FREE AMC 12 Algebra & Functions Questions and Answers

Question 1

What is the solution to the equation 2x + 5 = 15?

Accepted Answer

x = 3

Answer

x = 5

Answer

x = 10

Answer

x = 2

Question 2

What is the quadratic formula used to solve ax² + bx + c = 0?

Accepted Answer

-b ± √(b² - 4ac) / 2a

Answer

b ± √(a² - 4ac) / 2a

Answer

-b ± √(b² + 4ac) / 2a

Answer

b ± √(a² + b²) / 2c

Question 3

If f(x) = 2x + 3, what is f(4)?

Accepted Answer

f(4) = 11

Answer

f(4) = 8

Answer

f(4) = 7

Answer

f(4) = 5

Question 4

Which of the following is a factor of the quadratic expression x² - 5x + 6?

Accepted Answer

(x - 3)(x - 2)

Answer

(x - 6)(x - 1)

Answer

(x + 3)(x + 2)

Answer

(x + 6)(x - 1)

Question 5

What is the value of x in the equation 3(x - 2) = 12?

Accepted Answer

x = 6

Answer

x = 8

Answer

x = 5

Answer

x = 4

Question 6

If the roots of the equation x² - 7x + 10 = 0 are r₁ and r₂, what is r₁ + r₂?

Accepted Answer

r₁ + r₂ = 7

Answer

r₁ + r₂ = -7

Answer

r₁ + r₂ = 10

Answer

r₁ + r₂ = -10

Question 7

What is the slope of the line passing through the points (1, 2) and (3, 6)?

Accepted Answer

slope = 2

Answer

slope = 3

Answer

slope = 4

Answer

slope = 1

Question 8

Which of the following is a solution to the system of equations 2x + y = 10 and x - y = 2?

Accepted Answer

(x, y) = (4, 2)

Answer

(x, y) = (5, 1)

Answer

(x, y) = (3, 4)

Answer

(x, y) = (2, 6)

Question 9

What is the inverse of the function f(x) = 3x + 4?

Accepted Answer

f⁻¹(x) = (x - 4) / 3

Answer

f⁻¹(x) = 3x - 4

Answer

f⁻¹(x) = x / 3 + 4

Answer

f⁻¹(x) = x / 3 - 4