -3).
Question 6: What is the value of 5! (5 factorial)?
- 25
- 60
- 120 (Correct answer)
- 720
Correct answer: 120
5! = 5 × 4 × 3 × 2 × 1 = 120. Factorial is the product of all positive integers up to that number. Factorials are fundamental in permutations and combinations.
Tahsili Mathematics 2
What is the integral of ∫ 2x dx?