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## Mathematics Problems for 12 – 16 year olds

This section is a brief test to see if you could survive in the world of Egytian numerals and mathmatics. To find out if you have passed the test, email me to check your answers.

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Question 1 of 7## 1. Question

5 pointsProblem 1.

If pyramids have bricks

How many bricks are needed to build pyramids?

Correct

Problem 1

If 3 pyramids have 1572 bricks how many bricks are needed to build 5

pyramids?Answer 1.

Number of bricks to build one pyramid = 1572/3 = 524

Number of bricks to build 5 pyramids = 524*5 = 2620Ans: 2620 bricks

Incorrect

Question 2 of 7## 2. Question

10 pointsIf bucket of food feeds camels for days.

How many buckets are needed to feed camels for day?

Correct

Problem 2.

If 1 bucket of food feeds 2 camels for 3 days, how many buckets are needed

to feed 12 camels for 1 day?Answer 2.

Food for 2 camels for one day = 1/3

Food for 12 camels for one day = (12/2)*(1/3) = 6/3 = 2Ans: 2 buckets

Incorrect

Question 3 of 7## 3. Question

15 pointsProblem 3.

The kings of Megiddo and Kadesh are preparing to invade Egypt. But pharaoh Thutmose III has decided to cross the Sinai desert and attack his enemies before they are ready.He is taking men with him.

It takes him days to cross the desert and each man needs litres of water per day.How much water will he need to take?

Correct

Problem 3.

The kings of Meggido and Kadesh are preparing to invade Egypt. But Pharoah Thutmose III has decided to cross the Sinai Desert and attack his enemies before they are ready.He is taking 300,000 men with him. It takes him 30 days to cross the desert and each man needs 2 litres of water per day – how much water will he need to take?

Answer 3.

Total number of men = 300,001 (including Thutmose)

If each man needs 2 litres of water per day, total amount of water per day

=300,001*2 = 600,002 litres per day

Total amount of water for 30 days = 600,002*30 = 18,000,060Ans: 18,000,060 litres

Incorrect

Question 4 of 7## 4. Question

15 pointsBefore Thuthmose and his army reach Aaruna, at the foot of the hills in which Meggiddo stands, he is going to send men to reconnoitre a narrow pass.

The expedition is expected to last days. They are using camels to carry their food and water. Each person needs kilogram of food and litres of water per day, and each camel needs kilograms of food per day (they don’t need anything to drink because they’re camels, and camels don’t get thirsty very often).

If each camel can carry kilograms and the rest of the expedition equipment weighs kilograms.How many camels are needed to carry the water, food and equipment? (The density of water in ancient Egypt was kilogram per litre)

Correct

Before Thutmose and his army reach Aaruna, at the foot hills in which Meggido stands, he is going to send 3 people to reconnoitre a narrow pass.

The expedition is expected to last 10 days. They are using camels to carry their food and water. Each person needs 1 kilogram of food per day and 2 litres of water per day, and each camel needs 3 kilograms of food per day.

If each camel can carry 150 kilograms and the rest of the expedition equipment weighs 510 kilograms, how many camels are needed to carry the water, food and equipment. (assume density of water = 1 kg/litre)

Answer 4.

We have: 3 people needing 1 kg of food and 2 litres of water per day. plus 510 kg of expedition equipment.

For one day and 3 people, we need 3 kg of food and 3*2 = 6 litres of water.

For ten days and 3 people, we need 3*10 = 30 kg of food and 6*10 = 60 litres of water.

60 litres of water weighs 60 kg.

Total weight of food and water for expedition members = 30 kg (food) + 60 kg (water) = 90 kg

Total weight of kit = 510 + 90 = 600 kg.

Number of camels to carry kit = 600/150 = 4 camelsNow 4 camels need 3*4 = 12 kg of food per day so 120 kg of food for ten days.

Therefore we need an extra camel to carry the camels food, the extra camel will need to be fed as well, 3*10 = 30 kg of food.

Therefore total weight of camel’s food = 120 + 30 = 150 kg this may be carried by one camel so we need: 4 camels for the expedition kit, and 1 camel for the camels food.Hence a total of 5 camels.

Incorrect

Question 5 of 7## 5. Question

20 pointsAn Egyptian wants to build a pyramid in his back garden to bury his favourite cat.

His garden is meters wide and meters long.

He has goats which each need square metres of land to graze on and camels which each need square

meters of land to garze on.If his pyramid has a square base what is the maximum length of one side of the pyramid?

Correct

Problem 5a.

An Egyptian wants to build a pyramid in his back garden to bury his favourite cat. His garden is 30 metres wide and 35 metres long. He has 10 goats which each need 35 square metres of land to graze on, and 3 camels which each need 100 square metres of land to graze on.

If his pyramid has a square base what is the maximum length of one side of the pyramid?

Answer 5a.

Total area of garden = 30 * 35 = 1050 square metres.

Ten goats needing 35 square metres of land each means a total of 10 * 35 = 350 square metres of land for the goats.Three camels needing 100 square metres of land each means a total of 3 * 100 = 300 square metres of land for the camels.

Therefore unused land available for pyramid = 1050 – (350 + 300) = 400 square metres

If the pyramid has a square base and the area of the base is 400 square metres the length of one side = (400)^0.5 [square root of 400] = 20 metres.

Ans: 20 metres

Incorrect

Question 6 of 7## 6. Question

30 pointsWhat will the surface area of the pyramid be if the angle of elevation is degrees and the pyramid is smooth?

(ignore the base of the pyramid as that is on the ground)

Give the answer as a whole number.

Correct

What will the surface area of the pyramid be if the angle of elevation is 45 degrees and the pyramid is smooth (ignore the base of the pyramid as that is on the ground)? Give the answer as a whole number.

Answer 5b

Angle of elevation = 45 degrees.

Area of triangle = 0.5 * base * perpindicular height.

The vertical height of the pyramid, h, is given by:

h/10 = tan(45) [tangent of an angle = opposite/adjacent]

=> h = 10 * tan(45)

=> h = 10 metres.The perpindicular height of one side, from Pythagoras’ Theorem is:

[Pythagoras’ Theorem => hypotenuse = (opposite^2 + adjacent^2)^0.5 ]

perpindicular height = (h^2 + 10^2)^0.5 = 200^0.5The surface area of one side is found using the formula for the area of a

triangle, giving: area = 0.5 * length of base * perpindicular height of side.

area = 0.5 * 20 * (200^0.5) = 20000^0.5 = 141.4 square metres.There are four sides of the pyramid, so the total surface area

(ignoring the base) is 4 * 141.4 = 566 square metres (0 dp).Ans: 566 Square metres (0 dp)

Incorrect

Question 7 of 7## 7. Question

25 pointsThe Egyptian wants to paint the pyramid black (his cat was black) and a barrel of tar covers square metres how many barrels of tar will he need to buy?

(unfortunately the market only sells full barrels)

Correct

Problem 5c.

The Egyptian wants to paint the pyramid black (his cat was black). If a barrel of tar covers 22 square metres how many barrels of tar will he need to buy

(unfortunately the market only sells full barrels)?Total surface area to be painted = 566 square metres. If one barrel covers 22 square metres, he needs 566 / 22 = 25.7 barrels.

Therefore he needs to buy 26 barrels of tar.Ans: 26 Barrels

Incorrect

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