COMC Number Theory and Algebra Flashcards
6 cards from real COMC practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 COMC Number Theory and Algebra flashcards as text
What is the sum of the first 20 positive odd integers?
Answer: 400
The sum of the first n positive odd integers equals n², so the sum is 20² = 400.
In a geometric sequence with first term 2 and common ratio 3, what is the 5th term?
Answer: 162
Using aₙ = a₁ × r^(n−1): a₅ = 2 × 3⁴ = 2 × 81 = 162.
What is the coefficient of x² in the expansion of (1 + x)⁵?
Answer: 10
By the Binomial Theorem, the coefficient of x² in (1+x)⁵ is C(5,2) = 10.
What is the 15th term of the arithmetic sequence 3, 7, 11, 15, …?
Answer: 59
The general term is aₙ = 3 + (n−1)(4) = 4n − 1, so a₁₅ = 4(15) − 1 = 59.
If P(x) = x³ − 6x² + 11x − 6, what is P(2)?
Answer: 0
P(2) = 8 − 24 + 22 − 6 = 0, confirming that x = 2 is a root of the polynomial.
An arithmetic sequence has first term 5, last term 95, and exactly 19 terms. What is the sum of all terms?
Answer: 950
The arithmetic series sum is S = n(a₁ + aₙ)/2 = 19(5 + 95)/2 = 19 × 50 = 950.