Project 56

Project 56 — Maths

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MYP Standard

15 topics
%3.14

Number

Fractions, decimals, percentages, HCF/LCM, indices, standard form, surds, ratios.

x

Algebra

Expressions, linear equations, sequences, and inequalities.

Quadratics

Expand, factorise, and work with quadratic expressions involving areas.

Functions & Graphs

Linear functions, quadratics, and graph transformations.

Probability

Simple probability, combined events, tree diagrams, and conditional probability.

Sets & Venn Diagrams

Set notation, union, intersection, complement, and Venn diagram problems.

Geometry

Circle theorems, angles, tangents, and chords.

Area & Volume

Circles, prisms, cones, spheres, and composite shapes.

c

Pythagoras' Theorem

Right triangles, finding sides, distance, and 3D applications.

Similarity & Congruence

Scale factors, similar triangles, area/volume ratios, and congruence.

Statistics

Averages, spread, frequency tables, and grouped data.

Coordinate Geometry

Midpoints, gradients, equations of lines, and intersections.

$

Financial Maths

Interest, depreciation, profit & loss, exchange rates, and best buys.

N

Bearings

Three-figure bearings, back bearings, and distance/bearing problems.

Criterion B: Investigations

Guided pattern investigations for MYP assessment.

▼

MYP Extended

8 topics

Logarithms

Log rules, identities, change of base, and simultaneous equations using logarithms.

θ

Trigonometry

SOHCAHTOA, sine rule, cosine rule, and area formula.

Vectors

Column vectors, operations, magnitude, and geometric proofs.

Advanced Functions

Exponential, rational, trigonometric graphs, and domain & range.

Advanced Statistics

Standard deviation and correlation with scatter graphs.

Networks

Degree, Euler paths, spanning trees, and shortest paths.

±0.5

Bounds & Error

Upper and lower bounds, error intervals, and compound measures.

Linear Programming

Formulate and solve linear programming problems graphically.

Flashcards

Review key formulas and concepts with spaced repetition.

SRS

Test Generator

Build a custom test across any topics. Practice or exam mode with timer.

Custom Tests

Leaderboard

See how you rank against other students.

Top 20
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Achievements

Track your unlocked badges and milestones.

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📖 Formula Booklet

Official MYP Extended Mathematics formula reference.

Reference

Past Paper Generator

IB MYP eAssessment style context-based questions. Full paper or individual practice.

E-Assessment Practice

Progress Dashboard

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Your Progress

Logarithms

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Lessons

Introduction to Logarithms

Learn the definition, evaluation, and special values.

Lesson

Log Rules

Product, quotient, and power rules with worked examples.

Lesson

Common & Natural Logs

log, ln, and the change of base formula.

Lesson

Expanding & Condensing

Use log rules to rewrite and simplify expressions.

Lesson

Solving Log Equations

Solve logarithmic and exponential equations.

Lesson

Practice

Log Rules

Practise product, quotient, power, change of base, and identity rules.

Simultaneous Equations

Solve systems of equations using logarithm rules. Includes a scratchpad.

Logarithm Mastery

Adaptive practice that tracks your progress across all log skills. Builds from basics to advanced.

Adaptive

Log Rules Activity

IB MYP Level — Master the laws of logarithms

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Rules Reference

Log Simultaneous Equations

IB MYP Level — Solve systems using logarithm rules

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Your Answer

\(x =\)
\(y =\)
Reference

Quadratics

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Lessons

Factorising Quadratics

Factor pairs, trinomials, and difference of squares.

Lesson

Completing the Square

Vertex form, the method, and solving equations.

Lesson

The Quadratic Formula

Solving any quadratic using the formula and discriminant.

Lesson

Quadratic Graphs

Sketching parabolas, vertex, intercepts, and transformations.

Lesson

Quadratic Applications

Projectile motion, optimization, and real-world problems.

Lesson

Quadratic Inequalities

Solving and graphing quadratic inequalities.

Lesson

Practice

Expressions & Areas

Expand and factorise quadratic expressions using areas of shapes.

Quadratic Graphs

Sketch, interpret, and match equations to parabola graphs.

Word Problems

Projectiles, area optimization, revenue, and real-world quadratics.

Quadratic Inequalities

Solve and interpret quadratic inequalities with sign diagrams.

Mastery

Quadratic Mastery

Adaptive practice across all quadratic skills with prerequisite unlocking.

