Drawing Tangents to Curves: quick revision, 7 bites

What is a Tangent?

It's a line that 'kisses' a curve.

Takeaway. A tangent shows the direction of the curve at a single point.

Steps to Draw a Tangent

Master this simple 3-step drawing technique.

Takeaway. Precision in ruler placement is key to an accurate tangent.

Avoid Crossing the Curve

Don't let your tangent cut through!

Takeaway. A true tangent touches, it doesn't intersect.

Tangents Find Instantaneous Rate of Change

Unlock the 'speed at an instant'.

The primary application of drawing a tangent is to find the **instantaneous rate of change** of a quantity represented by a curve at a specific point.

Takeaway. The slope of the tangent reveals how fast something is changing at that exact moment.

Calculating Gradient of a Tangent

Turn your drawn line into a number.

Takeaway. The gradient formula quantifies the steepness of your tangent line.

Finding Instantaneous Speed

How fast were you going at 5 seconds?

Takeaway. A tangent's gradient on a distance-time graph directly gives instantaneous speed.

Practice Makes Perfect

Your drawing skill matters in exams.

Drawing accurate tangents is a visual skill that improves significantly with practice. Examiners look for tangents that are clearly touching at only one point and represent the curve's direction well.

Takeaway. Regular practice ensures precision and confidence in drawing tangents for calculations.