Complete 11+ Study Guide with Worked Examples
This study guide covers the revision topic families in Verbal Reasoning and Non-Verbal Reasoning. Each section explains the skill, gives practical tips and tricks, and includes a worked example.
Study routine for every topic: Understand the question type → look at a worked example → identify the rule → notice the common trap → try a question → check that you can prove your answer.
Topics
1. Making Words Across a Gap
What you need to understand: Find a hidden four-letter word spanning the end of one word and the start of the next.
Tips & tricks: Test possible split points systematically. Check spelling. Remember the hidden word may cross the gap 1+3, 2+2 or 3+1.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
The teacher filled the pen with ink.
How to solve it:
Look across each gap: teacher|filled, filled|the, the|pen, pen|with, with|ink. The hidden four-letter word is WITH across pen|with? No, that stays in one word, so reject it. Model the key habit: the hidden word must genuinely cross the boundary. Then use a clean example: “The cat chased it.” Across caT CHased gives TCH, so reject. Teacher should demonstrate several boundaries and insist on spelling checks.
Common mistake:
Do not accept a word that sits wholly inside one printed word. It must cross the gap.
2. Making Two New Words
What you need to understand: Move one letter from the first word to the second so both resulting words are real words.
Tips & tricks: Start with likely removable letters, especially vowels. After every move, verify BOTH new words.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
PAIR: PLANE / CAME. Move one letter from PLANE to CAME to make two new words.
How to solve it:
Try removing P, L, A, N, E one at a time. A strong strategy is to ask what real word PLANE could become after losing one letter, then see whether that removed letter can create a real word from CAME. The teacher should write each trial and cross out failures rather than guessing.
Common mistake:
Both resulting words must be valid. One valid word is not enough.
3. Analogies with Letter Changes
What you need to understand: Identify how one pair of letters changes and apply the same rule to another pair.
Tips & tricks: Write alphabet positions or count forwards/backwards. Check whether the two letters use the same or different movements.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
BC is to DE as NO is to ?
How to solve it:
B→D is +2 and C→E is +2. Apply +2 to N and O: N→P, O→Q. Answer: PQ.
Common mistake:
Write the alphabet above the question if counting mentally causes errors.
4. Complete the Third Pair
What you need to understand: Discover how the first word changes into the second, then apply that transformation to a new word.
Tips & tricks: Look for reversal, removal, addition or movement of letters. Test the rule on the entire first pair before applying it.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
BONE → EBON. Apply the same change to MAST.
How to solve it:
The last letter moves to the front: BONE → EBON. So MAST → T MAS = TMA S? Carefully move only the last letter: T + MAS = TMAS.
Common mistake:
Describe the transformation in words before touching the new word.
5. Closest in Meaning
What you need to understand: Find the two words, one from each group, with the most similar meanings.
Tips & tricks: Think of a simple synonym for each candidate. Watch for words with more than one meaning.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Find the closest pair: (tall, shoot, fair) and (leaf, pretty, stem).
How to solve it:
Compare meanings systematically. ‘Fair’ can mean pretty/beautiful in some contexts, so FAIR + PRETTY is the closest pair.
Common mistake:
Remember words can have more than one meaning. Test alternative meanings.
6. Most Different in Meaning
What you need to understand: Find the strongest opposite pair across two groups.
Tips & tricks: Identify word class first where useful. Do not confuse 'unrelated' with 'opposite'. Look for true antonyms.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Find the most opposite pair: (busy, rough, wonderful) and (ordinary, shiny, idle).
How to solve it:
Busy is opposite to idle. Rough/shiny are not exact opposites, and wonderful/ordinary are less direct. Answer: BUSY + IDLE.
Common mistake:
Look for the strongest dictionary-style antonym, not merely different words.
7. Analogies by Word Meaning
What you need to understand: Complete a relationship between meanings of words.
Tips & tricks: Turn the first pair into a sentence, such as 'a ruler measures centimetres', then reuse exactly that relationship.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
RULER is to CENTIMETRE as SCALE is to ?
