G3 Math Prerequisite Explorer: Find Useful Foundations

Algebraic fractions

To simplify algebraic fractions, factor first and cancel common factors, never separate terms. To add or subtract, use a common denominator; to divide, multiply by the reciprocal. Keep every restriction from the original expression.

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Factorisation and subject of formulaFactor numerator and denominator to expose whole factors that can be cancelled.Practise factorisation →
Find the Lowest Common Multiple (LCM) of two or more numbers by listing multiples or using prime factorisation. The LCM is the smallest number that is a multiple of all given numbers.Common denominators play the same role as an LCM: 1/6 + 1/4 becomes 2/12 + 3/12.Practise algebraic fractions →

Quadratic equations

A quadratic equation has a non-zero squared term as its highest power. Put it in the form ax² + bx + c = 0 before choosing a method. Factorisation is convenient when integer factors are clear; the formula also handles roots that do not factor neatly.

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Functions and graphs

For G3 Math graphs, start with the axes and scales, then identify the gradient, intercepts and any turning point. A straight line has constant gradient; a curve usually does not. The examples below connect equations to the features you need to read or sketch.

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Simultaneous equationsFor the graphical method, the common solution is the intersection of two lines. Read both coordinates.

Ratio and proportion

A ratio compares quantities multiplicatively. In direct proportion y/x is constant; in inverse proportion xy is constant. Decide which relationship the situation states rather than assuming that every increase must be proportional.

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Perform the four basic arithmetic operations: addition, subtraction, multiplication, and division on whole numbers, fractions, and decimals.Use equivalent quantities and consistent units before simplifying a ratio: 600 g : 150 g = 4 : 1.Practise ratio and proportion →

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Similarity and congruenceCompare corresponding sides in the same direction to obtain one length scale factor.

Trigonometry

Identify the triangle and label known sides and angles before selecting a rule. Sine, cosine and tangent as side ratios require a right triangle. For a general triangle, use the sine or cosine rule when the given information fits.

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Coordinate geometryHorizontal and vertical changes form perpendicular sides; Pythagoras gives the distance between the points.

Mensuration

Mensuration measures shapes. Sketch how a composite shape can be split into familiar parts and decide whether the question asks for a boundary, a surface or the space inside. Only exposed faces count towards external surface area.

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Recall and apply the formula for area of a circle: pi x r^2A cylinder base has area πr²; multiplying by its perpendicular height gives its volume.Practise mensuration →

Coordinate geometry

Use coordinate differences consistently. Gradient measures vertical change divided by horizontal change. Distance uses the squares of both changes. A line equation must fit every point given on the line.

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Vectors

For the vector from A to B, subtract the position of A from the position of B. Reversing the journey reverses both signs. This G3 Math guide works through direction, magnitude, translations and scalar multiplication before connecting them to geometric reasoning.

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Probability

Probability measures chance from 0 to 1. For equally likely outcomes, divide favourable outcomes by all possible outcomes. For successive events, track what changes after each step, especially when objects are not replaced.

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Basic probability and single eventsList single-event outcomes before building a two-step sample space or tree.Practise probability →

Factorisation

Factorising rewrites a sum as a product. Look for a common factor first, then decide whether the remaining expression fits a quadratic or a special identity. Expanding your factors checks that the expression has not changed.

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Expansion and products of algebraic expressionsExpansion checks your factors: (x + 2)(x − 3) expands to x² − x − 6.Practise factorisation →

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Algebraic fractionsFactor numerator and denominator to expose whole factors that can be cancelled.

Circle properties

Circle geometry connects angles and lengths through stated facts: equal radii, a tangent at a named point, or points on the circumference. Name the relevant chord or arc before applying an angle theorem.

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Angle properties of trianglesTwo radii form an isosceles triangle. Equal base angles and a 180° angle sum can determine an unknown angle.Practise circle properties →

Statistics

Statistics summarises a data set. A measure of centre describes a typical value, while spread describes variation. Choose both according to the context and inspect how the data were collected before making a comparison.

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Data collection, classification, and graphical representationInterpret the frequency table before averaging: a value appearing three times contributes three times to the total.Practise statistics →

Indices

Add indices when multiplying the same base: a² × a³ = a⁵. Do not add indices when adding terms: a² + a³ cannot be combined by an index law. This guide shows which rule fits products, quotients, brackets and fractional powers.

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Calculate the square of a number and recognize perfect squares.Recognise a square as repeated multiplication before distinguishing (a²)³ from a² + a³.Practise indices →

Simultaneous equations

Choose elimination when coefficients match or cancel easily; choose substitution when one variable is already isolated. Both methods find the pair that satisfies both equations. Compare them on the same example below, then check the answer in each original equation.

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Linear inequalities

An inequality describes a range of values. Adding or subtracting the same amount preserves order. Multiplying or dividing by a negative reverses order: 2 < 5 becomes −2 > −5 when both sides are multiplied by −1.

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Linear equations in one variableIsolating a variable uses the same balanced operations as equations, with an extra order reversal when dividing by a negative.Practise linear inequalities →

Sets and Venn diagrams

A set is a collection of distinct elements. A ∩ B means in both sets; A ∪ B means in either or both. A′ means outside A but inside the universal set. The notation n(A) counts elements; it is not the set itself.

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Set notation and symbolsDistinguish an element from a set and define the universal set before interpreting a complement or an intersection.Practise sets and venn diagrams →

Matrices

A matrix is a rectangular arrangement of entries. Its order is rows × columns. Add equal-order matrices entry by entry. For multiplication, the first matrix's column count must equal the second's row count; each output entry is a row–column dot product.

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Matrix representation and data interpretationIdentify row and column labels and dimensions before deciding whether an operation makes sense.Practise matrices →

Similarity and congruence

Congruent figures have the same shape and size. Similar figures have the same shape but may differ in size: if the length scale factor is k, the area scale factor is k². Congruent figures are the special case k = 1. Name the correspondence first; if triangle ABC corresponds to triangle DEF, then AB pairs with DE, BC with EF and AC with DF, regardless of orientation.

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Numbers and Operations

For Singapore O-Level G3 Math, Numbers and Operations brings together number sense, prime factorisation, approximation and standard form. Integers include negative and positive whole numbers and zero; rational numbers can be written as a ratio of integers, while real numbers also include values such as √2. Use a number line to compare values: numbers farther right are greater. Keep the sign and type of a number visible, use prime factors to find common factors or multiples, and estimate before trusting a calculator result. This guide focuses on N1 skills beyond index laws; use the dedicated Indices guide for those.

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Percentage

The key question in a percentage problem is: percentage of which original amount? A percentage comparison uses the stated reference quantity as its base. A result above 100% is larger than its base: for example, 130% of a quantity is 1.3 times that quantity. For a percentage change, multiply the original by a change multiplier; for a reverse percentage, undo that multiplier to recover the amount before the change.

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Rate and Speed

A rate compares two quantities with different units. Average speed is total distance divided by total time, so convert units before combining parts of a journey. When a question gives distance and time, identify what is being asked and keep the units attached to each value.

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Angles, Triangles and Polygons

For Singapore O-Level G3 Math geometry, name the angle fact that justifies each step before calculating. Angles on a straight line sum to 180°, angles at a point sum to 360°, and vertically opposite angles are equal. With parallel lines, corresponding and alternate angles are equal, while the interior angles between the lines sum to 180°. Then combine the result with triangle or polygon properties. Keep circle theorems and similarity criteria in their dedicated guides.

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