Mathematics Flashcards
7 cards from real IB practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Mathematics flashcards as text
A geometric sequence has first term 5 and common ratio 2. What is the sum of the first 8 terms?
Answer: 1275
Using S_n = a(r^n - 1)/(r - 1): S_8 = 5(2^8 - 1)/(2 - 1) = 5(255) = 1275.
If f(x) = ln(3x + 1), what is f'(x)?
Answer: 3/(3x + 1)
By the chain rule, d/dx[ln(3x+1)] = 3/(3x+1).
What is the value of ∫₀² (3x² − 2x) dx?
Answer: 4
[x³ − x²] from 0 to 2 = (8 − 4) − 0 = 4.
A matrix A = [[2, 1], [5, 3]]. What is det(A)?
Answer: 1
det(A) = (2)(3) − (1)(5) = 6 − 5 = 1.
The probability that event A occurs is 0.4 and event B occurs is 0.5. If A and B are independent, what is P(A ∩ B)?
Answer: 0.2
For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.
What is the equation of the line passing through (1, 2) and (3, 8)?
Answer: y = 3x − 1
Slope = (8−2)/(3−1) = 3; using point (1,2): y − 2 = 3(x − 1) → y = 3x − 1.
In a right triangle, the two legs measure 6 and 8. What is the length of the hypotenuse?
Answer: 10
By the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.
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