How to solve it:
A ruler measures in centimetres. A scale measures in grams/kilograms. If GRAM is an option, choose GRAM.
Common mistake:
Turn the relationship into a sentence and preserve the sentence exactly.
8. Incomplete Words
What you need to understand: Add a three-letter group to an incomplete word so the completed word fits the sentence.
Tips & tricks: Use grammar and sentence meaning to predict whether a noun, verb or adjective is needed. Test the missing letters at the beginning, middle or end.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
A PUF flew over the island. Add three letters to PUF to make a word that fits.
How to solve it:
The sentence needs a noun that can fly. Add FIN to make PUFFIN. The grammar and meaning of the sentence narrow the possibilities.
Common mistake:
Predict the type of word needed before trying letters.
9. Odd Ones Out
What you need to understand: Find two words that do not belong with the other three.
Tips & tricks: Find a rule that explains three words cleanly. Test alternative categories before committing.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
rain, wind, snow, hail, sunshine: find the two odd ones out if three belong together.
How to solve it:
Rain, snow and hail are forms of water falling from the sky. Wind and sunshine do not fit that group. Answer: WIND and SUNSHINE.
Common mistake:
Your grouping rule must explain exactly three words and leave exactly two.
10. Compound Words
What you need to understand: Choose words from two groups that join to make a correctly spelt compound word.
Tips & tricks: Try each first-group word at the beginning of likely second-group words. Check that the result is genuinely a word, not merely a plausible phrase.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Choose one from each group to form a compound word: (car, free, age, hood) + (pet, less, old, band).
How to solve it:
Test combinations. CAR + PET = carpet is a correctly spelt word. This demonstrates that pronunciation may change when the compound is formed.
Common mistake:
Check spelling and whether the joined result is genuinely one word.
11. Word Pairings
What you need to understand: Find one letter that completes the end of one word and the beginning of another in both pairs.
Tips & tricks: The SAME letter must work in both pairs. Test common consonant and vowel patterns methodically.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Complete both pairs with the same letter: rus(?) / (?)han and mas(?) / (?)ape.
How to solve it:
Try letters methodically. rusT and Than work; masT and Tape also work. Therefore T completes all four words.
Common mistake:
The same letter must satisfy all four sides.
12. Double Meanings
What you need to understand: Find one word that goes equally well with two pairs of words.
Tips & tricks: Check every candidate against both pairs and consider different meanings of the same word.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Which word fits both pairs: (break, split) and (fork, part)? Options include pack, breach, fork, part, peace.
How to solve it:
PART works with both ideas: break/split into parts, and ‘part’ itself can mean a section or to separate. Teacher should test each candidate against both pairs.
Common mistake:
A double-meaning answer often uses two different senses of one word.
13. Word Creation
What you need to understand: Use numbered letter positions to construct a missing word following the pattern shown.
Tips & tricks: Number letters carefully, including repeated letters. Build the code from known examples before solving the missing word.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Suppose the outside letters are numbered 1 2 3 4 and the middle word is built from positions 5 6 7 8. Use the known examples to identify which numbered positions spell the missing word.
How to solve it:
Teacher should first label every letter position visibly. Repeated letters must receive their own positions. Then copy the position pattern from the completed examples before decoding the missing word.
Common mistake:
Never number repeated letters as if they were the same physical position.
14. Letters and Words with Number Codes
What you need to understand: Calculate with letter values or infer number codes assigned to words.
Tips & tricks: For arithmetic codes, substitute values before calculating. For word codes, look for repeated letters and repeated digits to expose mappings.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
If A=2, B=4, C=6, D=8, E=9, find A + B × C.
How to solve it:
Substitute first: 2 + 4 × 6. Apply multiplication before addition: 2 + 24 = 26.
Common mistake:
Substitute values first, then use normal order of operations.
15. Alphabet Pair Sequences
What you need to understand: Find the missing pair in a sequence of letter pairs.
