Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Can you hit the target functions using a set of input functions and a little calculus and algebra?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Derive an equation which describes satellite dynamics.
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
An algebra task which depends on members of the group noticing the needs of others and responding.
Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
Can you prove that twice the sum of two squares always gives the sum of two squares?
Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
Five equations... five unknowns... can you solve the system?
Find relationships between the polynomials a, b and c which are polynomials in n giving the sums of the first n natural numbers, squares and cubes respectively.
Can you fit polynomials through these points?
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
Prove that the product of the sum of n positive numbers with the sum of their reciprocals is not less than n^2.
Label this plum tree graph to make it totally magic!
Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.
Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
Find all the solutions to the this equation.
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
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?
Can you find the value of this function involving algebraic fractions for x=2000?
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.
By proving these particular identities, prove the existence of general cases.
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .
The sums of the squares of three related numbers is also a perfect square - can you explain why?
The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
Relate these algebraic expressions to geometrical diagrams.
Can you find the lap times of the two cyclists travelling at constant speeds?
To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
Can you find a rule which relates triangular numbers to square numbers?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?