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
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.
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