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Resources tagged with Graphs similar to Hyperbolic Thinking:

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Broad Topics > Functions and Graphs > Graphs

Exponential Trend

Age 16 to 18 Challenge Level:

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

Gosh Cosh

Age 16 to 18 Challenge Level:

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Which Is Cheaper?

Age 14 to 16 Challenge Level:

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

Cubic Spin

Age 16 to 18 Challenge Level:

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

Without Calculus

Age 16 to 18 Challenge Level:

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.

Age 14 to 16 Challenge Level:

Here are some more quadratic functions to explore. How are their graphs related?

Age 14 to 16 Challenge Level:

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

Climbing

Age 16 to 18 Challenge Level:

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Guess the Function

Age 16 to 18 Challenge Level:

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Age 14 to 16 Challenge Level:

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Age 14 to 16 Challenge Level:

Explore the two quadratic functions and find out how their graphs are related.

Which Is Bigger?

Age 14 to 16 Challenge Level:

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Steve's Mapping

Age 16 to 18 Challenge Level:

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Age 14 to 16 Challenge Level:

Four vehicles travelled on a road. What can you deduce from the times that they met?

After Thought

Age 16 to 18 Challenge Level:

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Small Steps

Age 16 to 18 Challenge Level:

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

Real(ly) Numbers

Age 16 to 18 Challenge Level:

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Motion Sensor

Age 14 to 16 Challenge Level:

Looking at the graph - when was the person moving fastest? Slowest?

Mathsjam Jars

Age 14 to 16 Challenge Level:

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Parabolic Patterns

Age 14 to 18 Challenge Level:

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.

Three Ways

Age 16 to 18 Challenge Level:

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

More Parabolic Patterns

Age 14 to 18 Challenge Level:

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Cubics

Age 14 to 18 Challenge Level:

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

Parabolas Again

Age 14 to 18 Challenge Level:

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

Graphic Biology

Age 16 to 18 Challenge Level:

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

Immersion

Age 14 to 16 Challenge Level:

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Maths Filler 2

Age 14 to 16 Challenge Level:

Can you draw the height-time chart as this complicated vessel fills with water?

Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

Age 14 to 16 Challenge Level:

Explore the relationship between quadratic functions and their graphs.

Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

Interpolating Polynomials

Age 16 to 18 Challenge Level:

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

What's That Graph?

Age 14 to 16 Challenge Level:

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

Alison's Mapping

Age 14 to 16 Challenge Level:

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Bus Stop

Age 14 to 16 Challenge Level:

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Lap Times

Age 14 to 16 Challenge Level:

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

How Many Solutions?

Age 16 to 18 Challenge Level:

Find all the solutions to the this equation.

Parabella

Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

Ellipses

Age 14 to 18 Challenge Level:

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

Matchless

Age 14 to 16 Challenge Level:

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Power Up

Age 16 to 18 Challenge Level:

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x

Perpendicular Lines

Age 14 to 16 Challenge Level:

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

Golden Construction

Age 16 to 18 Challenge Level:

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Curve Fitter

Age 16 to 18 Challenge Level:

Can you fit a cubic equation to this graph?

Surprising Transformations

Age 14 to 16 Challenge Level:

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?

Real-life Equations

Age 16 to 18 Challenge Level:

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Bio Graphs

Age 14 to 16 Challenge Level:

What biological growth processes can you fit to these graphs?

Graphical Interpretation

Age 14 to 16 Challenge Level:

This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.

Curve Match

Age 16 to 18 Challenge Level:

Which curve is which, and how would you plan a route to pass between them?