AMC 8 Algebra & Patterns

Question 1

Solve for x: 3x + 7 = 22.

Accepted Answer

5

Answer

3x = 22 − 7 = 15, so x = 5.

Question 2

What is the next term in the sequence: 2, 5, 10, 17, 26, …?

Accepted Answer

37

Answer

The differences between terms are 3, 5, 7, 9 (increasing by 2), so the next difference is 11 and 26 + 11 = 37.

Question 3

If f(x) = 2x² − 3, what is f(4)?

Accepted Answer

29

Answer

f(4) = 2(4²) − 3 = 2(16) − 3 = 32 − 3 = 29.

Question 4

Solve for x: 5(x − 2) = 3x + 4.

Accepted Answer

7

Answer

Expanding: 5x − 10 = 3x + 4, so 2x = 14 and x = 7.

Question 5

What is the value of 3a − 2b when a = 4 and b = −1?

Accepted Answer

14

Answer

3(4) − 2(−1) = 12 + 2 = 14.

AMC 8 - American Mathematics Competition 8 Practice Test