Tips & tricks: Separate the first and second letters into two sequences. One may move forwards while the other moves backwards.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
DQ, EO, FM, GK, ?
How to solve it:
First letters: D,E,F,G so next H. Second letters: Q,O,M,K, moving back 2 each time, so next I. Answer HI.
Common mistake:
Split pairs into two independent sequences.
16. Letter Codes
What you need to understand: Infer how each letter in a word is transformed into its coded letter.
Tips & tricks: Compare letter by letter and count alphabet movement. Do not assume one shift until multiple positions confirm it.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
If KITE → IGRC, what does DMSP mean?
How to solve it:
K→I, I→G, T→R, E→C: every coded letter is 2 places back. Reverse the rule to decode DMSP by moving each letter forward 2: F O U R = FOUR.
Common mistake:
When decoding, reverse the direction of the encoding rule.
17. Number Sequences
What you need to understand: Find the rule governing a number sequence and continue it.
Tips & tricks: Write differences first. Then test alternating rules, multiplication/division, squares, cubes and changing differences.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
2, 3, 4, 6, 6, 9, 8, ?
How to solve it:
Separate alternate positions. Odd positions: 2,4,6,8 (+2). Even positions: 3,6,9,... (+3). Next even term = 12.
Common mistake:
If one rule fails, test odd-position and even-position sequences separately.
18. Number Patterns and Equations
What you need to understand: Find relationships between grouped numbers or balance an equation.
Tips & tricks: Work from known examples. Respect operation order. In equations, calculate each side separately and find the value needed to balance them.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
(15 [5] 3), (21 [3] 7), (12 [?] 6)
How to solve it:
The middle number is first ÷ last: 15÷3=5; 21÷7=3; 12÷6=2. Answer 2.
Common mistake:
Find a rule that works for every completed bracket before using it on the missing one.
19. Introducing Logic
What you need to understand: Organise supplied information to solve constraints and ordering problems.
Tips & tricks: Convert prose into a table, diagram, list or timeline. Cross out impossibilities as soon as they are proved.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Chloe, Erin and Kate each have a different pet: dog, cat, rabbit. Chloe does not have the dog. Erin has the cat. Kate does not have the rabbit. Who has the dog?
How to solve it:
Make a small table. Erin=cat. Chloe cannot dog, so Chloe=rabbit. Therefore Kate=dog.
Common mistake:
Tables prevent you from repeatedly rereading the clues.
20. True Statement
What you need to understand: Determine which option must be true from supplied facts.
Tips & tricks: Use only stated information. 'Could be true' is not enough. Test each option against every fact.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Amy and Eve live on different roads but both take 10 minutes to walk to school. Which statement must be true?
How to solve it:
Only facts forced by the information count. ‘They take the same amount of time to walk to school’ must be true. Distance or who lives closer cannot be proved.
Common mistake:
Separate what is stated from what merely seems likely.
21. Deduction
What you need to understand: Combine several facts to reach a necessary conclusion.
Tips & tricks: Break the passage into individual facts, order events or people, and calculate step by step rather than holding everything mentally.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Homework starts 6:50pm, lasts 20 min; snack 5 min; homework then takes 10 min longer than teacher predicted. What time is it finished?
How to solve it:
Teacher predicted finish: 7:10. Snack: 7:10–7:15. Extra 10 minutes of homework: 7:15–7:25. Answer 7:25pm.
Common mistake:
Build a timeline and account for every duration exactly once.
22. Letter, Word and Number Facts
What you need to understand: Recall alphabet order, vowels/consonants, multiplication facts and common number patterns.
Tips & tricks: Know A-Z forwards/backwards, common letter pairs, tables to 10×10, even/odd, square, cube, triangular and prime numbers.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
What comes next: 1, 4, 9, 16, 25, ?
How to solve it:
These are square numbers: 1²,2²,3²,4²,5². Next is 6²=36.
Common mistake:
Memorise common square, cube, triangular and prime numbers to recognise patterns quickly.
23. Question Types and Strategies
What you need to understand: Understand non-verbal formats such as most unlike/most like, grids, repeated changes and spatial questions.
