For most students, visualising how the net folds to form a cube, is a difficult concept. These questions are a regular occurrence in 11 plus entrance exams and are also important for the CEM (Durham University) exam.
Three different types of questions can be asked:
Type 1: A net is given and the student must identify the cube that can be formed from the given net.
Type 2: A net is given and the student must identify the cube that cannot be formed from the given net.
Type 3: Three or four different views of the same cube are given and the student must identify the correct net of the cube.
In this series of videos we show you how to approach these questions.
The video tutorials can also be used as a revision aid before the 11 plus entrance exams. In each video we show you the theory needed to solve the questions and we also give two or three worked examples of typical exam questions. We also use animations to show you how the cubes are formed.
Video 1 shows you how the 11 nets can be folded to form the corresponding cubes.
Video 2 shows you how to fold nets with numbers on each face.
Video 3 shows you how to identify the correct cube if there are diagrams/shapes on the faces.
Non-verbal Reasoning Type 13: Plans and Elevations of 3D shapes
When an architect designs a building he/she has to make 2-dimensional drawings to show what the building will look like from each side. These drawings are called plans and elevations.
Plan and elevations are all different perspectives of the same 3D shape.
The view from the top is called the plan.
The plan is just a bird’s eye view of the shape.
Front and Side elevations
The views from the front and sides are called the elevations.
In a question, you will get an indication of which perspective is the front and which one is the side.
You will also be given a grid on which you can do your drawings of the plan and the elevations.
In this type of questions you are given a 3D shape and you must identify the drawings of the plan, the front elevation and the side elevation.
In this video we use animations to show the pupil what the plan and elevations of a 3D shape will look like.
Plans and Elevations of 3D shapes (Bird’s eye view) VIDEO!
For the Eleven Plus and CEM exams, pupils need to be able to
- Substitute numbers into formulae and evaluate the formula.
- Example 1: Work out the value of 3a – 2b + 4c if a = 5, b = 3 and c = 2
- Example 2: C = 5 x (F – 32) ÷ 9. What is C when F is (a) 50 and (b) 5?
- Simplify algebraic expressions (collect like terms).
- The angles of a triangle are a, 2a and 2a + 30. Work out the value of a.
- Solve equations with the unknown on one side.
- What is n if 6n – 5 = 37?
- Solve equations with the unknown on both sides (accompanying video)
- Work out the value of x if 5x + 7 = 25 – x
- Solve equations with 2 or more variables.
- There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
- Form algebraic expressions and equations (accompanying video)
- The newsagent charges x pence for a biro and y pence for a pencil. Write down an expression using x and y for the cost of three biros and two pencils.
Forming expressions and equations Video!
Solve equations with the unknown on both sides of the equal sign Video!
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
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.