Area of maths |
Style |
Question |
Description |
Rates of change |
 |
Maths Filler 2 |
Practise looking at rates of change as this vessel fills with
water. |
 |
Immersion |
Various solids are lowered into a beaker of water. How does the
water level rise in each case? |
 |
Brimful |
Rotate the curves to make some mathematical vessels. |
 |
Brimful 2 |
Which of these mathematical flasks will eventually fill up with
water? |
Curves |
 |
Curve Fitter |
Use your skill to try to fit a cubic equation through these
three points. |
 |
Curve Fitter 2 |
Can you make a cubic which has a certain distance between the
turning points? |
 |
Implicitly |
Can you find the shape of this implicity defined function? |
 |
Whose line graph is it anyway? |
Which line graphs, processes and equations go together? |
 |
|
Can you sketch these difficult curves, which have uses in
mathematical modelling? |
Calculus |
Calculus is involved in many problems on stemNRICH.
See the physNRICH and engNRICH pages for
various particular examples. |
 |
|
Can you hit the target functions using a set of input function
and a little calculus and algebra? |
 |
Integration Matcher |
Which curves, integrals and differentials go together? |
 |
|
What functions can you make using the function machines
RECIPROCAL and PRODUCT and the operator machines DIFF and INT? |
Differential equations |
You will also find lots of differential equations
problems in various sections on the physNRICH and engNRICH
pages |
 |
Differential Equation Matcher |
Match the descriptions of physical processes to these
differential equations. |
 |
|
Explore the possible mathematical solutions to the non-linear
order of reaction equation from chemistry. |
Series and expansions |
 |
Production Equation |
Each week a company produces X units and sells p per cent of
its stock. How should the company plan its warehouse space? |
 |
Stirling Work |
See how enormously large quantities can cancel out to give a
good approximation to the factorial function. |
 |
What Do Functions Do for Tiny x? |
How do these familiar functions behave for very small
values? |
 |
|
Get further into power series using the fascinating Bessel's
equation. |
Powers, roots and logarithms |
See also the Logarithms and pH problems on the chemNRICH
pages |
 |
Power Match |
Can you locate these values on this interactive logarithmic
scale? |
 |
Debt Race |
Who will be the first investor to pay off their debt? |
Probability and distributions |
 |
pdf Matcher |
What scientific stories can you match to these pdf curves? |
 |
Circle PDF |
How can an arc of a circle be a pdf? |
 |
Scale Invariance |
By exploring the concept of scale invariance, find the
probability that a random piece of real-world data begins with a
1. |
 |
Into the Exponential Distribution |
Get into the exponential distribution through an exploration of
its pdf. |
 |
Into the Normal Distribution |
Get into the normal distribution through an exploration of its
pdf. |
Statistics |
 |
Stats Statements |
This question gives you 10 statistical statements. Develop your
statistical intuition by asking yourself are they sometimes,
always, nearly always, almost never or never true?' |
 |
Overbooking |
Why do airlines overbook? |
 |
The Wrong Stats |
Why MUST these statistical statements be at least a little bit
wrong? |
 |
Aim High |
How much wheat should this farmer plant to minimise his
expected loss? |
 |
Time to Evolve 2 |
How would you model the time between your birth and that of
your grandfather? |
Trigonometry |
 |
Flight Path |
Use simple trigonometry to calculate the distance along the
flight path from London to Sydney. |
 |
Loch Ness |
Draw graphs of the sine and modulus functions and explain the
humps. |
 |
Spherical Triangles on Very Big Spheres |
Find out about spherical triangles and decide if telecoms
engineers need to know about such things. |
 |
Taking Trigonometry Seriesly |
Look at the advanced way of viewing sin and cos through their
power series. |
Complex numbers |
 |
|
A nice introduction to complex numbers, including many
exercises for the reader. |
|
More on the way |
More on the way |
Vectors |
 |
Spotting the Loophole |
A visualisation problem in which you search for vectors which
sum to zero from a jumble of arrows. Will your eyes be quicker than
algebra? |
 |
|
Starting with two basic vector steps, which destinations can
you reach on a vector walk? |
 |
|
Follow Ulaf, Vicky and Wilber on a vector walk to determine the
locations nearest to the origin. |
 |
Air Routes |
An application of vectors and scalar products in a very
practical setting. |
 |
|
Explore the meaning of the scalar and vector products and see
how the two are related |
Vectors and matrices |
 |
|
What quadrilaterals can you transform this pair of squares
into? |
 |
|
Explore the mathematics of matrix transformations with these 10
individual questions. |
 |
|
Explore the algebraic and geometric properties of matrices with
these 5 individual questions. |
 |
Crystal Symmetry |
Use vectors and matrices to explore the symmetry properties of
Caesium Chloride. |
 |
|
Explore how matrices can fix vectors and vector
directions.? |
 |
|
Can you make matrices which will fix one lucky vector and crush
another to zero? |
Numerical methods |
 |
Root Hunter |
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign. |
 |
The Monte Carlo Method |
Estimate areas using random grids. |
 |
Building Approximations for Sin(x) |
Build up the concept of the Taylor series. |
Decision making and algorithms |
 |
Testing Strategy |
Investigate ways in which you could implement a scoring system
for a multiple choice test. |
. |
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