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

Challenge Level

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?

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?

Challenge Level

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

Challenge Level

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.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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.

Challenge Level

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.

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

Explore the relationship between resistance and temperature

Challenge Level

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

Challenge Level

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?

Challenge Level

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

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

Challenge Level

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.

Challenge Level

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.

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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!

Challenge Level

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.

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