Academic Tuition Programmes

Number & Place Value

• Reading, writing, ordering numbers
• Comparing numbers
• Understanding place value (units, tens, hundreds, thousands, etc.)
• Rounding numbers (GOV.UK)

Addition and Subtraction

• Mental methods and formal written methods
• Estimation
• Solving word / problem-based questions (GOV.UK)

Multiplication and Division

• Times tables (often up to 12 × 12)
• Mental & written methods
• Division with remainders, etc.

Fractions, Decimals and Percentages

• Equivalent fractions, simplifying
• Adding, subtracting, multiplying, dividing fractions
• Converting between fractions, decimals, percentages

Measurement

• Length, mass, volume / capacity
• Perimeter, area, sometimes volume
• Converting units (metric and sometimes imperial)
• Time – reading clocks, using time, calendars etc.

Geometry & Statistics

• Properties of shapes (2D and 3D), angles, symmetry
• Position & direction: coordinates, transformations (translations, reflections), and sometimes rotations
• Reading and interpreting data (charts, graphs, tables)
• Averages (mean, mode, median possibly)
• Probability in some cases, depending on the test board

Ratio, Proportion & Algebra

• Ratio & Proportion (sometimes in upper KS2)
• Basic Algebra (very simple): patterns, simple equations
• Missing number problems etc. (Grammar School Pathway)

Reading Comprehension

• Understanding passages: main ideas, inference, summarising
• Literal vs implicit meaning
• Answering questions based on texts (Grammar School Pathway)

Vocabulary

• Synonyms and antonyms
• Prefixes, suffixes, roots, etymology in some cases
• Word meanings in context
• Spelling rules, commonly misspelt words (11plushelp.co.uk)

Grammar & Punctuation

• Parts of speech (noun, verb, adjective, adverb, pronoun, conjunction, preposition etc.)
• Tenses, subject-verb agreement
• Sentence types (statements, questions, commands, exclamations)
• Clauses: main vs subordinate, relative clauses etc.
• Use of punctuation: full stops, commas, apostrophes, quotation/inverted commas, semi-colons, colons, brackets/parentheses, dashes etc. (GOV.UK)

Spelling (in some exams, or as part of English)

• Common rules (e.g. doubling consonants, dropping the 'e', etc.)
• Prefixes/suffixes spelling, irregular words etc. (11plushelp.co.uk)

Creative / Extended Writing (if included)

• Writing stories, essays, imaginative / descriptive writing
• Organising ideas, paragraphs, style & tone, audience awareness (Grammar School Pathway)

Logic & Reasoning Topics

These are logic / reasoning questions using words. Not part of the national curriculum, so schools and exam boards vary.

• Analogies (word analogies)
• Opposites / antonyms
• Synonyms
• Word meanings, vocabulary in context
• Cloze texts (fill in missing words)
• Codes & code words (simple ciphers)
• Hidden words / missing letters
• Word puzzles: making words from letters, rearrangements (anagrams)
• Letter series / number-letter codes
• Word-number connections (e.g. letters represent numbers etc.)
• Following instructions with words, logical word problem statements (Education Quizzes)

Spatial, Pattern & Visual Logic

These test spatial, pattern, and visual logic skills. More variable between exam boards / regions.

• Shape series (what comes next in a sequence of figures)
• Pattern / abstract shapes
• Matrices (figure matrices)
• Similar shapes / matching / odd one out in shape sets
• Codes using shapes / symbols
• Rotations, reflections of shapes
• Symmetry, mirror images
• Spatial reasoning: fitting shapes, visual puzzles etc.

Components / Structure

• Three papers: Non-calculator written paper, Calculator paper, and Mental arithmetic (short timed test).
• Levels: Foundation, Core, and Additional (Higher / more challenging for more able pupils).

1. Number

• Place value (integers, decimals), ordering, rounding.
• Negative numbers, fractions, decimals, percentages.
• Prime numbers; factors; multiples; highest common factor (HCF), lowest common multiple (LCM); prime factorisation.

