Mathematics Knowledge Advanced Flashcards

What is the value of x in the equation 3x² - 12 = 0?

Answer: x = ±2

Divide both sides by 3 to get x² = 4, so x = ±2.

A triangle has sides of length 5, 12, and 13. What type of triangle is it?

Answer: Right

Since 5² + 12² = 25 + 144 = 169 = 13², it satisfies the Pythagorean theorem.

Simplify: (2x³y²)(3x²y⁴)

Answer: 6x⁵y⁶

Multiply coefficients (2×3=6) and add exponents: x^(3+2)=x⁵ and y^(2+4)=y⁶.

What is the slope of a line perpendicular to y = 4x − 3?

Answer: -1/4

Perpendicular slopes are negative reciprocals; the reciprocal of 4 is 1/4, negated gives -1/4.

What is the sum of the interior angles of a hexagon?

Answer: 720°

Using the formula (n-2)×180°, a hexagon has (6-2)×180° = 720°.

If f(x) = x² − 5x + 6, what are the roots?

Answer: x = 2 and x = 3

Factor the quadratic as (x−2)(x−3) = 0, giving roots x = 2 and x = 3.

A cylinder has a radius of 3 and height of 10. What is its volume?

Answer: 90π

Volume of a cylinder = πr²h = π(3²)(10) = 90π.