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Resources tagged with Graphs similar to Random Inequalities:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Sequences, Functions and Graphs > Graphs

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How Many Solutions?

Stage: 5 Challenge Level: Challenge Level:1

Find all the solutions to the this equation.

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Sangaku

Stage: 5 Challenge Level: Challenge Level:1

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.

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Without Calculus

Stage: 5 Challenge Level: Challenge Level:1

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.

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Cubic Spin

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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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.

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Climbing

Stage: 5 Challenge Level: Challenge Level:1

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

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Four on the Road

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

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

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Interpolating Polynomials

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Mathsjam Jars

Stage: 4 Challenge Level: Challenge Level:1

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

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Parabolas Again

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

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

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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?

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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.

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Power Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Motion Sensor

Stage: 4 Challenge Level: Challenge Level:1

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

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More Parabolic Patterns

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

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.

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Three Ways

Stage: 5 Challenge Level: Challenge Level:1

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

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Ellipses

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

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

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Graphic Biology

Stage: 5 Challenge Level: Challenge Level:1

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

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Steve's Mapping

Stage: 5 Challenge Level: Challenge Level:1

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

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Real(ly) Numbers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

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

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Equation Matcher

Stage: 5 Challenge Level: Challenge Level:1

Can you match these equations to these graphs?

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On the Road

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at. . . .

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Maths Filler 2

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

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

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?

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Quadratic Transformations

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

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

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Lap Times

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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More Quadratic Transformations

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Which Is Bigger?

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

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

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After Thought

Stage: 5 Challenge Level: Challenge Level:1

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

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Alison's Mapping

Stage: 4 Challenge Level: Challenge Level:1

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

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Immersion

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

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

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Guess the Function

Stage: 5 Challenge Level: Challenge Level:1

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

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Exploring Quadratic Mappings

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between quadratic functions and their graphs.

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Graphical Interpretation

Stage: 4 Challenge Level: Challenge Level:1

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

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Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

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

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Spaces for Exploration

Stage: 3 and 4

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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Golden Construction

Stage: 5 Challenge Level: Challenge Level:1

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

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Parabella

Stage: 5 Challenge Level: Challenge Level:1

This is a beautiful result involving a parabola and parallels.

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

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

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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

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

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More Realistic Electric Kettle

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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Exponential Trend

Stage: 5 Challenge Level: Challenge Level:1

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.

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Small Steps

Stage: 5 Challenge Level: Challenge Level:1

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

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Bus Stop

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Bio Graphs

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

What biological growth processes can you fit to these graphs?

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Curve Fitter

Stage: 5 Challenge Level: Challenge Level:1

Can you fit a cubic equation to this graph?

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Curve Match

Stage: 5 Challenge Level: Challenge Level:1

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


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