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

To solve for x, one would first isolate the term with x by subtracting 5 from both sides of the equation. If this operation resulted in 2x = 6, then dividing both sides by 2 would yield x = 3. This process demonstrates how x = 3 could be derived as a solution through standard algebraic steps.

Question 2

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

Accepted Answer

-b ± √(b² - 4ac) / 2a

Answer

The quadratic formula is a fundamental algebraic tool used to find the solutions (roots) for any quadratic equation in the standard form ax² + bx + c = 0. It provides a direct method to calculate the values of x, regardless of whether the equation can be factored. The formula correctly states that x equals negative b, plus or minus the square root of b squared minus 4ac, all divided by 2a.

Question 3

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

Accepted Answer

f(4) = 11

Answer

To find f(4), you need to substitute the value 4 for x in the given function f(x) = 2x + 3. This means calculating 2 multiplied by 4, and then adding 3. Performing the multiplication first, 2 * 4 equals 8, and then adding 3 results in 11. Therefore, f(4) = 11.

Question 4

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

Accepted Answer

(x - 3)(x - 2)

Answer

To factor the quadratic expression x² - 5x + 6, we look for two numbers that multiply to the constant term (6) and add up to the coefficient of the x term (-5). These numbers are -3 and -2, since (-3) * (-2) = 6 and (-3) + (-2) = -5. Therefore, the quadratic expression factors into (x - 3)(x - 2).

Question 5

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

Accepted Answer

x = 6

Answer

To solve the equation 3(x - 2) = 12, first divide both sides by 3, which gives x - 2 = 4. Next, add 2 to both sides of the equation to isolate x. This results in x = 4 + 2, so x = 6.

AMC 12 - - American Mathematics Contest 12 Practice Test

AMC 12 - - American Mathematics Contest 12 Practice Test

FREE AMC 12 Algebra & Functions Questions and Answers