The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

Estimating the gradient of a curve

Maths

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more real-life graphs

Calculating the rate of change

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Estimating journeys from non-linear graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.

Real-life graphs

The gradient of the hypotenuse of the triangle is not the exact gradient of the curve between $$x=2$$ and $$x=6$$, it is only __________.

Estimate the gradient of this curve between $$x=2$$ and $$x=6$$

Estimate the gradient of this curve between $$x=-6$$ and $$x=-4$$

Nothing. It is quick and accurate to estimate this gradient this way.

The distance between the hypotenuse and the curve means it lacks accuracy.

The changes in $$x$$ and $$y$$ are not both $$+11$$

What is wrong with using the coordinate pairs (-7, 12) and (-2, 1) to estimate the gradient of this curve?

Match the intervals to the estimated gradient of the curve in those intervals.

The interval $$x=0$$ to $$x=$$__________ would be poor because it would give you an estimated gradient of $$0$$

rate of change in $$y$$-direction with respect to positive $$x$$-direction

rate of change in $$y$$-direction with respect to negative $$x$$-direction

What is the gradient of the line going through coordinate pairs $$(18,73)$$ and $$(50,233)$$?

What is the gradient of the line going through coordinate pairs $$\left(-{{1}\over{4}},{{5}\over{3}}\right)$$ and $$\left({{7}\over{3}},-{{16}\over{5}}\right)$$?

Estimating the gradient of a curve

Lesson outcome