## Exam-Style Questions on Similarity## Problems on Similarity adapted from questions set in previous Mathematics exams. |

## 1. | GCSE Higher |

A triangle, ABC, is drawn (not to scale) with AC = 12.6 cm.

A line segment, DE, is drawn with length 6.2cm on the triangle parallel to AB with DC = 4.2 cm.

(a) Calculate the length of AB.

(b) Calculate the length of BE if BC = 10.5 cm.

## 2. | GCSE Higher |

(a) Victor estimates the height of a flag pole by holding a ruler vertically so the height of the flag pole is exactly covered by the ruler when he is standing 240 centimetres from the flag pole.

The ruler is 30 cm long.

The horizontal distance of his eyes from the ruler is 40cm.

Calculate an estimate of the height of the flag pole.

(b) Give two reasons why this method may not be suitable to estimate the height of a very tall building.

## 3. | GCSE Higher |

(a) Find the area of a regular octagon if the distance from its centre to any vertex is 10cm.

(b) If the octagon had been cut from a piece of square card that was only just large enough, work out the area of the original square piece of card.

(c) A table top is made in the shape of a regular octagon with sides five times as long as the card model. Find the ratio of the area of the table top to the area of the card model.

## 4. | GCSE Higher |

Two similar pentagonal based pyramids have surface areas 200 cm^{2} and 50 cm^{2} respectively.

The volume of the larger pyramid is 800 cm^{3}.

Show that the volume of the smaller pyramid is 100 cm^{3}.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Aruna Upadhyayula, Bahrain

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."

Madiwa Otieno, Kenya

Tuesday, February 5, 2019

"A very great site.Nice questions."

Yuli, Woodmansterne

Tuesday, April 2, 2019

"This website is amazing it helps me with my maths to get good marks in my upcoming test. Thanks."