Tips & tricks: Read the instruction before studying the pictures. Decide exactly what relationship is being tested.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
MOST UNLIKE: four shapes are outlines and one is solid black. Which should you choose?
How to solve it:
Ignore decorative differences and identify the feature shared by four. The solid shape is most unlike because fill is the distinguishing feature.
Common mistake:
For ‘most unlike’, first state what four have in common.
24. Making Connections
What you need to understand: Identify common connections, odd-one-out relationships, direction, angles, symmetry and similarities/differences.
Tips & tricks: Compare one feature at a time: shape, number, shading, orientation, symmetry and position.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Five squares: four contain one diagonal; one contains two diagonals. Find the odd one out.
How to solve it:
Count features rather than relying on visual impression. Four have one diagonal; one has two. The latter is the odd one out.
Common mistake:
Compare shape, count, direction, shading, symmetry and position one feature at a time.
25. Breaking Codes
What you need to understand: Decode image features represented by two- or three-letter codes.
Tips & tricks: Find one shared feature at a time. Compare images sharing a code letter to discover what that letter represents.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Codes: two pictures labelled RM share a red/filled centre; two labelled RV share the same outer shape. What might R represent?
How to solve it:
Compare items sharing the letter R. The common feature across all R-coded pictures reveals R. Then use other code letters to identify the second feature.
Common mistake:
Decode one letter at a time using intersections of shared features.
26. Finding Relationships
What you need to understand: Apply changes in shape, shading, size, position, reflection or movement.
Tips & tricks: Describe the transformation in words before selecting an answer. Check every feature, not just the most obvious.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
A shape becomes its mirror image and changes from white to black. Apply the same relationship to a new white shape.
How to solve it:
There are two changes, not one: reflection plus shading change. The answer must satisfy both.
Common mistake:
List every change explicitly: rotate/reflect, move, resize, add/remove, shade/unshade.
27. Spotting Patterns
What you need to understand: Solve 2×2 and 3×3 grids by finding row/column relationships.
Tips & tricks: Work row by row and column by column. Look for addition/removal, rotation, shading, size and position rules.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
2×2 grid: top-left has one circle, top-right two circles; bottom-left has two squares. What should bottom-right contain if the rule is +1 object across each row?
How to solve it:
Across the top row 1→2 objects. Apply the same rule to bottom row: 2→3 squares.
Common mistake:
Check both rows and columns where possible. A valid grid rule should be consistent.
28. Completing Sequences
What you need to understand: Continue visual sequences involving repeating, alternating or multi-step changes.
Tips & tricks: Track each feature separately. Some features repeat every two or three steps while another changes each step.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
Sequence: ▲, △, ▲, △, ?
How to solve it:
The shading alternates filled, outline, filled, outline. Next is filled ▲.
Common mistake:
Track independent features separately. One feature may alternate while another rotates.
29. Spatial Reasoning
What you need to understand: Solve nets/cubes, paper folding, hidden shapes, rotations, plans and elevations.
Tips & tricks: Choose an anchor face or feature and track neighbours. For folds, reverse the folding mentally one step at a time.
Check your understanding: Before choosing an answer, explain the rule in your own words and ask yourself, “How can I prove this answer?”
Worked example:
A cube net has a star face directly beside a circle face. Which finished cube could be correct?
How to solve it:
Use the star as an anchor. Faces joined by an edge in the net remain adjacent when folded. Reject any option placing known opposite faces together or separating required neighbours.
Common mistake:
Do not mentally spin the whole cube at once. Track one anchor face and its neighbours.
Universal exam tips
- Read the instruction twice when the question type changes.
- Do not guess from appearance. State the rule.
- Write down alphabet movements, number gaps and logic facts.
- Eliminate answers that break even one part of the rule.
- For two-part questions, verify both parts.
- If stuck, move on and return later rather than spending too long.
- After an error, identify the error type: instruction, rule, calculation, vocabulary, visual tracking or rushing.