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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Calculating with ratio & proportion

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Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

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Temperature

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

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Orange Drink

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

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Pumpkin Pie Problem

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

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Oh for the Mathematics of Yesteryear

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

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Two Ladders

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Areas and Ratios

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

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Straw Scaffold

Stage: 3 Challenge Level: Challenge Level:1

Build a scaffold out of drinking-straws to support a cup of water

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Toad in the Hole

Stage: 3 Challenge Level: Challenge Level:1

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

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The Fastest Cyclist

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

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Tray Bake

Stage: 3 Challenge Level: Challenge Level:1

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

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Make Your Own Solar System

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Making a scale model of the solar system

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Retiring to Paradise

Stage: 3 Challenge Level: Challenge Level:1

When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?

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Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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Nutrition and Cycling

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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Why Multiply When You're about to Divide?

Stage: 5 Challenge Level: Challenge Level:1

A brief introduction to PCR and restriction mapping, with relevant calculations...

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Diamonds Aren't Forever

Stage: 5 Challenge Level: Challenge Level:1

Ever wondered what it would be like to vaporise a diamond? Find out inside...

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Gassy Information

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Do each of these scenarios allow you fully to deduce the required facts about the reactants?

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Eudiometry

Stage: 5 Challenge Level: Challenge Level:1

When a mixture of gases burn, will the volume change?

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Striking Gold

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

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Extreme Dissociation

Stage: 5 Challenge Level: Challenge Level:1

In this question we push the pH formula to its theoretical limits.

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Exact Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Which exact dilution ratios can you make using only 2 dilutions?

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Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

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Dilution Series Calculator

Stage: 4 Challenge Level: Challenge Level:1

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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Using the Haemocytometer

Stage: 4 Challenge Level: Challenge Level:1

Practise your skills of proportional reasoning with this interactive haemocytometer.

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Conversion Sorter

Stage: 4 Challenge Level: Challenge Level:1

Can you break down this conversion process into logical steps?

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Mixed up Mixture

Stage: 4 Challenge Level: Challenge Level:1

Can you fill in the mixed up numbers in this dilution calculation?

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How Random!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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Eight Ratios

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

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Wedge on Wedge

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

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Once Upon a Time

Stage: 2 Challenge Level: Challenge Level:1

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

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Half a Triangle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

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Bus Stop

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

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The Tree and the Greenhouse

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Mum, Dad, Tim and Jill moved into a new house. If they cut down the big tree, will it miss the greenhouse?

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Cherry Buns

Stage: 2 Challenge Level: Challenge Level:1

Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?

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Hello Again

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

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Arrh!

Stage: 4 Challenge Level: Challenge Level:1

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

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A Shade Crossed

Stage: 4 Challenge Level: Challenge Level:1

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

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Halving the Triangle

Stage: 5 Challenge Level: Challenge Level:1

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

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Conical Bottle

Stage: 4 Challenge Level: Challenge Level:1

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

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Chord

Stage: 5 Challenge Level: Challenge Level:1

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

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Golden Ratio

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

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Roasting Old Chestnuts 3

Stage: 3 and 4

Mainly for teachers. More mathematics of yesteryear.

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Five Circuits, Seven Spins

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

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Do Unto Caesar

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .

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Square Pegs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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Burning Down

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

One night two candles, one of which was 3 cm longer than the other were lit. The longer one was lit at 5.30 pm and the shorter one at 7 pm. At 9.30 pm they were both the same length. The longer. . . .

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Gift of Gems

Stage: 4 Challenge Level: Challenge Level:1

Four jewellers possessing respectively eight rubies, ten saphires, a hundred pearls and five diamonds, presented, each from his own stock, one apiece to the rest in token of regard; and they. . . .

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Contact

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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Plane to See

Stage: 5 Challenge Level: Challenge Level:1

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.