Mastery

Quadratic Expressions & Areas

IB MYP Level — Expand and factorise using areas

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Quadratic Graphs

Sketch, interpret, and match equations to parabolas

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Quadratic Word Problems

Projectiles, optimization, and real-world applications

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Quadratic Inequalities

Solve and interpret quadratic inequalities

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Number

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Lessons

Indices

Learn the laws of indices and fractional powers.

Lesson

Surds

Learn to simplify surds, add/subtract, and rationalise.

Lesson

Fractions, Decimals & Percentages

Converting between fractions, decimals, and percentages.

Lesson

HCF & LCM

Highest Common Factor and Lowest Common Multiple.

Lesson

Standard Form

Writing very large and small numbers in standard form.

Lesson

Ratios & Proportion

Simplifying ratios, sharing in a ratio, and proportion.

Lesson

Recipe Scaling

Upscaling and downscaling ingredient lists using ratios.

Lesson

Absolute Values

Distance from zero, solving equations with |x|, and modulus.

Lesson

Recurring Decimals

Converting between fractions and recurring decimals.

Lesson

Metric Conversions

Converting units of length, mass, area, and volume.

Lesson

Practice

Fractions, Decimals & Percentages

Convert between forms, operations, percentage increase/decrease.

HCF & LCM

Find highest common factor and lowest common multiple.

Indices

Laws of indices with integer, negative, and fractional powers.

Standard Form

Convert to/from standard form, calculations.

Surds

Simplify, rationalise denominators, operations with surds.

Ratios & Proportion

Simplify ratios, share in ratio, direct and inverse proportion.

Absolute Values

Evaluate |x|, solve equations and inequalities with modulus.

Recurring Decimals

Convert recurring decimals to fractions and back.

Metric Conversions

Convert between metric units of length, mass, area, volume.

Mastery

Number Mastery

Adaptive practice across all number skills with prerequisite unlocking.

Mastery

Fractions, Decimals & Percentages

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HCF & LCM

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Indices

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Standard Form

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Surds

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Ratios & Proportion

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Algebra

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Lessons

Algebraic Expressions

Collecting terms, expanding, and factorising.

Lesson

Linear Equations

One-step, two-step, and equations with brackets.

Lesson

Sequences

Arithmetic, geometric, and nth term formulas.

Lesson

Algebraic Identities

Perfect squares and difference of squares.

Lesson

Inequalities

Solving and representing linear inequalities.

Lesson

Rearranging Formulae

Change the subject of a formula step by step.

Lesson

Simultaneous Equations

Solving pairs of linear equations by elimination and substitution.

Lesson

Practice

Expressions

Simplify, expand brackets, and factorise algebraic expressions.

Linear Equations

Solve one-step, two-step, and equations with brackets.

Sequences

Arithmetic and geometric sequences, find the nth term.

Inequalities

Solve and represent linear inequalities.

Rearranging Formulae

Change the subject involving squares, square roots, and fractions.

Mastery

Algebra Mastery

Adaptive practice across all algebra skills with prerequisite unlocking.

Mastery

Algebraic Expressions

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Linear Equations

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Sequences

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Inequalities

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Functions & Graphs

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Lessons

Linear Functions

Gradient, y-intercept, parallel and perpendicular lines.

Lesson

Quadratic Functions

Parabolas, vertex, axis of symmetry, discriminant.

Lesson

Graph Transformations

Shifts, reflections, and stretches of functions.

Lesson

Function Notation

f(x) notation, evaluating, composite and inverse functions.

Lesson

Practice

Linear Functions

Gradient, y-intercept, equations of lines, parallel and perpendicular.

Quadratic Functions

Vertex, roots, axis of symmetry, sketching parabolas.

Graph Transformations

Translations, reflections, and stretches of functions.

Function Notation

Evaluate f(x), find composite and inverse functions.

Composite Functions

f(g(x)), fg(x), triple composition, inverse composites, and decomposition.

Mastery

Functions Mastery

Adaptive practice across all functions & graphs skills.

Mastery

Linear Functions

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Quadratic Functions

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Graph Transformations

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Geometry

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Lessons

Circle Angles

Centre angle, semicircle, and same segment theorems.

Lesson

Tangents & Cyclic Quads

Tangent properties, two tangents, and cyclic quadrilaterals.

Lesson

Chords & Alternate Segment

Chord bisector and alternate segment theorems.

Lesson

Angles in Polygons

Interior angles, exterior angles, and regular polygon properties.

Lesson

Practice

Circle Theorems

Angles, tangents, chords, and cyclic quadrilaterals.

