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Question 15 - Sevenoaks School Year 7 Entrance Exam 2023

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Question 16 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 15 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 18 Haberdashers Monmouth Girls School HABS Entrance Examination 2015

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Question 44 - Merchant Taylors School 11 Plus Maths Specimen Paper 2

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Learn about Triangles for 11 Plus Exams

1. Triangles and their types

1.1 What is a triangle?

A triangle is a 2D shape with three sides. It has three angles and three vertices.

11+ Topicwise Triangles Article Image 01

1.2 Types of triangles

Based on length, there are three types of triangles:

      a) Equilateral Triangle

          An equilateral triangle has all three sides of equal length. Also, all the three angles     

          are equal and measure  60° each.

11+ Topicwise Triangles Article Image 02

      b) Isosceles Triangle

          An isosceles triangle has two sides of equal length. Angles opposite to two equal sides are            also equal

11+ Topicwise Triangles Article Image 03

      c) Scalene Triangle

          A scalene triangle has all three sides of different lengths. All three angles are also of                    different measures.

11+ Topicwise Triangles Article Image 04

What are Right-angled triangles?

 A triangle in which one of the angles measures 90° is called a right-angled triangle.

11+ Topicwise Triangles Article Image 05

A right-angled triangle has one right angle and two acute angles.

1.3 Inequality Rule

       The sum of lengths of any two sides of a triangle must be greater than the third side. 

        For example:

11+ Topicwise Triangles Article Image 06

       According to the rule, a + b > c                                            

                                       b + c > a

                                       a + c > b

       Example: Is it possible to form a triangle with the following measures?

         12 cm     15 cm    8 cm

       Solution:

        Let a=12 cm

             b=15 cm

             c=8 cm

       According to the Inequality rule,

       a + b > c

       a + b = 12 + 15 = 27  

       27 > 8

       b +c>a

       b + c = 15 + 8 = 23

       23 > 12

       c + a > b

       c + a = 10 + 9 = 19   

       19 > 12 

       As the measures given follow the inequality rule, they can form a triangle.

2. Angles in triangles

     A triangle has three angles. Doesn’t matter, which type of triangle it is, the sum of all the three angles in a triangle will always be equal to 180 degrees.

11+ Topicwise Triangles Article Image 07

     The above triangle has three angles a, b, and c. So a + b + c = 180°.

2.1  Example Question on working out missing angles in triangles.   

       For the triangle shown below, find the value of x. 

11+ Topicwise Triangles Article Image 08

       Solution:   

       Given triangle has one right angle, so it's a right-angled triangle.

       So one angle is 90°.

       Other acute angle is 50°.

       Sum of all the angles in a triangle is 180°.

        x + 90° + 50° = 180°

                 x + 140° = 180°

                             x = 180° - 140° 

                             x = 40°      

2.2   Example Question on missing angles in an isosceles triangle    

        Work out the value of the angle marked x for the isosceles triangle shown below.

11+ Topicwise Triangles Article Image 09

    Solution:

    For an isosceles triangle, angles opposite to equal sides are equal.

11+ Topicwise Triangles Article Image 10

   The Sum of all the angles in a triangle is 180°.

    x + x + 65° = 180°

        2x + 65° = 180°

                  2x = 180° - 65° = 115°

                    x = 115°÷ 2

                    x = 57.5°     

3. Perimeter and area of triangles      

Perimeter of a triangle: Sum of all the sides of a triangle.

Let us see the same triangle we used above.

11+ Topicwise Triangles Article Image 11

The perimeter of the above triangle is a + b + c

Formula for Area of Triangle:

Area of a triangle can be calculated by multiplying its height by the base and dividing by 2.

Its formula is Area of triangle = 1⁄2 × base × height

Line joining one of their sides (called the base) with the opposite point at 90 degrees is known as height.

3.2 Solved Example

Calculate the perimeter and the area of the triangle shown below.

11+ Topicwise Triangles Article Image 12

Solution:

Perimeter of a triangle = Sum of lengths of all three sides

                                          =7 + 9 + 4

                                         = 20 cm

Area of a triangle = 1⁄2 × h = 1⁄2 × 9 × 3  

                                 = 13.5 cm²

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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.

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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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