### There are 21 results

Broad Topics >

Functions and Graphs > Gradients

##### Age 16 to 18 Challenge Level:

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

##### 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?

##### 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

##### Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

##### 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?

##### Age 14 to 16 Challenge Level:

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

##### 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 14 to 16 Challenge Level:

Can you find the lap times of the two cyclists travelling at constant speeds?

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

##### 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?

##### Age 16 to 18 Short Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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

##### 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?

##### Age 14 to 16 Challenge Level:

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. . . .

##### 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.

##### 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?

##### Age 14 to 16 Short Challenge Level:

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

##### 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 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 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.