Creating and Manipulating Linear and Quadratic Expressions - Stage 4

2-digit Square

Age 14 to 16
Challenge Level

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?

Plus Minus

Age 14 to 16
Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

What's Possible?

Age 14 to 16
Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Why 24?

Age 14 to 16
Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Always Perfect

Age 14 to 18
Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

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?

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?

Multiplication Square

Age 14 to 16
Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Finding Factors

Age 14 to 16
Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

Factorising with Multilink

Age 14 to 16
Challenge Level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Pythagoras Perimeters

Age 14 to 16
Challenge Level

If you know the perimeter of a right angled triangle, what can you say about the area?

Difference of Two Squares

Age 14 to 16
Challenge Level

What is special about the difference between squares of numbers adjacent to multiples of three?

Hollow Squares

Age 14 to 16
Challenge Level

Which armies can be arranged in hollow square fighting formations?

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?

Creating and Manipulating Linear and Quadratic Expressions - Short Problems

Age 11 to 16

A collection of short problems on creating algebraic expressions.

Square Number Surprises

Age 14 to 16
Challenge Level

There are unexpected discoveries to be made about square numbers...

Puzzling Place Value

Age 14 to 16
Challenge Level

Can you explain what is going on in these puzzling number tricks?

Brian's Number

Age 14 to 16 Short
Challenge Level

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

Choir Boys

Age 14 to 16 Short
Challenge Level

Can you work out how many members this choir has from these percentages?

Cuboid Perimeters

Age 14 to 16 Short
Challenge Level

Can you find the volume of a cuboid, given its perimeters?

Third Side

Age 14 to 16 Short
Challenge Level

What are the possible lengths for the third side of this right-angled triangle?

Stolen Pension

Age 14 to 16 Short
Challenge Level

How much money did the pensioner have before being robbed?

Clever Calculation

Age 14 to 16 Short
Challenge Level

Find the shortcut to do this calculation quickly!

Order the Products

Age 14 to 16 Short
Challenge Level

Can you put these products in order of size?

Length, Width and Area

Age 14 to 16 Short
Challenge Level

The area of a rectangle is 225 square units. Find its width.

Find the Factor

Age 14 to 16 Short
Challenge Level

Find a factor of $2^{48}-1$.