OxBridge Centre Year 4 Advanced Problem Solving Sample Workbook

Problem Solving 49 =

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Algebra Warm Up! A

I think of a number, I add 9 to my number and my answer is 12. What number am I thinking of?

B

B − 4 = 15. What is the value of B?

C

There are N number of people in the back row. 3 more people join them. How many people are in the back row now?

Work Out! A

A school is hosting a summer fair. It is on during the weekends. On Saturday, X number of people came. On Sunday, 738 people came. Altogether 1329 people came to the fair. Find the value of X.

B

Andy bought X amount of sweets at a shop. Sam bought 15 more than Andy. How many sweets did Sam buy?

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C

The cost of a sandwich is £S. How much would it cost for me to buy 4 sandwiches?

D

A calculator costs £C. I want to buy 2 calculators and a pencil case. If the pencil case costs £5 and the total cost is £11, how much does a calculator cost?

E

The cost of 7 game consoles is £G. How much would it cost for 1 game console?

F

The cost of a boat trip and dinner for 2 people is £150 altogether. The dinner costed £42 altogether. How much is the boat trip per person?

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Cool Down!

A

I think of a number, I double my number and my answer is 20. What number was I thinking of?

B

Ronald had a P number of cookies. He bought 10 more cookies and ate 6 of them.

He now has 6 cookies left. How many cookies did Ronald have at first?

C

D

In a cupcake mixture, 500g of flour and 400g of butter was added and now it weighs 1400g. How much did the mixture weigh before adding the flour and butter?

I think of a number, I halve it and I’m left with 12. What number am I thinking of?

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Mean, Median, Mode and Range

Warm Up!

Using the numbers below, answer questions A, B and C. 2, 4, 5, 7, 7 A

What is the mode of the numbers?

B

Calculate the range.

C

Find the mean.

Tip!

Mean is the average of the numbers. It is calculated by adding up the numbers and dividing by the number of numbers there are.

1, 2, 2, 2, 3 The mean of the numbers would be (1 + 2 + 2 + 2 + 3) ÷ 5 = 10 ÷ 5 = 2

Median is the middle number. When finding the median, make sure you put the numbers in order before finding the median!

1, 2, 2, 2, 3 The median would be 2.

Mode is the most common number (the most popular number) in a set of numbers 1, 2, 2, 2, 3 The mode would be 2 as it appears the most.

Range is the difference between the highest number and the lowest number in a set of numbers.

1, 2, 2, 2, 3

The range would be 3 − 1 = 2.

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Work Out! A

The following numbers: 6, 3, 2, 5. What is the mean?

B

The temperature in London was recorded over a 5 day period. The temperatures were 14°C, 8°C, 10°C, 11°C and 17°C. What is the range?

Here are some numbered cards:

6

5

4

6

C

Choose 3 numbers so that the mean would be 5 and there is no mode.

D

A numbered card 9 is added to the set of cards. Calculate the mean.

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E

The temperature in London was recorded over a 7 day period. The range was 10°C. If the highest temperature was 25°C, what was the temperature of the coldest day over the 7 day period?

F

The mean of 2 numbers is 9. A 3rd number is added and the mean increase to 10.

What is the value of the 3rd number?

G

The mean of 5 numbers is 4. Another number is added and the mean increases to 5. What is the value of the 5th number?

H

The mean of 4 numbers is 7. What is the total of the numbers?

Hint!

You may have to use your knowledge of algebra.

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Cool Down!

A

Charlie puts down the numbered cards 1, 2, 2, 3, 3, 3 and 4. The numbers 5 and 6 are added to the pile. Does the median change? What would the median be after the numbers have been added?

B

Charlie wants to know the range of the numbers before the 5 and 6 were added.

What is the range of the original 7 numbers?

C

There are 4 numbers: 9, 3, 7 and A. The mean is 6. What is the value of A?

D

Another number B is added to the above. The range is 7. What are the possible values for B?

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Decimals Warm Up! A

What is 2.9 + 4.2?

B

Find the difference between £9.40 and £2.50.

C

A hamster weighs 1.2kg and a rabbit weighs 1.8kg.

How many kilograms is the hamster lighter than the rabbit?

Work Out! A

The distance from home to work is 26.8 miles. How many miles will I have to travel in a week? (Assuming I go work 5 days a week).

B

The length of my rectangular bed is 125.53 cm. The width of the bed is 74.21cm Calculate the perimeter of the bed.

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C

A pack of 6 batteries costs £4.68. Calculate the cost of 18 batteries.

Hint!

Find how many packs you need first.

D

£15.70 is equally shared between 5 people. How much would they each get?

E

A car travels 15.5 miles per hour. Assuming the car drives at the same speed, how far would it travel in 8 hours?

F

In the classroom, Milly recorded the temperature of 16.2°C. By noon, the temperature increased by 5.7°C. By 3pm the temperature dropped by 8.2°C. What is the temperature at 3pm?

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G

Georgia wants to buy 3 items: an MP3 player, headphones and a portable charger. They cost £79.21, £23.11 and £15 respectively. How much would it cost Georgia to buy the 3 items?

H

For a test, Oscar studied 24.5 hours over the course of a week. On average, how many hours did he study each day?

I

The weight of a horse is 123.63kg and the weight of a dog is 52.2kg. How many kilograms heavier is the horse compared to the dog?

J

Tyler was competing in a triple long jump competition. He jumps 2.43 m the first jump, 1.48m the second jump. Altogether he jumped 7.45 m. How far did he jump in the 3rd jump?

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Cool Down!

A

The weight of one apple is 0.24kg and another is 0.139kg. What is the weight of both apples?

B

Ariel has 2 different pens. One has 2.42 ml of ink and another has 3.2 ml of ink.

How many millilitres of ink are there altogether?

C

The cost of a bunch of bananas is ÂŁ0.77. How much would it cost to buy 2 bunches of bananas?

D

A bottle holds 1.5 litres of water. By the end of the day, only 0.68 litres of water remains. How many litres of water was drunk that day?

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Advanced A

Extra Homework

In a farm, there are 2 different types of animals: chicken and sheep. There are 7 animals on the farm. Altogether there are 20 animals legs. How many chicken and sheep are there?

Chicken: Sheep:

B

The mean of six numbers is 12. The mean of two of those numbers is 10.

What is the mean of the other 4 numbers?

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