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Broad Topics > Information and Communications Technology > smartphone

### Tangled Trig Graphs

##### Stage: 5 Challenge Level:

Can you work out the equations of the trig graphs I used to make my pattern?

### Arclets

##### Stage: 4 Challenge Level:

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

### Where to Land

##### Stage: 4 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

### The Legacy

##### Stage: 4 Challenge Level:

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

### Cubestick

##### Stage: 5 Challenge Level:

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

##### Stage: 4 Challenge Level:

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .

### Areas of Parallelograms

##### Stage: 4 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

### Far Horizon

##### Stage: 4 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Inscribed in a Circle

##### Stage: 4 Challenge Level:

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

### Semi-detached

##### Stage: 4 Challenge Level:

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

##### Stage: 4 Challenge Level:

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Chances Are

##### Stage: 4 Challenge Level:

Which of these games would you play to give yourself the best possible chance of winning a prize?

### Tet-trouble

##### Stage: 4 Challenge Level:

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

### Napkin

##### Stage: 4 Challenge Level:

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

### In a Box

##### Stage: 4 Challenge Level:

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

### Gutter

##### Stage: 4 Challenge Level:

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

### Trapezium Four

##### Stage: 4 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

### Funnel

##### Stage: 4 Challenge Level:

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

### The Spider and the Fly

##### Stage: 4 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

### Making Sixty

##### Stage: 4 Challenge Level:

Why does this fold create an angle of sixty degrees?

### Three by One

##### Stage: 5 Challenge Level:

There are many different methods to solve this geometrical problem - how many can you find?

### Salinon

##### Stage: 4 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?

### Beelines

##### Stage: 4 Challenge Level:

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### One and Three

##### Stage: 4 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. . . .

### Hexy-metry

##### Stage: 4 Challenge Level:

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

### Nicely Similar

##### Stage: 4 Challenge Level:

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

### Sitting Pretty

##### Stage: 4 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?

### Three Cubes

##### Stage: 4 Challenge Level:

Can you work out the dimensions of the three cubes?

### Orbiting Billiard Balls

##### Stage: 4 Challenge Level:

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

### Curvy Areas

##### Stage: 4 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

##### Stage: 4 Challenge Level:

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

### Harmonic Triangle

##### Stage: 4 Challenge Level:

Can you see how to build a harmonic triangle? Can you work out the next two rows?

##### Stage: 4 Challenge Level:

If a sum invested gains 10% each year how long before it has doubled its value?

### What's Possible?

##### Stage: 4 Challenge Level:

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

### Plus Minus

##### Stage: 4 Challenge Level:

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

### Pair Products

##### Stage: 4 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

### The Root of the Problem

##### Stage: 4 and 5 Challenge Level:

Find the sum of this series of surds.

### Areas and Ratios

##### Stage: 5 Challenge Level:

Do you have enough information to work out the area of the shaded quadrilateral?

### Tiny Nines

##### Stage: 4 Challenge Level:

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

### Difference Sudoku

##### Stage: 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

### Expenses

##### Stage: 4 Challenge Level:

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

### Negative Power

##### Stage: 4 Challenge Level:

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

### Fair Shares?

##### Stage: 4 Challenge Level:

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?

### Odd Differences

##### Stage: 4 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.

### Why 24?

##### Stage: 4 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.

### Matchless

##### Stage: 4 Challenge Level:

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

### CD Heaven

##### Stage: 4 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

### Minus One Two Three

##### Stage: 4 Challenge Level:

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

### Partly Circles

##### Stage: 4 Challenge Level:

What is the same and what is different about these circle questions? What connections can you make?

### Take Three from Five

##### Stage: 4 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?