AMC 8 Algebra & Patterns 2 ā Questions and Answers
Question 1: If 2^x = 32, what is x?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
2^5 = 32, so x = 5.
Question 2: Two numbers have a sum of 30 and a difference of 8. What is the larger number?
- 17
- 18
- 19 (Correct answer)
- 21
Correct answer: 19
Adding the two equations: 2x = 38, so x = 19 and y = 11.
Question 3: What is the sum of the first 10 positive integers?
- 45
- 50
- 55 (Correct answer)
- 60
Correct answer: 55
Using Gauss's formula: n(n+1)/2 = 10 Ć 11/2 = 55.
Question 4: What pattern does the sequence 1, 4, 9, 16, 25, ā¦ follow?
- Add consecutive even numbers
- Multiply by 4
- Perfect squares (Correct answer)
- Add 3 each time
Correct answer: Perfect squares
The sequence is 1Ā², 2Ā², 3Ā², 4Ā², 5Ā², ā¦ ā the perfect squares of the positive integers.
Question 5: Solve for y: 4y/3 = 20.
- 12
- 15 (Correct answer)
- 18
- 20
Correct answer: 15
Multiplying both sides by 3: 4y = 60, so y = 15.
Question 6: What is the 100th term of the sequence 5, 8, 11, 14, ā¦?
- 299
- 300
- 302 (Correct answer)
- 305
Correct answer: 302
aāāā = 5 + (100ā1) Ć 3 = 5 + 297 = 302.
AMC 8 Algebra & Patterns 2
If 2^x = 32, what is x?