Number
What is 3⁴ − 2³?
Mathematics practice
Topic-tagged lessons with worked examples, practice questions and a mini-quiz.
Algebra Basics
Translate words to letters, simplify expressions, expand brackets, collect like terms.
Angles & Parallel Lines
Angles on a straight line, at a point, in triangles, and with parallel lines (co-interior, alternate, corresponding).
Area
Area of squares, rectangles, triangles, parallelograms, trapezia, circles, and composites.
Decimals & Place Value
Operate fluently with decimals: add, subtract, multiply, divide, round, and convert to/from fractions.
Deductive Reasoning
Use ‘if … then …’, conditionals, contrapositive and chains of clues to draw watertight conclusions.
Linear Equations
Solve one- and two-step linear equations; translate word problems into equations.
Financial Maths
GST, profit/loss, simple interest, discount chains, change-from-a-note word problems.
Formulae & Substitution
Plug numbers into letters; rearrange formulae to make a different letter the subject.
Fractions
Equivalence, comparison, four operations, mixed numbers and fraction–decimal–percentage conversions.
Integers & Directed Numbers
Add, subtract, multiply, divide positive and negative integers; handle absolute value.
Logical Reasoning
Multi-step puzzles and deduction grids — a hallmark of Selective Entry maths.
Matrix Reasoning
Find the missing tile in a 3×3 or 2×2 grid that follows a row+column rule.
Measurement & Units
Convert between metric units; spot wrong units quickly in a question.
Number
Place value, divisibility, primes, factors, multiples and BIDMAS — the bedrock of every Selective Entry question.
Number Logic Puzzles
Cryptarithms, number-grid puzzles and clue-based number deductions.
Pattern Recognition
Identify the rule that turns one term into the next — numerical, alphabetic or pictorial.
Patterns & Sequences
Recognise arithmetic and geometric sequences, work out the n-th term, predict missing terms.
Percentages & Money
Percentage-of, percentage change, GST add-on, best-buy unit pricing and discount chains.
Polygons & Composite Shapes
Interior + exterior angle sums; angles in regular polygons; composite-shape area decomposition.
Probability
Single-event and compound probabilities, with-replacement vs without-replacement, complement rule.
Ratios & Proportions
Split a quantity in a ratio, simplify a ratio, recognise direct vs inverse proportion.
Scale & Maps
Convert between map distances and real distances using a scale ratio.
Shape Logic & Spatial Reasoning
Net of a cube, rotation/reflection of 2-D shapes, mirror images and reflected words.
Statistics — Mean, Median, Mode
Compute and contrast central-tendency measures and range; read frequency tables.
Tables & Graphs
Read column charts, line graphs, pictograms, two-way tables and pie charts accurately under time pressure.
Time & Speed
Time durations across midnight; speed = distance ÷ time; km/h ↔ m/s conversions.
Triangles & Quadrilaterals
Triangle angle sum, types of triangles, properties of quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium, kite).
Volume & Surface Area
Volume of prisms (V = cross-section × length); surface area as the sum of all faces.
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1-on-1 expert sessions or 4-session intensive packages — Maths and English specialists.
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