Kreative Learning Platform Secondary Maths

Even a 3-D question,step by step.

A tetrahedron, and a craftsman's claim about the angle between two of its faces. Press Next step. The solid turns, its faces are lifted out flat, and the working is written out line by line.

Question (7 marks)

The figure shows a tetrahedron $ABCD$. Let $P$ be a point lying on $AD$ such that $BP$ is perpendicular to $AD$. A craftsman finds that $ {AC=AD=CD=13\text{ cm}}$, $ {BC=8\text{ cm}}$, $ {BD=12\text{ cm}}$ and $ {\angle ABD=72^\circ}$.
(a) Find
(i) $\angle BAD$,
(ii) $CP$.
(b) The craftsman claims that $\angle BPC$ is the angle between the face $ABD$ and the face $ACD$. Is the claim correct? Explain your answer.

3-D trigonometry

Example question

Solution

  1. The working appears here, one line per step.

Every DSE paper, 2012–2026

Paper 1 and Paper 2 of all 15 years: 30 papers and 961 questions, each one its own animation, in both English and Chinese. Every question is also filed under its topic, so a topic can be revised across every year at once. The topics below are ranked by the marks they carried; the darker the box, the more marks on that topic that year.

Marks on each topic, year by year (Paper 1 and Paper 2 together, each Paper 2 question 1 mark)

Topic201220132014201520162017201820192020202120222023202420252026 2012–2026
Polynomials, Identities and Factorization171815162418182016191916221820276
Coordinate Geometry14.512.511.512.512.514.515.5513.514.524.518.5212225238
Statistics15191413181614.51715161616161615236
Trigonometry12121117101510914.58108113.510161
Deductive Geometry3.55.578.51810.512.521.510109.513.5101010160
Rate, Ratio and Variation9816887151111.5889.512.5118150
Mensuration151097881188.51199.591110144
Arithmetic and Geometric Sequences151467767.5879.55.510189120
Functions and Graphs of Quadratic Functions27210710289.584.52.5810898
Inequalities and Linear Programming6610666666106666698
Probability751410675373.56666698
Indices, Surds and Logarithms5695596366755.510694
Percentages52663165555556974
Basic Properties of Circles4.5238257108.5236.522268
Locus5.514.512.511114.54.5744.5144
Numbers, Estimation and Errors26531642411211241
Quadratic Equations in One Unknown13232121425.53.522236
More about Equations54153402.5043010032
Permutation and Combination11111143131111122
More about Graphs of Functions101002160000.500012

Marks in a year: 01–34–67–1011 or more

2026 is the first exam on the revised syllabus.

Form 1 to Form 6, chapter by chapter

Each chapter is one lesson in five parts, every question animated. After it comes a Chapter Test with different questions each time it is sat, marked at once.

  1. Summary
  2. Level 1
  3. Level 2
  4. Level 3
  5. Test and exam questions
  6. Chapter Test
Junior secondary Form 1 to Form 3, 37 chapters Show the chapters
  1. Revision on Fundamental Arithmetic
  2. Basic Mathematics
  3. Directed Numbers and the Number Line
  4. Introduction to Algebra
  5. Linear Equations in One Unknown
  6. Introduction to Geometry
  7. Introduction to Statistics and Statistical Charts
  8. Percentages (I)
  9. Approximate Values and Numerical Estimation
  10. Areas and Volumes (I)
  11. Manipulation of Simple Polynomials
  12. Angles related to Lines
  13. Introduction to Coordinates
  14. Errors in Measurement
  15. Identities and Factorization
  16. Algebraic Fractions and Formulas
  17. Angles related to Rectilinear Figures
  18. Congruence
  19. More about Statistical Charts
  20. Rate, Ratio and Proportion
  21. Similar Triangles
  22. Linear Equations in Two Unknowns
  23. Pythagoras' Theorem and Irrational Numbers
  24. Areas and Volumes (II)
  25. Trigonometric Ratios
  26. More about Factorization of Polynomials
  27. Laws of Integral Indices
  28. Linear Inequalities in One Unknown
  29. Percentages (II)
  30. Quadrilaterals
  31. Special Lines and Centres in a Triangle
  32. Areas and Volumes (III)
  33. Coordinate Geometry of Straight Lines
  34. Trigonometric Relations
  35. Applications of Trigonometry
  36. Measures of Central Tendency
  37. Introduction to Probability
Senior secondary Form 4 to Form 6, 25 chapters Show the chapters
  1. Quadratic Equations in One Unknown (I)
  2. Quadratic Equations in One Unknown (II)
  3. Functions and Graphs
  4. Equations of Straight Lines
  5. More about Polynomials
  6. Exponential Functions
  7. Logarithmic Functions
  8. More about Equations
  9. Variations
  10. More about Trigonometry
  11. Basic Properties of Circles
  12. Tangents to Circles
  13. Inequalities
  14. Linear Programming
  15. Applications of Trigonometry in 2-dimensional Problems
  16. Applications of Trigonometry in 3-dimensional Problems
  17. Equations of Circles
  18. Locus
  19. Measures of Dispersion
  20. Permutation and Combination
  21. More about Probability
  22. Arithmetic and Geometric Sequences
  23. Summation of Arithmetic and Geometric Sequences
  24. More about Graphs of Functions
  25. Uses and Abuses of Statistics

