Other tags that relate to French Test
Creating and manipulating expressions and formulae. Measures of spread. Making and testing hypotheses. Maths Supporting SET. Handling data. Speed and acceleration. Spreadsheets. Generalising. Interpreting data. Averages.There are 131 results
Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae
How Do You React?
Age 14 to 16
Challenge Level
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Dating Made Easier
Age 14 to 16
Challenge Level
If a sum invested gains 10% each year how long before it has doubled its value?
Training Schedule
Age 14 to 16
Challenge Level
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
How Much Can We Spend?
Age 11 to 14
Challenge Level
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Unusual Long Division - Square Roots Before Calculators
Age 14 to 16
Challenge Level
However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?
Lap Times
Age 14 to 16
Challenge Level
Can you find the lap times of the two cyclists travelling at constant speeds?
Mediant Madness
Age 14 to 16
Challenge Level
Kyle and his teacher disagree about his test score - who is right?
Hike and Hitch
Age 14 to 16
Challenge Level
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. . . .
Can They Be Equal?
Age 11 to 14
Challenge Level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Around and Back
Age 14 to 16
Challenge Level
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
Temperature
Age 11 to 14
Challenge Level
Is there a temperature at which Celsius and Fahrenheit readings are the same?
Odd Differences
Age 14 to 16
Challenge Level
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
There and Back
Age 14 to 16
Challenge Level
Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?
One and Three
Age 14 to 16
Challenge Level
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
Hand Swap
Age 14 to 16
Challenge Level
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .
DOTS Division
Age 14 to 16
Challenge Level
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Salinon
Age 14 to 16
Challenge Level
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Your Number Is...
Age 7 to 14
Challenge Level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
' Tis Whole
Age 14 to 18
Challenge Level
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?
Triangles Within Triangles
Age 14 to 16
Challenge Level
Can you find a rule which connects consecutive triangular numbers?
Perfectly Square
Age 14 to 16
Challenge Level
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Triangles Within Squares
Age 14 to 16
Challenge Level
Can you find a rule which relates triangular numbers to square numbers?
Your Number Was...
Age 11 to 14
Challenge Level
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
Gutter
Age 14 to 16
Challenge Level
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Number Pyramids
Age 11 to 14
Challenge Level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Triangles Within Pentagons
Age 14 to 16
Challenge Level
Show that all pentagonal numbers are one third of a triangular number.
Three Four Five
Age 14 to 16
Challenge Level
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.
Sitting Pretty
Age 14 to 16
Challenge Level
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Unit Interval
Age 14 to 18
Challenge Level
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Lower Bound
Age 14 to 16
Challenge Level
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
How Big?
Age 11 to 14
Challenge Level
If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
The Pillar of Chios
Age 14 to 16
Challenge Level
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
Chocolate Maths
Age 11 to 14
Challenge Level
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
How Many Miles to Go?
Age 11 to 14
Challenge Level
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
Special Sums and Products
Age 11 to 14
Challenge Level
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Never Prime
Age 14 to 16
Challenge Level
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.
Diagonal Sums
Age 7 to 14
Challenge Level
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Simplifying Doughnut
Age 14 to 18
Challenge Level
An algebra task which depends on members of the group noticing the needs of others and responding.
Algebra from Geometry
Age 11 to 16
Challenge Level
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
Puzzling Place Value
Age 14 to 16
Challenge Level
Can you explain what is going on in these puzzling number tricks?
The Number Jumbler
Age 7 to 14
Challenge Level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Always a Multiple?
Age 11 to 14
Challenge Level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Generating Triples
Age 14 to 16
Challenge Level
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
NRICH is part of the family of activities in the Millennium Mathematics Project.