"The difference between students who excel and students who just pass is rarely intelligence. It is almost always foundation."
— Caelitus Academy Teaching Philosophy
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students max
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year ahead
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year pathway · yr 6–12
What we teach
Two subjects, one approach — every concept understood from first principles.
We don't teach to the test. We build the mathematical mind.
Every concept is taught from first principles — the kind of understanding that earns marks in questions students have never seen before.
P(H) = 1 / 2
Begin with one fair coin and two equally likely outcomes.
Yr 6
Students begin Year 7 content — number, algebra and problem-solving foundations.
Yr 7
Year 8 content: linear equations, geometry and working with data.
Yr 8
Year 9 content: indices, trigonometry and quadratic techniques.
Yr 9
Year 10 content: functions, further trigonometry and probability.
Yr 10
Students begin Year 11 Advanced and Extension 1 coursework.
Yr 11
Students complete HSC-level content ahead of schedule.
Yr 12
Students prepare for HSC exams and complete full practice papers.
One full year ahead of your peers
How a lesson works
Structured with intent.
Structured with intent.
0:00
Introduction
15 minReal-world anchor. Connects abstract concept to lived experience.
0:15
Explanation & Demonstration
30 minFirst principles. Formal definition. Two worked examples.
0:45
Practice
60 minA full hour of deliberate practice, climbing section by section.
A–B · Guided — Worked alongside the mentor, step by step.
C–D · Independent — Attempted solo, mentor on call.
E · Challenge — Exam-level extension for those ready.
1:45
Reflection
15 minWhat did we learn? What's next? Exit check.
2:00
Lesson ends
Not a tutoring session. A masterclass.
The Caelitus Workbook
Every lesson, yours to keep.
The learning should not disappear when class ends. Every lesson is captured in a purpose-written printed workbook, so students can return to the explanations, examples and reasoning whenever they need them.
Learning objectives, named upfront
Each lesson opens with exactly what a student will be able to do by the end of it — no ambiguity about the goal.
Vocabulary before it is used
Key terms are defined in a reference table before they appear in a question, so nothing is assumed.
A worked example, every time
Observe, interpret, apply — a full model answer walks through the reasoning before students attempt it alone.
Difficulty that climbs deliberately
Five sections per lesson move from recall through applied reasoning to exam-level challenge, so every student is stretched, not just kept busy.
Meet the mentors
Mentorship, not tutoring.
Sean
Founding Mathematics Specialist
Sean designed the Caelitus mathematics programme — Extension-level content taught a full year ahead, built from first principles. He believes marks follow understanding, never the other way around. In six years and 2,500+ tutoring hours, his students have earned Band 6 across Extension 1, Advanced and Biology — including a Sydney Grammar student ranked 3rd in Year 10 after joining in Year 7, and a Knox Grammar student carried from Class 3 to DaVinci within two years.
Rowena
Founding Science Specialist
Rowena leads the science programme, carrying students from an integrated foundation through to senior science. Her classes turn definitions into models students can reason with. In five years tutoring Mathematics and Physics, more than 20 of her students have achieved Band 6 and gone on to their first-choice degree — including one who was asked to step down to General Mathematics, and instead completed the HSC with Band 6 in both Advanced and Extension 1.
Caelitus Praxis
Practice that reads the working, not just the answer.
Praxis is our iPad-first mathematics practice space. Students choose a syllabus topic, write their full solution by hand, and receive marks with feedback tied to the steps they actually wrote.
- 01
Choose with purpose
Practise by year, syllabus topic and difficulty.
- 02
Write naturally
Use an Apple Pencil and show every line of working.
- 03
Learn from the attempt
Receive marks and specific feedback before the next question.
Secure access for Caelitus students
Caelitus Academy
Praxis
Mathematics · Differentiation
Differentiate with respect to x
y = (3x² + 1)⁵
Your working
u = 3x² + 1
dy/dx = 5u⁴ · 6x
= 30x(3x² + 1)⁴
Feedback on your method
2 / 2 marksCorrect use of the chain rule. Your final simplification is equivalent.
Term Pricing
Clear term pricing. Small classes. No surprises.
Caelitus classes run in 10-week terms, capped at 5 students. Pricing and class length differ between our Junior and Senior programs — choose your stage below.
Single Subject
Mathematics or Science
10 × 2-hour classes · $70 per hour
No payment required to enquire.
Mathematics + Science
The complete STEM pathway
$2,600 per term for both subjects · $65 per hour
Save $100 per subject.
Both subjects, one enrolment.
All plans include — small classes · level placement · progress tracking · mentor access · parent updates
Frequently Asked Questions
Everything you need to know.
Caelitus Academy is a private tutoring academy in Sydney teaching Extension 1 Mathematics and specialist Sciences (Biology, Chemistry, Physics) to students, one full year ahead of the standard NSW curriculum. Classes are capped at 5 students and taught by subject-specialist mentors, not generalist tutors.