Mastery

Geometry Mastery

Adaptive practice across all geometry skills.

Mastery

Circle Theorems

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Rules Reference

Trigonometry

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Lessons

Trigonometric Ratios

SOHCAHTOA — sin, cos, tan in right triangles.

Lesson

Sine & Cosine Rules

Sine rule, cosine rule, and the area formula for any triangle.

Lesson

Trigonometry Applications

3D problems, elevation/depression, and multi-step problems.

Lesson

Practice

Trigonometry Practice

SOHCAHTOA, sine rule, cosine rule, area, and multi-step problems.

Trig Identities

Pythagorean identities, tan = sin/cos, simplification, and proofs.

Radians

Degree-radian conversion, arc length, sector area, and exact trig values.

Mastery

Trigonometry Mastery

Adaptive practice across all trigonometry skills.

Mastery

Trigonometry Practice

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Trig Identities

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Radians

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Composite Functions

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Vectors

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Lessons

Introduction to Vectors

Column vectors, addition, subtraction, scalar multiplication.

Lesson

Vectors in Geometry

Magnitude, position vectors, and expressing vectors in terms of a and b.

Lesson

Practice

Vectors Practice

Addition, subtraction, magnitude, resultants, and geometric vector problems.

Mastery

Vectors Mastery

Adaptive practice across all vector skills.

Mastery

Vectors Practice

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Probability

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Lessons

Introduction to Probability

Outcomes, sample spaces, and basic probability.

Lesson

Combined Events

Independent events, tree diagrams, and conditional probability.

Lesson

Tree Diagrams

Drawing tree diagrams, with/without replacement, and conditional probability.

Lesson

Conditional Probability

P(A|B), independence testing, total probability, and percentage difference.

Lesson

Practice

Probability Practice

Simple probability, combined events, tree diagrams, and more.

Mastery

Probability Mastery

Adaptive practice across all probability skills with prerequisite unlocking.

Mastery

Probability Practice

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Statistics

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Lessons

Averages & Spread

Mean, median, mode, and range.

Lesson

Frequency Tables & Grouped Data

Averages from tables and grouped data estimates.

Lesson

Cumulative Frequency & Box Plots

Quartiles, IQR, cumulative frequency curves, and box-and-whisker plots.

Lesson

Data Collection

Sampling methods, questionnaire design, and bias.

Lesson

Histograms

Frequency density, unequal class widths, and reading histograms.

Lesson

Practice

Statistics Practice

Mean, median, mode, range, frequency tables, and grouped data.

Data Collection

Identify sampling methods, critique questionnaires, spot bias.

Histograms

Draw, read, and interpret histograms with unequal widths.

Mastery

Statistics Mastery

Adaptive practice across all statistics skills with prerequisite unlocking.

Mastery

Statistics Practice

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Sets & Venn Diagrams

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Lessons

Sets & Venn Diagrams

Set notation, operations, and Venn diagrams.

Lesson

Venn Diagrams & Set Operations

Union, intersection, complement, and solving Venn diagram problems.

Lesson

Practice

Sets Practice

Set notation, union, intersection, Venn diagrams, and more.

Mastery

Sets Mastery

Adaptive practice across all sets skills with prerequisite unlocking.

Mastery

Sets & Venn Diagrams Practice

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Absolute Values

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Recurring Decimals

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Bounds & Error

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Metric Conversions

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Rearranging Formulae

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Linear Programming

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Function Notation

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Exponential Functions

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Rational Functions

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Trigonometric Graphs

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Domain & Range

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Networks

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Data Collection

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Standard Deviation

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Histograms

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Correlation & Scatter Graphs

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Criterion B: Investigations

Guided pattern investigations

Lessons

Investigation Methodology

How to approach pattern investigations for MYP Criterion B.

Lesson

Practice

Matchstick Patterns

Investigate patterns in geometric shapes made from matchsticks.

Number Sums

Discover patterns in sums of consecutive numbers.

Dot Patterns

Explore triangular, square, and other figurate numbers.

Pizza Cuts

Investigate the maximum number of regions from straight cuts.

Handshakes

How many handshakes when everyone shakes hands with everyone?

Matchstick Patterns

Investigation

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Number Sums

Investigation

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Dot Patterns

Investigation

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Pizza Cuts

Investigation

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Handshakes

Investigation

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Area & Volume

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Lessons

Areas of 2D Shapes

Rectangles, triangles, parallelograms, trapeziums, and circles.

Lesson

Volume & Surface Area

Cuboids, prisms, cylinders, cones, and spheres.

