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Resources tagged with Gradients similar to Power Up:

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Broad Topics > Functions and Graphs > Gradients

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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

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Climbing

Age 16 to 18 Challenge Level:

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

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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?

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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?

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Motion Sensor

Age 14 to 16 Challenge Level:

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

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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?

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Parabella

Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

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Lap Times

Age 14 to 16 Challenge Level:

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

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Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

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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?

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Bus Stop

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. . . .

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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?

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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.

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Mediant Madness

Age 14 to 16 Challenge Level:

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

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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?

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Snookered

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?

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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?

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Triangular Slope

Age 14 to 16 Short Challenge Level:

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

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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.

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Spot the Difference

Age 16 to 18 Short Challenge Level:

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

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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.