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Mathematics

Explore resources for time, data handling, statistics, functions, graphs, and three-dimensional geometry.

Hoppy Gold Quiz Collection

Open a printable mathematics quiz or practise interactively in Hoppy.

Equations of Straight Lines

English 10 questions

Practise equations of straight lines in coordinate geometry.

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Laws of Probability and Conditional Events

English 10 questions

Practise the laws of probability and conditional events.

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Tangents and Circle Angle Chasing

English 5 questions

Practise tangent properties and angle chasing in circles.

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Angles and Distances in 3-D Solids

English 5 questions

Practise angles between lines and planes, dihedral angles, and distances in three-dimensional solids.

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School level

Secondary School

Equation Graph 2D Geometry Diagrams 3D Shapes Box Whisker Plot Bar Chart Stacked Bar Chart Broken Line Graph
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Equation Graph

Generates function graphs, lines, segments, labelled points, coordinate axes, intersections and feasible regions based on the question, clearly presenting the conditions expressed by equations and inequalities to help students understand the question, interpret graphical information and analyse the mathematical relationships involved.

Live Examples
Hoppy quiz showing two straight-line equations and their graphs
Hoppy linear-programming quiz showing constraints, a feasible region, and the maximum value
Examples
Linear Programming Feasible Region Linear Programming Feasible Region
Function Transformation Function Transformation
Sine Function Sine Function
Circle-Line Intersection Circle-Line Intersection
Quadratic Parabola Quadratic Parabola
Logarithmic Function Comparison Logarithmic Function Comparison
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2D Geometry Diagrams

Generates diagrams for secondary and HKDSE-style geometry questions, including similar triangles, circles, tangents, chords, angle marks, and construction lines.

Live Examples
Tangent and Central Angles
Two Tangents and Central Angles
Equal Chords and Circle Angles
Examples
Parallel Lines and Similar Triangles Parallel Lines and Similar Triangles
Altitude in a Right Triangle Altitude in a Right Triangle
Equal Chords and Circle Angles Equal Chords and Circle Angles
Chords Equidistant from the Centre Chords Equidistant from the Centre
Two Tangents and Central Angles Two Tangents and Central Angles

3D Shapes

Visualises vertices, hidden edges, reference points, internal lines and highlighted planes in clear solid models, helping students reason about spatial relationships and solve 3-D trigonometry problems.

Live Examples
Rectangular block midpoint angle question in the Hoppy app
Examples
Orthographic Shape3D widget showing cube ABCDEFGH with the diagonal cross-section GDAF highlighted Cube with a Diagonal Cross-section
Orthographic Shape3D widget showing a cuboid with a reference point and line Cuboid with a Point on an Edge
Orthographic Shape3D widget showing triangular prism ABCDEF with midpoint M and reference line MC Triangular Prism with a Midpoint Line
Orthographic Shape3D widget showing a square pyramid with highlighted reference planes Square Pyramid with Highlighted Planes
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Box Whisker Plot

Statistical box-and-whisker plot showing five-number summary: smallest, Q1, median, Q3, and largest values.

Live Examples
Box whisker IQR question
Examples
Box Whisker Plot Widget Score Distribution Example
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Bar Chart

Vertical bar chart with configurable axes, labels, and values. Perfect for data interpretation questions.

Live Examples
Bar chart temperature question
Examples
Bar Chart Widget Quarterly Sales Example
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Stacked Bar Chart

Vertical stacked bar chart with multiple data series. Supports up to 4 series with automatic color assignment and legend.

Live Examples
Stacked bar chart household expenses question
Stacked bar chart activity participation
Examples
Stacked Bar Chart Widget Quarterly Revenue by Product
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Broken Line Graph

Line chart where data points are connected by straight line segments. Supports multiple series with different colors for trend comparison.

Live Examples
Broken line graph daily steps question
Broken line graph weekly temperature
Examples
Broken Line Graph - Single Series Single Series (Temperature)
Broken Line Graph - Multiple Series Multiple Series (Comparison)
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