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Resources tagged with Gradients similar to Spot the Difference:

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Broad Topics > Sequences, Functions and Graphs > Gradients

Spot the Difference

Stage: 5 Short Challenge Level:

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

Parabella

Stage: 5 Challenge Level:

This is a beautiful result involving a parabola and parallels.

At Right Angles

Stage: 4 Challenge Level:

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

Stage: 4 Challenge Level:

Can you adjust the curve so the bead drops with near constant vertical velocity?

Perpendicular Lines

Stage: 4 Challenge Level:

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

Lap Times

Stage: 4 Challenge Level:

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

Surprising Transformations

Stage: 4 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?

Mediant

Stage: 4 Challenge Level:

If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.

Which Is Bigger?

Stage: 4 Challenge Level:

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

Which Is Cheaper?

Stage: 4 Challenge Level:

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

Snookered

Stage: 4 and 5 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?

Towards Maclaurin

Stage: 5 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.

Electric Kettle

Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

Climbing

Stage: 5 Challenge Level:

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

Power Up

Stage: 5 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

From All Corners

Stage: 4 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

Stage: 3, 4 and 5

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

Stage: 4 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?

Motion Sensor

Stage: 4 Challenge Level:

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

Bus Stop

Stage: 4 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. . . .