Lesson

Surface Area

Total surface area of cuboids, cylinders, cones, and spheres.

Lesson

Practice

Area & Volume Practice

Mixed questions on areas, volumes, and surface areas.

Mastery

Area & Volume Mastery

Adaptive practice across all mensuration skills with prerequisite unlocking.

Mastery

Area & Volume Practice

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Rules Reference

Pythagoras' Theorem

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Lessons

Pythagoras' Theorem

The theorem, finding sides, and Pythagorean triples.

Lesson

Applying Pythagoras

Distance, 3D problems, and real-world applications.

Lesson

Practice

Pythagoras Practice

Find missing sides, check right triangles, and solve problems.

Mastery

Pythagoras Mastery

Adaptive practice across all Pythagoras skills with prerequisite unlocking.

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Pythagoras Practice

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Similarity & Congruence

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Lessons

Similar Shapes

Scale factors, missing sides, and similarity tests.

Lesson

Area & Volume Scale Factors

k² for area, k³ for volume, and congruence.

Lesson

Practice

Similarity Practice

Scale factors, missing lengths, area and volume ratios.

Mastery

Similarity Mastery

Adaptive practice across all similarity skills with prerequisite unlocking.

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Similarity Practice

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Coordinate Geometry

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Lessons

Coordinate Geometry Basics

Midpoint, distance, gradient, and y-intercept.

Lesson

Equations of Lines

y = mx + c, parallel and perpendicular lines, intersections.

Lesson

Rectangles on the Coordinate Plane

Perpendicular proof, missing vertices, side lengths, and diagonals.

Lesson

Practice

Coordinate Geometry Practice

Midpoints, gradients, equations, and parallel/perpendicular lines.

Mastery

Coordinate Geometry Mastery

Adaptive practice across all coordinate geometry skills with prerequisite unlocking.

Mastery

Coordinate Geometry Practice

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Financial Maths

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Lessons

Financial Maths Basics

Percentages, profit & loss, VAT, and exchange rates.

Lesson

Interest & Depreciation

Simple interest, compound interest, and depreciation.

Lesson

Practice

Financial Maths Practice

Interest, profit, exchange rates, and reverse percentages.

Mastery

Financial Maths Mastery

Adaptive practice across all financial maths skills with prerequisite unlocking.

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Financial Maths Practice

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Bearings

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Lessons

Introduction to Bearings

Three-figure bearings, measuring from north, and compass directions.

Lesson

Bearings Problems

Back bearings, distance problems, and three-point bearings.

Lesson

Practice

Bearings Practice

Reading bearings, back bearings, and distance/bearing calculations.

Mastery

Bearings Mastery

Adaptive practice across all bearings skills with prerequisite unlocking.

Mastery

Bearings Practice

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Achievements

Your unlocked badges and milestones

Leaderboard

Top 20 students by questions answered

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Progress Dashboard

Your stats across all topics

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Past Paper Generator

IB MYP eAssessment Style

Full Paper Mode

8 questions (Q1-7 mixed topics + Q8 Criterion B), 120 minutes + 5 min reading time.

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Mark Scheme

Model answers and marking criteria

Advanced Functions

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Lessons

Exponential Functions

Growth and decay, y = ab^x, and real-world models.

Lesson

Rational Functions

Simplifying, asymptotes, and graphing rational expressions.

Lesson

Trigonometric Graphs

Graphs of sin, cos, tan — amplitude, period, and phase.

Lesson

Domain & Range

Finding domain and range of functions from rules and graphs.

Lesson

Practice

Exponential Functions

Growth, decay, graphs, and solving exponential equations.

Rational Functions

Simplify, find asymptotes, and sketch rational functions.

Trigonometric Graphs

Sketch and transform sin, cos, and tan graphs.

Domain & Range

Determine domain and range from equations and graphs.

Advanced Statistics

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Lessons

Standard Deviation

Measure of spread — calculating and interpreting standard deviation.

Lesson

Correlation & Scatter Graphs

Scatter diagrams, lines of best fit, and correlation strength.

Lesson

Practice

Standard Deviation

Calculate standard deviation from lists and frequency tables.

Correlation

Describe correlation, draw lines of best fit, make predictions.

Bounds & Error

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Lessons

Bounds & Error

Upper and lower bounds, error intervals, and truncation.

Lesson

Practice

Bounds & Error

Upper and lower bounds, error intervals, compound measures.

Linear Programming

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Lessons

Linear Programming

Optimise objectives subject to linear constraints.

