Functions & Graphs - Stage 4


This is part of ourĀ Secondary Curriculum collection of favourite rich tasks arranged by topic.

Back Fitter

Stage: 4 Challenge Level: Challenge Level:1

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

Can you work out which processes are represented by the graphs?

Surprising Transformations

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Steady Free Fall

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you adjust the curve so the bead drops with near constant vertical velocity?

Perpendicular Lines

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Negatively Triangular

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

At Right Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Doesn't Add Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Cubics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

Parabolic Patterns

Stage: 4 and 5 Challenge Level: Challenge Level:1

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Tangled Trig Graphs

Stage: 5 Challenge Level: Challenge Level:1

Can you work out the equations of the trig graphs I used to make my pattern?

Functions and Graphs Stage 4 - Short Problems

Stage: 4

A collection of short Stage 4 problems on graphs of functions.