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### There are 31 results

Broad Topics > Functions and Graphs > Gradients

### How Steep Is the Slope?

##### Age 11 to 14 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?

### 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?

### Translating Lines

##### Age 11 to 14 Challenge Level:

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

### Reflecting Lines

##### Age 11 to 14 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.

### 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?

### Diamond Collector

##### Age 11 to 14 Challenge Level:

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

### 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?

### Parallel Lines

##### Age 11 to 14 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?

### Steady Free Fall

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

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

### Up and Across

##### Age 11 to 14 Challenge Level:

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

### How Far Does it Move?

##### Age 11 to 14 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.

### Walk and Ride

##### Age 7 to 14 Challenge Level:

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

### Parabella

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

This is a beautiful result involving a parabola and parallels.

### 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?

### Triangular Slope

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

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

### Electric Kettle

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

Explore the relationship between resistance and temperature

### 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?

### 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?

### Spot the Difference

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

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

### Motion Sensor

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

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

### 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.

### 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.

### 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. . . .

### 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.

### 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?

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

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

### Lap Times

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

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

### Lying and Cheating

##### Age 11 to 14 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!

### 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.

### 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