Resources tagged with: Gradients
There are 27 NRICH Mathematical resources connected to Gradients, you may find related items under Coordinates, functions and graphs.
Broad Topics > Coordinates, functions and graphs > Gradients
Which Is Bigger?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Which Is Cheaper?
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?
How Steep Is the Slope?
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
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
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Reflecting Lines
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
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Diamond Collector
Collect as many diamonds as you can by drawing three straight lines.
Perpendicular Lines
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
Parallel Lines
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
Up and Across
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
How Far Does it Move?
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.
Parabella
This is a beautiful result involving a parabola and parallels.
Doesn't Add Up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Ladder and Cube
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
Can you find the gradients of the lines that form a triangle?
Electric Kettle
Explore the relationship between resistance and temperature
Spot the Difference
If you plot these graphs they may look the same, but are they?
Muggles, Logo and Gradients
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Towards Maclaurin
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.
Walls
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.
Climbing
Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.
Snookered
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?
Mediant Madness
Kyle and his teacher disagree about his test score - who is right?
Lying and Cheating
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
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
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