Maths I - Application of Derivatives (Slope of Tangent & Normal)

What is a tangent to a curve at a point?

• A line that cuts the curve at two points

• A line that touches the curve at exactly one point

• A line perpendicular to the curve

• A horizontal line

What is a normal to a curve at a point?

• A line that touches the curve at one point

• A line with zero slope

• A line perpendicular to the tangent at that point

• A line parallel to the curve

What does the slope of a tangent represent?

• Area under the curve

• Rate of change at a point

• Height of the curve

• Angle with the x-axis

What does a displacement–time graph show in physics?

• Energy vs time

• Slope of tangent as acceleration

• How displacement changes over time ie Velocity

• All of the above

Name a historical monument with a visible slope.

• Eiffel Tower

• Pyramid of Giza

• Red Fort

• Lotus Temple

How does the slope of a tangent help us in maths?

• Measures symmetry

• Shows height of object

• Tells us the rate of change at a point

• Indicates object’s weight

In economics, marginal profit means:

• Profit for every 100 units

• Change in total profit due to selling one more unit

• Average profit

• Total revenue

What does rate of change mean in a chemical reaction graph?

• Reaction temperature

• Speed of mixing chemicals

• Change in concentration over time

• Total energy released

Why do monuments often have sloped structures historically?

• For better symmetry

• To resist gravity and improve stability

• To save material

• Just for decoration

You are given: 𝑦 = x² - 1 at 𝑥 = 2. What is the slope of the tangent?

• 2

• 4

• 3

• 1