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There are **27** NRICH Mathematical resources connected to **Gradients**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Which Is Bigger?

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Is Cheaper?

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Steep Is the Slope?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Surprising Transformations

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Translating Lines

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reflecting Lines

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### At Right Angles

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

Age 14 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Diamond Collector

Collect as many diamonds as you can by drawing three straight lines.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perpendicular Lines

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parallel Lines

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Age 11 to 14

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
### 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
### Parabella

This is a beautiful result involving a parabola and parallels.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Doesn't Add Up

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangular Slope

Can you find the gradients of the lines that form a triangle?

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Electric Kettle

Explore the relationship between resistance and temperature

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

Article
Primary curriculum
Secondary curriculum
### Muggles, Logo and Gradients

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Towards Maclaurin

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Walls

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Climbing

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mediant Madness

Kyle and his teacher disagree about his test score - who is right?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lying and Cheating

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### From All Corners

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Age 14 to 16

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