Mathematical Concepts and Formulas

The video provides a comprehensive guide to essential ACT Math formulas and concepts, including linear equations, geometry, quadratic and trigonometric concepts, matrix and vector operations, logarithms, counting principles, volume and area formulas, special triangles, and trigonometric graphs. It aims to equip students with the knowledge needed to excel in the ACT Math section.

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

• Sum of y-values over sum of x-values

• Difference of x-values over difference of y-values

• Sum of x-values over sum of y-values

• Difference of y-values over difference of x-values

In the slope-intercept form y = mx + b, what does 'b' represent?

• X-intercept

• Y-intercept

• Slope

• Midpoint

How do you calculate the midpoint between two points?

• Add the x-values and y-values separately, then divide by 2

• Subtract the x-values and y-values separately, then divide by 2

• Divide the x-values and y-values separately, then add 2

• Multiply the x-values and y-values separately, then divide by 2

What is the formula for the area of a circle?

• 2πd

• πd

• πr²

• 2πr

How is the length of an arc calculated?

• πd times the fraction of the central angle over 360

• 2πr times the fraction of the central angle over 360

• πr² times the fraction of the central angle over 360

• 2πd times the fraction of the central angle over 360

What does the quadratic formula help you find?

• The slope of a line

• The midpoint of a segment

• The roots of a quadratic equation

• The area of a circle

In trigonometry, what does SOHCAHTOA help you remember?

• The properties of exponential growth

• The relationships between sine, cosine, and tangent

• The formulas for area and circumference

• The rules for matrix multiplication

What is the probability of rolling a 1 or a 3 on a six-sided die?

• 1/3

• 1/2

• 1/6

• 2/3

What is the standard form equation of a circle?

• x² - y² = r²

• x² + y² = r²

• (x - h)² + (y - k)² = r²

• (x + h)² + (y + k)² = r²

What does the exponential growth formula y = a(1 + r)^t represent?

• Decay over time

• Growth over time

• Linear increase

• Constant rate