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E-Math resources

Explore E-Math foundations

Choose a topic to see useful foundations, why they matter and where the skills are used. This is a learning map, not an assessment of your readiness.

18 topics match. All topic sections remain available below.

The same checked graph connections appear on the topic guides. They are learning hints, not compulsory steps or an official SEAB sequence. All sections and practice links are available below, even without JavaScript. Source and scope notes.

Algebraic fractions

An algebraic fraction follows the same arithmetic rules as a numerical fraction. Factor before cancelling, and cancel whole common factors only. For addition, rewrite both fractions over a common denominator before combining numerators.

Practise algebraic fractions with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use these operations when rearranging formulae and solving fractional equations. Check excluded values before accepting any solution.

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.

Practise quadratic equations with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Roots locate x-axis intersections of quadratic graphs. In length or time problems, substitute back and reject roots that are impossible in the stated context, not simply all negative roots.

Functions and graphs

A graph shows pairs of input and output values. Read the axes and scales first. A line has constant gradient; a curve generally has a changing gradient. For a quadratic, the turning point, symmetry and intercepts help you sketch and interpret it.

Practise functions and graphs with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Graphs connect equations to intersections and represent rates in context. Coordinate geometry develops straight-line equations and distances from the same coordinate system.

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.

Practise ratio and proportion with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Proportion appears in similar figures, trigonometric ratios and scale drawings. Rates additionally compare quantities with different units, such as distance per hour.

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.

Practise trigonometry with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use trigonometry for heights, bearings and triangle areas. Coordinate distance and vector magnitude also use Pythagoras.

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.

Practise mensuration with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Apply mensuration to capacity, material use and scale models. Trigonometry can supply a missing height before a volume calculation.

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.

Practise coordinate geometry with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use equal gradients to check parallel lines and distances to compare side lengths. Vectors describe the same coordinate changes as directed movements.

Vectors

A vector describes a directed displacement. Its horizontal and vertical components tell you how far to move along each axis. The vector from A to B is position B minus position A; reversing the direction changes both signs.

Practise vectors with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Combine vector paths to reason about ratios and parallel lines. Coordinate geometry offers a second way to check lengths and positions.

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.

Practise probability with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use tree diagrams for multi-step choices and compare predicted probabilities with observed data. Statistics describes the observations; finite observed frequencies can differ from theoretical probabilities.

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.

Practise factorisation with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use factors to solve quadratic equations, find graph intercepts and simplify algebraic fractions. Expansion is the quickest check when signs are uncertain.

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.

Practise circle properties with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Combine circle properties with triangle angle sums, Pythagoras and trigonometry in multi-step geometry. Arc length and sector area are a related mensuration application, not a replacement for angle reasons.

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.

Practise statistics with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Compare distributions using centre and spread together. Probability uses counts of outcomes too, but an observed frequency is not automatically the exact probability of a future event.

Indices

An index describes a power. First identify the operation and the base: multiplying equal bases adds indices, while raising a power to another power multiplies them. Addition is a different operation and does not obey either rule.

Practise indices with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Index laws help simplify algebraic fractions and interpret power graphs. Expansion shows why a power of a sum cannot be split into separate powers.

Simultaneous equations

A simultaneous solution must satisfy both equations at once. Elimination is efficient when coefficients match or can be made to match; substitution is convenient when one unknown is already isolated.

Practise simultaneous equations with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Graph each equation as a straight line: the solution is their intersection. Parallel distinct lines have no common solution; coincident lines have infinitely many. Use equations to model two related quantities before solving.

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.

Practise linear inequalities with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use one-variable inequalities for budgets or capacity limits. Solving an equation finds a boundary; the inequality also says which side of that boundary is allowed.

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.

Practise sets and venn diagrams with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Disjoint Venn regions help count outcomes for probability. Define the universal set before using a complement in a probability calculation.

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.

Practise matrices with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Matrices organise repeated calculations such as revenue for several days. Before a contextual product, check that a row's quantities correspond to the prices in the column in the same order.

Similarity and congruence

Congruent figures have the same shape and size; similar figures have the same shape but may differ in size. 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.

Practise similarity and congruence with worked answers

Useful foundations to check

These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.

Applications and next topics

Use similarity for scale drawings and indirectly measured lengths. Mensuration then converts a length scale into area, capacity or material requirements.