Mathematical Concepts and Formulas

Kat, an ACT expert, guides students through essential math formulas needed for the ACT. The video covers topics such as slope, line equations, the quadratic formula, imaginary numbers, statistics, probability, geometry, and trigonometry. Kat emphasizes the importance of memorizing these formulas, as they are not provided during the test. The video includes practical examples and tips for understanding and applying these concepts effectively.

What is the formula for finding the slope of a line given two points?

• x1 - x2 / y1 - y2

• y1 - y2 / x1 - x2

• x2 - x1 / y2 - y1

• y2 - y1 / x2 - x1

In the equation y = mx + b, what does 'b' represent?

• The slope of the line

• The midpoint

• The x-intercept

• The y-intercept

What is the quadratic formula used to solve ax^2 + bx + c = 0?

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

What is the value of i^2 in imaginary numbers?

• i

• -1

• 1

• 0

How do you calculate the mean of a set of numbers?

• Add all numbers and divide by the number of items

• Find the middle number in the sorted list

• Identify the most frequently occurring number

• Subtract the smallest number from the largest

What is the probability of drawing a king or a queen from a standard deck of cards?

• 1/13

• 2/13

• 4/52

• 8/52

What is the Pythagorean theorem formula?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = 2c^2

• a^2 - b^2 = 2c^2

What is the formula for the volume of a sphere?

• πr^2

• 1/3 πr^2h

• 4/3 πr^3

• 2πr

In logarithms, what does the base represent?

• The number being raised to a power

• The power itself

• The result

• The exponent

What does 'SOH' in SOHCAHTOA stand for in trigonometry?

• Sine = Hypotenuse / Opposite

• Sine = Opposite / Hypotenuse

• Sine = Adjacent / Hypotenuse

• Sine = Hypotenuse / Adjacent