Calculus Concepts and Applications

The video tutorial covers solving calculus and 3D geometry problems from a November 2023 exam. It begins with finding the gradient of a tangent and normal line, deriving the equation of the normal line, and using a graphing calculator to find intersection points. The second part introduces a 3D geometry problem, calculating distances and angles using the distance formula and cosine rule.

What is the main topic of the first question discussed in the video?

• Geometry

• Statistics

• Calculus

• Algebra

To find the gradient of the tangent, which mathematical operation is primarily used?

• Integration

• Addition

• Multiplication

• Differentiation

What is the gradient of the tangent line at point A?

• 0

• 2

• -2

• 4

How is the gradient of the normal line related to the gradient of the tangent line?

• They are both zero

• They are negative reciprocals

• They are both positive

• They are equal

What is the gradient of the normal line at point A?

• -2

• -1/2

• 2

• 1/2

Which formula is used to write the equation of the normal line?

• y - y1 = m(x - x1)

• x = my + c

• ax + by = c

• y = mx + c

What are the coordinates of point A?

• (-4, -24)

• (4, -24)

• (4, 24)

• (-4, 24)

What is the equation of the normal line?

• y = 1/2x - 26

• y = -2x - 26

• y = -1/2x + 26

• y = 2x + 26

What tool is suggested for finding the intersection of the normal line with the graph?

• Protractor

• Compass

• Ruler

• Graphing Calculator

What is the x-coordinate of the second intersection point B?

• 7.5

• 6.5

• 5.5

• 4.5