Higher only · curved graphs

Gradient of a curve.
Area under a curve.
Tangents and trapezia.

two estimates,
two meanings

a curve keeps changing steepness, so —

Tangent

a line that just touches the curve

same gradient as the curve there

step 1 of 4

Draw a tangent

1. Find the gradient when t = 2 seconds.

2. Ruler on the point. Match the slope.

✓ It touches once and does not cross

step 2 of 4

1. On the tangent: (2, 2) and (4, 6).

2. Rise ÷ run = 4 ÷ 2 = 2.

✓ On a speed-time graph that is
acceleration: 2 m/s²

step 3 of 4

1. Split into strips 1 second wide.

2. Each is a trapezium: ½(a + b) × width.

✓ 0.25 + 1.25 + 3.25 + 6.25 = 11

step 4 of 4

1. Area under speed-time = distance.

2. The straight tops sit above the curve.

✓ About 11 m: a slight overestimate

on a curved graph —

Gradient

draw a tangent, then rise ÷ run

Area

split into trapezia and add

Speed-time graph:
gradient is acceleration,
area is distance.

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