Book 2: Advanced

3D Spatial Reasoning

240 practice questions with full explanations, for ages 10 to 12.

Every question. One true answer.

The cover of 3D Spatial Reasoning, Book 2: Advanced.

The series

The cover of 3D Spatial Reasoning, Book 1: Foundation.
Ages 9 to 11

Book 1: Foundation

Start here: the four kinds of 3D question, 200 in all, with four options each.

See Book 1
The cover of 3D Spatial Reasoning, Book 2: Advanced.
Ages 10 to 12

Book 2: Advanced

Harder questions with five options each, and two timed tests: 240 in all.

You are here

Four kinds of question, 50 of each

Each section starts with what to do, three tips and two worked examples, then 50 questions in sets of 10 that get harder as you go, each set with a score box. The book ends with two timed tests of 20 mixed questions. The pictures below are real questions from the book.

Question 35 from the book: cube nets.
50 questions

Cube nets

Each net folds up to make a cube, with the patterns on the outside. Find the one cube, out of five, that the net could make. Most patterns in this book point one way, so check which way each one points as well as where it is. From Set 4 the question turns round: four cubes can be made, and you find the one that cannot.

Question 85 from the book: views of 3d shapes.
50 questions

Views of 3D shapes

Each shape is made of the number of cubes stated, and every cube sits on the table or on top of another cube. Some cubes may be hidden, but the number of cubes tells you where they must be. Arrow F marks the front and arrow S the side. Find the view asked for.

Question 135 from the book: turning 3d shapes.
50 questions

Turning 3D shapes

All the shapes are made of 6 cubes joined face to face. Find the one option that is the first shape turned around. A mirror image does not count.

Question 185 from the book: paper folding.
50 questions

Paper folding

A square of paper is folded two or three times as shown, then two holes are punched through all the layers. Find the paper as it looks when it is opened out flat.

New in Book 2

A new look, harder questions and a timed finish, for children who are ready to go further.

  • Six new patternsArrow, flag, heart, half-shaded square, hourglass and target. Most point one way, so their direction matters.
  • Five options, A to EEvery question has five options and exactly one right answer.
  • Which cube could it NOT make?From Set 4 the net questions turn round: four cubes can be made, and you find the one that cannot.
  • Harder shapesHidden cubes and side views, shapes of 6 cubes, and paper folded two or three times with two holes.
  • Sets that get harderIn each section, the five sets of 10 run from easier to harder.
  • Two timed tests20 mixed questions in 20 minutes each, with a practice answer sheet.
Part of the page How to read the drawings: the six patterns, and a cube net drawn with bold outside edges and dashed folds.
How to read the drawingsOne page at the front sets out the rules: the six patterns, the bold outlines and dashed folds, and where the light comes from.
The practice answer sheet for the first timed test, with a row of lozenges A to E for each question.
A real test, at homeEach timed test has 20 questions, five of each kind, to do in 20 minutes, with an answer sheet like the ones machines mark.

Quick to mark, with every answer explained

Mark a set in a minute with the one-page answer key, then read why the right answer is right and why each of the others is wrong, so a mistake becomes something to learn from.

The top of the quick answer key page, with the answer letters in rows of 10.
Quick answer keyAll 240 answers on one page, one row per set of 10.
Part of an explanations page: each answer with the reason it is right and why each other option is wrong.
Every answer explainedWhy the right answer is right, and why each wrong option is wrong.

Every question has exactly one right answer

Each question was made from exact geometry and checked by computer, twice, by two independent methods, before it was printed. A question was used only if both methods found exactly one correct option and the drawing itself settled the answer.

  • 2independent checking methods for every question
  • 989faulty questions planted on purpose to test the checks: all caught
  • 57candidate questions rejected while the book was made
  • 3,481ways to join 6 cubes, all checked for the turning questions

Try 40 questions free

The free sample has the page on how to read the drawings and, from each section, its opening pages, two worked examples and first 10 questions, with the answer key and explanations for all 40.

  • Cube nets: questions 1 to 10
  • Views of 3D shapes: questions 51 to 60
  • Turning 3D shapes: questions 101 to 110
  • Paper folding: questions 151 to 160

No sign-up needed. Print it, or use it on screen.

The cover of the free sample, marked Free sample.

Get the book

The same 240 questions, as a paperback or as a PDF to print at home.

Paperback

The printed book, A4

  • 108 pages, black and white, on white paper
  • Room to work in the book itself
  • Printed and posted by Amazon
PDF edition

A download to print at home, A4

£5.99

  • 108 pages and a colour cover
  • Print the pages you need, for your own family or pupils
  • Tap the contents or the answer key to jump to a page

Questions

Who is this book for?

Children aged 10 to 12 who are ready for harder questions, especially those preparing for the 11+, where many non-verbal reasoning papers include 3D and spatial questions. The questions are original and are not taken from any test.

Which book should we start with?

Book 1: Foundation, for ages 9 to 11, starts from the beginning. Book 2: Advanced, for ages 10 to 12, has harder questions, five options in every question and two timed tests. If the free sample of Book 2 feels hard, start with Book 1.

How should we use it?

Work through a set of 10, mark it with the quick answer key, then read the explanations for any mistakes. Short, regular sessions work better than long ones. Keep the timed tests for the end, when the sections feel comfortable.

Can I print the PDF?

Yes. You may print or copy pages for your own family or pupils. Please do not share the file itself.

Is it linked to an exam board or test provider?

No. This book is not affiliated with, or endorsed by, any 11+ test provider or exam board.

What does UNATUM mean?

It comes from the Latin unum tantum, ‘only one’: every question has only one right answer.

Found something that looks wrong?

Every answer was checked twice, but if something looks wrong, please write to support@bitygan.com.