Maths Posts

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Algebra for the 11 plus entrance exam

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!

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Area and Perimeter of compound shapes.

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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Fractions for 11 + entrance exams 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.

 

 

 

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Percentage of an amount video

Percentages

For the 11+ and Independent School Entrance Exams, pupils need to be able to do the following percentage calculations:

  • Percentages to fractions
  • Percentages to decimals
  • Percentage of an amount
  • Increase/decrease an amount by a certain percentage
  • write one number as a percentage of another number
  • simple reverse percentages

This video shows you how to find a percentage of an amount.

We first work out 10% of the amount – divide by 10

To find 5% : divide the 10% by 2

To find 2 1/2 percent : divide 5%  by 2

To find 1% – divide the amount by 100.

 

 

 

Angles in a triangle Video!

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