2. Algebra

• Expressions, equations, inequalities.
• Sequences, nth term.
• Manipulation like expanding, factorising.
• Substitution into formulae.

3. Ratio, Proportion & Rates of Change

• Ratios, proportional reasoning.
• Scaling, maps, diagrams.

4. Geometry & Measures

• Properties of shapes (2D & 3D), classification, angles, lines, polygons.
• Perimeter, area, volume (including of prisms, cylinders).
• Transformations: reflection, rotation, translation, enlargement / scale factor.
• Coordinates; measurement units; conversion; time, speed, distance etc.

5. Statistics & Probability

• Data handling: mean, median, mode, range.
• Probability basics.

Components / Structure

• Two papers: One “Reading” (comprehension & analysis) and one “Writing”.
• Levels: Usually “Foundation” (easier) or “Core” (standard).
• Extracts: Prose, poetry, drama. May include unseen passages.

Skills / Topics Tested

• Reading comprehension: literal understanding, inference, summarising, comparing texts.
• Analysis of language: how grammar, syntax, punctuation, literary/trope devices affect meaning (e.g. metaphor, simile, imagery, alliteration etc.).
• Vocabulary in context, meaning of words, shades of meaning.
• Writing styles/formats: narrative, descriptive, persuasive, argumentative, letter, report, essay etc.
• Grammar, punctuation, spelling accuracy, register and tone.

Verbal Reasoning in 13+

VERBAL REASONING is not always compulsory in CE 13+, unlike some 11+ grammar exams. When used (pre-tests or specific schools), topics typically include:

• Synonyms, antonyms.
• Analogies.
• Word codes, letter series.
• Following instructions, word puzzles.
• Cloze tests (fill in missing words).

Non-Verbal Reasoning in 13+

Similarly optional for 13+ entrance, but topics often include:

• Pattern recognition / shape series.
• Matrices of shapes.
• Matching, odd one out.
• Rotations, reflections, transformations in visual form.
• Mirror images.

Mostly used in pre-tests or specific school entrance tests.

Pure Mathematics

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Applied Mathematics

• Statistics: sampling, data presentation, probability, distributions, hypothesis testing
• Mechanics: kinematics, forces, Newton’s laws, moments, energy, power, momentum

Core Mathematics Modules

• Complex numbers
• Matrices
• Roots of polynomials
• Series and summation
• Hyperbolic functions
• Further calculus
• Polar coordinates
• Vectors and 3D geometry
• Differential equations
• Proof (incl. induction)

Cellular & Molecular Biology

• Biological molecules
• Cells and membranes
• Exchange of substances in organisms
• Genetic information, variation and relationships
• Biodiversity and evolution

Physiology, Genetics & Ecology

• Energy transfers (photosynthesis, respiration)
• Organisms respond to changes (nervous, hormonal systems)
• Genetics, populations, evolution and ecosystems
• Control of gene expression
• Immunity and disease
• Ecology and ecosystems

Physical & Inorganic Chemistry

• Atomic structure and the periodic table
• Bonding and structure
• Amount of substance / formulae, equations, redox
• Energetics
• Kinetics
• Equilibria
• Group chemistry (Group 2, Group 7, transition metals)
• Periodicity

Organic Chemistry & Analysis

• Organic chemistry: introduction, alkanes, alkenes, halogenoalkanes, alcohols
• Organic analysis / spectroscopy
• Further organic: carbonyls, carboxylic acids and derivatives, aromatic chemistry, amines, polymers, amino acids and DNA
• Advanced analysis: NMR, chromatography, mass spectrometry

Core Physics Principles

• Measurements and errors / Working as a physicist
• Particles and radiation / Atomic/nuclear physics
• Waves
• Mechanics and materials
• Electricity and electric circuits

Advanced & Nuclear Physics

• Further mechanics and thermal physics
• Fields (gravitational, electric, magnetic) and their consequences
• Nuclear physics