Resources tagged with: Gradients

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There are 20 results

Broad Topics > Coordinates, Functions and Graphs > Gradients

Doesn't Add Up

Age 14 to 16 Challenge Level:

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

Ladder and Cube

Age 14 to 16 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?


Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.


Age 14 to 18 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?

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?

Which Is Cheaper?

Age 14 to 16 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?

At Right Angles

Age 14 to 16 Challenge Level:

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

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?


Age 16 to 18 Challenge Level:

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

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

Mediant Madness

Age 14 to 16 Challenge Level:

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

Triangular Slope

Age 14 to 16 Short Challenge Level:

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

Spot the Difference

Age 16 to 18 Short Challenge Level:

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

Diamond Collector

Age 11 to 16 Challenge Level:

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

Towards Maclaurin

Age 16 to 18 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.

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?

From All Corners

Age 14 to 16 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.

Muggles, Logo and Gradients

Age 11 to 18

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


Age 16 to 18 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.

Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature