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Question 13 - Sevenoaks School Year 7 Entrance Exam 2023

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Interpreting Word Problems for 11 Plus Exams

1.What are Word Problems?

Word problems are mathematical problems that are presented in the form of a real-life situation or scenario. They often require students to use their critical thinking skills to analyze and interpret the information given in the problem and apply their mathematical knowledge to find a solution. Word problems can involve a range of mathematical concepts such as addition, subtraction, multiplication, division, fractions, percentages, ratios, and more. They are commonly used in math textbooks, tests, and exams to test students' understanding of mathematical concepts and their ability to apply them in real-life situations.

1.1 Vocabulary used in Word Problems

Children must be aware about the vocabulary associated while solving word problems:
Look at the table below to understand the logic of how to analyse a word problem:

01-Word Problems-11+ Topicwise Article

1.2 What sort of Word Problems may you encounter in your 11 plus exam?

You may encounter Word Problems from the following nine strands in your 11 plus exams:

  1. Number and Place Value
  2. Calculations
  3. Fractions, Decimals & Percentages
  4. Ratio and Proportion
  5. Algebra
  6. Measurement
  7. Geometry: Properties of Shapes
  8. Geometry: Position & Direction
  9. Statistics

1.3 Solved Examples

Example 1:
Jessica has 5 cards with the digits 9, 5, 7, 1 and 8 written on them.

9 5 7 1 8

Write down the smallest number Jessica can make using all of these cards:

Solution:
The cards given are: 9, 5, 7, 1, 8
Arranging the cards in ascending order: 1, 5, 7, 8, 9
Smallest five digit number formed is: 15789

Example 2:
Six friends shared the cost of a tennis court (priced at  3 million pounds) equally. How much did each of them pay?

Solution:

3 million pounds = £3,000,000

£3,000,000 ÷ 6 = £500,000

Each of the friends have to pay £500000.

Example 3:

Sam spends 1/3 of his money. He then spends 1/3 of what he has left. What fraction of his money did he spend altogether?

Solution:

First time, Sam spends = 1/3 of his money

Remaining money = 1 - 1/3 = 2/3 of his money

Second time, Sam spends = 1/3 of his remaining money

= 1/3 × 2/3 of his money

= 2/9 of his money

Total spending = 1/3 of his money + 2/9 of his money

= 1/3 + 2/9

= 3/9 + 2/9

= 5/9

Sam spends 5/9 of his money altogether.

Example 4:
A drink is made by mixing fruit juice with water. 39 ml of fruit juice is needed to make 600 ml of the drink. How much water is needed to make 800 ml of the drink?

Solution:

39 ml of fruit juice is required to make 600 ml of the drink.

(600 - 39) = 561 ml of water required to make 600 ml of drink

Required water to make 200 ml of the drink = 561 ÷ 3 = 187 ml

Required water to make 800 ml of the drink = 187 x 4 = 748 ml

Example 5:
Miley and Seema are collecting money for charity. Miley collects £10 more than Seema. Altogether they collect £240. How much did Seema collect?

Solution:

Let Seema collect = £x

Then, Miley collected = £(x + 10)

Total money = £240

x + x + 10 = 240

2x + 10 = 240

2x = 240 - 10

2x = 230

x = 230 ÷ 2

x = £115

Seema collected £115.

Example 6:

Add together 5 metres, 5 centimetres and 5 millimetres. Give your answer in millimetres.

Solution:

5 m = 5000 mm & 5 cm = 50 mm

5 m+ 5 cm + 5 mm

= 5000 mm + 50 mm + 5 mm

= 5055 mm

Example 7:

Saif puts five dots on a piece of paper in such a way that no three dots are in a straight line. He joins every dot to every other dot with a straight line. How many lines does he draw?

Solution:

Saif draws 5 dots such that no three dots are in a straight line.
The dots represent the vertices of a pentagon Thus, the number of lines can be found using,

02-Word Problems-11+ Topicwise Article

Thus, 10 lines can be drawn.

Example 8:

Give the size of the obtuse angle between the compass directions NE and S.

Solution:

03-Word Problems-11+ Topicwise Article

The angle between Northeast to East = 45°

The angle between East to South = 90°

The obtuse angle between NE and S = 45° + 90° = 135°

Example 9:
The bar graph below shows the number of pet sets in each house in a street.

04-Word Problems-11+ Topicwise Article

(a) How many houses have 1 pet?

(b) How many houses are there in the street?

(c) How many pets are there in the street?

Solution:

(a) 14 houses have 1 pet.

(b) 9 + 14 + 4 + 3 = 30

There are 30 houses in the street.

(c) (9 x 0) + (14 x 1) + (2 x 4) + (3 x 3)

= 0 + 14 + 8 + 9

= 31

There are 31 pets in the street.

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  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

    How to prepare for the 11+ Maths exam?

    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

    Can I cancel my subscription?

    Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.

    You should, therefore, make sure that the Maths online subscriptions fulfil your needs before you subscribe.

    As these are digital products, we advise parents to go through our Free Past Papers provided on our website and once decided they can buy subscriptions.

    Maths:
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    What kind of questions are asked in the 11 Plus Maths exam?

    The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.

    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
    • Ratio and proportion.
    • Algebra.
    • Measurement.
    • Geometry (properties and position of shapes, coordinates)
    • Statistics.

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