Creating and manipulating expressions and formulae

There are 198 NRICH Mathematical resources connected to Creating and manipulating expressions and formulae
System Speak
problem
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System speak

Age
16 to 18
Challenge level
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Five equations... five unknowns... can you solve the system?
Sitting Pretty
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Sitting pretty

Age
14 to 16
Challenge level
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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?
Dating made Easier
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Dating made easier

Age
14 to 16
Challenge level
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If a sum invested gains 10% each year how long before it has doubled its value?
Your number was...
problem
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Your number was...

Age
11 to 14
Challenge level
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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?
Iff
problem
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Iff

Age
14 to 18
Challenge level
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Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Diagonal Sums
problem
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Diagonal sums

Age
7 to 14
Challenge level
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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?

Gutter
problem
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Gutter

Age
14 to 16
Challenge level
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Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Perimeter Expressions
problem
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Perimeter expressions

Age
11 to 14
Challenge level
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Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Legs Eleven
problem
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Legs eleven

Age
11 to 14
Challenge level
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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Special Numbers
problem
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Special numbers

Age
11 to 14
Challenge level
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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?