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Listed under:  Secant lines

### Differential calculus: non-linear graphs

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller, the rocket's average velocity approaches its instantaneous velocity. Use the slider to ...

### Differential calculus: the derivative

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look for ...

### Differential calculus: power functions

Observe the non-linear graphs of various power functions (such as f(x) = x², or f(x) = x³) and select the expressions for finding the gradient of the secant between small changes in x represented by Δx. Tabulate the values of f'(x) and plot the derivative of each function. Determine the pattern between the graphs for each ...

### Differential calculus: cubic function

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t³ – 2. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

### Differential calculus: quartic function

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

### Differential calculus: linear and non-linear graphs

Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work ...

### Differential calculus: derivatives and power functions

Observe the non-linear distance-time graph of a rocket travelling at a changing velocity. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and derive a formula for finding the instantaneous velocity at a given point. In the second activity, observe ...

### Differential calculus: cubic and quartic functions

Observe the non-linear time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formulas: s(t) = t³ – 2 and s(t) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results ...

### Introduction to differential calculus

This collection of 17 digital curriculum resources (all learning objects) is organised into three sections: rates of change; differential calculus; and review of differential calculus via three learning objects. Students explore rates of change through liquid-pouring activities, and are introduced to the gradient of secants ...

### TIMES Module 26: Measurement and Geometry: circle geometry - teacher guide

This is a 44-page guide for teachers. It contains theorems on chords, arcs, angles and secants associated with circles.