Tahsili Mathematics 2

Question 1

What is the integral of ∫ 2x dx?

Accepted Answer

x² + C

Answer

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?

Accepted Answer

32

Answer

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?

Accepted Answer

(x-2)² + (y+3)² = 25

Answer

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?

Accepted Answer

7/8

Answer

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)

Accepted Answer

x - 3

Answer

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).

Tahsili Practice Test

Tahsili Practice Test

Tahsili Mathematics 2