AI keeps track of every student.Parents never have to guess.

Every step watched and every test question answered goes into the record. From it, AI works out each student's level chapter by chapter, forecasts the next test or exam, and works out what to revise first and for how long. Parents see it all on their own account.

  1. Records

    Every step watched and every test question answered, automatically.

  2. Assesses

    The level of every chapter and every DSE topic, updated after each test.

  3. Forecasts

    The next Chapter Test and the next school test or exam: a score and its range. Every forecast is checked against the real result.

  4. Advises

    Which chapters to revise first, and what 5, 10 or 20 more hours would bring, at the student's own pace.

ExampleWhat a parent sees. The student is made up.
Leung Ching YinForm 5Saturdays 10:00–11:30
Questions watched
412
Chapter Tests sat
18
Studied
5 of the last 7 days
Target
75%
Exam forecastNext: Uniform Test, Fri 16 Oct, in 15 daysChapters: Quadratic Equations in One Unknown (I); Equations of Straight Lines; More about Polynomials; Functions and Graphs

If the Uniform Test were tomorrow

66%

05973100
Paper 1 out of 100about 63 (54–72)
Paper 2 out of 100about 69 (61–77)
Totalabout 66% (59–73%)

An estimated range from your child's learning data, not a promise: eight times in ten the result should land inside it.

Level by chapter

  • Quadratic Equations in One Unknown (I)Secure
  • Equations of Straight LinesMostly there
  • More about PolynomialsNeeds work
  • Functions and GraphsNeeds work

Study time

3 h 30 min

this week

Week of 10 Aug: 1 h 30 minWeek of 17 Aug: 2 hWeek of 24 Aug: 1 hWeek of 31 Aug: 2 h 30 minWeek of 7 Sep: 3 hWeek of 14 Sep: 2 hWeek of 21 Sep: 2 h 45 minWeek of 28 Sep: 3 h 30 min

18 h 15 min in the last 8 weeks

More revision

60%70%80%0 h5 h10 h15 h20 htarget 75%The 75% target: about 12.5 hours12.5 hNow: about 66%66%5 more hours: about 71%71%10 more hours: about 74%74%20 more hours: about 77%77%
5 more hoursabout 71%
10 more hoursabout 74%
20 more hoursabout 77%

To reach 75%: about 12.5 hours of revision.

Revise first

How the next 10 hours are best spent

  1. 1Functions and Graphsabout 2 h 10 min
  2. 2More about Polynomialsabout 1 h 40 min
  3. 3Equations of Straight Linesabout 1 h 15 min

If the Uniform Test were tomorrow, the learning data point to about 66% overall. Functions and Graphs needs the most work: about 2 h 10 min on it first, then More about Polynomials. About 12.5 hours of revision should reach the 75% target.

Every answer leaves a trace.Answers from AI do too.

A chatbot answers any homework question in seconds. The homework looks perfect, and what was never learnt shows only in the exam. The platform's AI looks at how every Chapter Test and class quiz is answered, not only at the answers, and picks out work that does not look like the student's own.

  1. Analyses

    How every Chapter Test and class quiz is answered, from the first question to the hand-in, not just the answers.

  2. Flags

    When the signs add up, the case goes to the teacher with the evidence as soon as the paper is handed in.

  3. Teacher confirms

    The teacher weighs the evidence. Nothing changes until it is confirmed.

  4. Shows parents

    Once confirmed, the result counts as zero, and the parent's page shows it in red, at the top.

ExampleWhat the parent sees once the teacher confirms. The student is made up.

At the top of the parent's page, in red

⚠ Answering honestly: please read

  • Chapter Test: Logarithmic Functions, Paper 1 · 1 Oct, 21:42
    Counts as zero.

The teacher has confirmed signs that this was answered with the help of AI or another tool, so it counts as zero. Please talk it over with your child: a test is there to find what is not yet understood, and answers that are not their own hide exactly that from the teacher and from you.

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