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There are **49** NRICH Mathematical resources connected to **Graph sketching**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Mathsjam Jars

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's That Graph?

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fill Me Up

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Back Fitter

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tangled Trig Graphs

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Immersion

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curve Fitter

This problem challenges you to find cubic equations which satisfy different conditions.

Age 14 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Maths Filler

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Negatively Triangular

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speeding Up, Slowing Down

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squareness

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Slide

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Area L

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exploring Cubic Functions

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabolic Patterns

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Witch of Agnesi

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Folium of Descartes

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Interpolating Polynomials

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bird-brained

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curve Hunter

This problem challenges you to sketch curves with different properties.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guessing the Graph

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guess the Function

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rational Request

Can you make a curve to match my friend's requirements?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Graphic Biology

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Scientific Curves

Can you sketch these difficult curves, which have uses in mathematical modelling?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ideal Axes

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Whose Line Graph Is it Anyway?

Which line graph, equations and physical processes go together?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curve Match

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reaction Types

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maths Filler 2

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Integration Matcher

Can you match the charts of these functions to the charts of their integrals?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bio Graphs

What biological growth processes can you fit to these graphs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spot the Difference

If you plot these graphs they may look the same, but are they?

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### How Does Your Function Grow?

Compares the size of functions f(n) for large values of n.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polar Flower

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pitchfork

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Parabolic Patterns

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.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maltese Cross

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Up

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

Age 16 to 18

Challenge Level