AMC 8 Algebra & Patterns 2

Question 1

If 2^x = 32, what is x?

Accepted Answer

5

Answer

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?

Accepted Answer

19

Answer

Adding the two equations: 2x = 38, so x = 19 and y = 11.

Question 3

What is the sum of the first 10 positive integers?

Accepted Answer

55

Answer

Using Gauss's formula: n(n+1)/2 = 10 × 11/2 = 55.

Question 4

What pattern does the sequence 1, 4, 9, 16, 25, … follow?

Accepted Answer

Perfect squares

Answer

The sequence is 1², 2², 3², 4², 5², … — the perfect squares of the positive integers.

Question 5

Solve for y: 4y/3 = 20.

Accepted Answer

15

Answer

Multiplying both sides by 3: 4y = 60, so y = 15.

AMC 8 - American Mathematics Competition 8 Practice Test