The individual numbers of a set are not given, but the mean and the count (how many numbers there are) are given. The student needs to work out the mean of a class if the mean of the boys and the mean of the girls are given. Similar questions appeared in the CSSE 11 plus exam in 2018, 2019, 2020, 2021, 2022 and 2023 maths papers. Suitable for all 11+ entry exams: Secondary school entrance exams, ISEB, CSSE, GL assessment, Grammar School entrance, Private schools, CEM and Bond.

Click on the link below to do a full set of practice questions.

https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.png00johan1https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.pngjohan12023-06-18 17:02:282023-06-18 17:02:28CSSE 11+ Maths: Very Important Concepts – Reverse mean

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11 Plus Entrance Exams including CEM (Durham University) exams.

Area and Perimeter of compound shapes.

This is an important and a popular topic for all the entrance exams (11 plus as well as independent school entrance exams). In the CSSE exam there was a question on composite shapes every year for the past 11 years. It also appeared in the CEM (Durham University) exams over the past two years.

For the 11 plus entrance exam, pupils need to be able to

work out the perimeter of 2-dimensional shapes:

normally some of the side-lengths are unknown and pupils must first work out the lengths of all the sides.

all sides can be given as letters and pupils need to use algebraic manipulation to find the perimeter.

work out the area of the following 2-dimensional shapes

area of a square

area of a rectangle

area of a parallelogram

area of a triangle

area of a trapezium

work out the area of compound/composite shapes,

work out the number of tiles needed to cover a certain area,

work out the amount of paint needed to paint a certain area,

find the lengths of sides from given coordinates to work out the area and perimeter.

The accompanying videos show you how to work out the area of a compound shape and how to work out the number of tiles needed to cover a certain area.

Area of compound shapes Video

Number of tiles needed to cover a certain area video

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A good knowledge of fractions is essential for the eleven plus and independent school entrance exams. A student must be familiar with the following topics:

Simplifying fractions (equivalent fractions)

Change fractions to decimals

Change fractions to percentages

Change improper fractions to mixed numbers

Finding a fraction halfway between two other fractions

Arrange fractions, decimals and percentages in order

Add fractions with different denominators

Subtract fractions with different denominators

Multiply fractions

Divide fractions

Finding a fraction of a known quantity

Fractions of unknown quantities

The accompanying video shows you how to work with fractions of unknown quantities. In these questions the student must first find the unit fraction (a fraction with a numerator of 1) and then find the whole number. (Divide everything by the numerator of the fraction and then times with the denominator of the fraction.)

The most difficult questions on Fractions of unknown quantities are problems like the following example.

I spend ½ of my money on food and ^{1}/_{5} on games. This left me with £21 pounds in my pocket. How much money did I have at the beginning?

In this case, the student must first add ½ and ^{1}/_{5}, and then subtract it from 1 to find the fraction that is left. They then need to be able to find the unit fraction to work out the amount at the beginning.

https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.png00johan1https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.pngjohan12016-05-30 17:00:362020-11-17 12:25:23Fractions for 11 + entrance exams video

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Prior knowledge you need to have in order to work out the size of unknown angles in triangles are:

Angles on straight lines add up to 180°

Angles around a point add up to 360°

When two straight lines cross the opposite angles are equal

This video starts by looking at the properties of the different types of triangles like namely scalene, isosceles, equilateral and right-angled triangle. It then covers the following angle properties:

Interior angles of a triangle adds up to 180°

Exterior angles of a triangle equals the sum of the opposite interior angles

https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.png00rohanc3https://www.11plusgenie.com/wp-content/uploads/2015/12/logo-original.pngrohanc32016-05-07 16:14:392020-11-17 12:26:14Angles in a triangle Video!

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