Lesson

Practice

Linear Programming

Formulate and solve linear programming problems graphically.

Networks

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Lessons

Networks & Graph Theory

Vertices, edges, traversability, and shortest paths.

Lesson

Route Inspection (Chinese Postman)

The algorithm for finding minimum-weight routes that traverse every edge.

Lesson

Practice

Networks

Degree, Euler paths, spanning trees, and shortest paths.

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Learning Pathway

Your guided route through Maths

Flashcards

Spaced repetition review

MYP Extended Mathematics

Formula Booklet

For use during the course and in examinations

Area

Parallelogram\(A = bh\)
Triangle\(A = \tfrac{1}{2}bh\)
Trapezium\(A = \tfrac{1}{2}(a + b)h\)
Circle\(A = \pi r^2\)
Circumference\(C = 2\pi r\)
Sector area\(A = \tfrac{\theta}{360} \pi r^2\)
Arc length\(l = \tfrac{\theta}{360} \times 2\pi r\)

Surface Area & Volume

Cylinder SA\(SA = 2\pi r h + 2\pi r^2\)
Cylinder V\(V = \pi r^2 h\)
Cone SA\(SA = \pi r l + \pi r^2\)
Cone V\(V = \tfrac{1}{3}\pi r^2 h\)
Sphere SA\(SA = 4\pi r^2\)
Sphere V\(V = \tfrac{4}{3}\pi r^3\)
Cuboid V\(V = l \times w \times h\)
Prism V\(V = Ah\)
Pyramid V\(V = \tfrac{1}{3}Ah\)

Pythagoras' Theorem & Trigonometric Ratios

Pythagoras\(a^2 + b^2 = c^2\)
Trig identity\(\tan\theta = \dfrac{\sin\theta}{\cos\theta}\)
Sine\(\sin B = \dfrac{\text{opp}}{\text{hyp}}\)
Cosine\(\cos B = \dfrac{\text{adj}}{\text{hyp}}\)
Tangent\(\tan B = \dfrac{\text{opp}}{\text{adj}} = \dfrac{\sin B}{\cos B}\)
Sine rule\(\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\)
Cosine rule\(c^2 = a^2 + b^2 - 2ab\cos C\)
Cosine rule (rearranged)\(\cos C = \dfrac{a^2 + b^2 - c^2}{2ab}\)
Area of triangle\(A = \tfrac{1}{2}ab\sin C\)

Linear Functions

Gradient\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
Equation of a line\(y = mx + c\;;\; ax + by + d = 0\)
Distance\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
Midpoint\(M = \left(\dfrac{x_1+x_2}{2},\;\dfrac{y_1+y_2}{2}\right)\)

Quadratic Functions

Standard form\(y = ax^2 + bx + c\)
Quadratic formula\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Discriminant\(\Delta = b^2 - 4ac\)
Axis of symmetry\(x = -\dfrac{b}{2a}\)
Vertex form\(y = a(x-h)^2 + k\)

Sequences

Arithmetic term\(u_n = u_1 + (n-1)d\)
Arithmetic sum\(S_n = \tfrac{n}{2}(2u_1 + (n-1)d)\)
Geometric term\(u_n = u_1 \cdot r^{n-1}\)
Geometric sum\(S_n = \dfrac{u_1(r^n - 1)}{r - 1},\; r \neq 1\)

Exponents & Logarithms

Definition\(a^x = b \;\Leftrightarrow\; x = \log_a b\)
Exponential form\(a^x = e^{x\ln a}\)
Inverse\(\log_a a^x = x = a^{\log_a x}\)
Product rule\(\log_c a + \log_c b = \log_c(ab)\)
Quotient rule\(\log_c a - \log_c b = \log_c\!\left(\tfrac{a}{b}\right)\)
Power rule\(\log_c a^r = r\log_c a\)
Change of base\(\log_a b = \dfrac{\log_c b}{\log_c a}\)

Statistics & Probability

Mean\(\bar{x} = \dfrac{\sum x}{n}\)
Grouped mean\(\bar{x} = \dfrac{\sum f x}{\sum f}\)
IQR\(\text{IQR} = Q_3 - Q_1\)
Probability\(P(A) = \dfrac{n(A)}{n(S)}\)
Complement\(P(A') = 1 - P(A)\)
Mutually exclusive\(P(A \cap B) = 0\)
Independent events\(P(A \cap B) = P(A) \times P(B)\)
Combined events\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
Conditional\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\)
Std deviation\(\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}\)

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