Our IP programme focuses on building the fundamentals and understanding of the mathematical concepts that are essential building blocks for more advanced problem-solving techniques at IP5, IP6 and A-Level.

Details

Yishun/Online Classes

  • IP1 (2026): TBC
  • IP2 (2026): TBC
  • IP3 (2026): Sunday @ 10.00am
  • IP4 (2026): Sunday @ 4.30pm

Toa Payoh/Online Classes

  • IP1 (2026): TBC
  • IP2 (2026): TBC
  • IP3 (2026): TBC
  • IP4 (2026): Sunday @ 9.30am

For IP5/IP6:

Click here to check out our H2 Maths Classes >

For alternate slots, kindly register your interest for alternate slot.

  • Core Concepts Focus: Our IP Maths tuition builds a solid foundation in every topic of the IP3 and IP4 Maths syllabus, with greater emphasis on core topics such as advanced trigonometry, functions, differentiation and integration. These topics are the bedrock for H2 Mathematics in IP5 and IP6. Our tutors’ experience with the A-Level exam helps us understand which areas matter most.
  • Learning through Calibrated Revision: Our Integrated Maths programme incorporates regular assessments that not only track progress but also allow our tutors to optimise revision methods for every student group. This approach ensures a personalised, effective and tailored learning experience.
  • Beyond-Class Support: Zoom and WhatsApp provide the convenience of additional support from our math tutor. Our tutor takes a dedicated approach to ensure all students receive the assistance they need. Beyond the regular classroom, students are encouraged to clarify their doubts and seek further guidance in Integrated Maths whenever necessary.

Toa Payoh Central

Blk 190 Lor 6 Toa Payoh
#04-508A
Singapore 310190

Yishun Chong Pang:

Blk 101 Yishun Ave 5,
#02-95
Singapore 760101

Click here for location maps

Click here for our 1-on-1  private coaching availability.

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Isabelle Lau profile picture
Isabelle Lau
2134 days ago
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Teacher Anthony is literally the best MATH tuition teacher!!! Through the 3 years taking me through h1 A level math , from a super duper weak student to being able to handle the full papers. Words alone cannot express my gratitude for him. His classes are very engaging and entertaining , and he always pushes me to do my best with never ending encouragement! 100/10 recommend teacher Anthony:) go to Orion and your grades will be changed forever 😳 🎉
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Krish Subra
2299 days ago
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The Teachers here especially Mr Anthony (Maths and Physics) are extremely passionate and knowledge about the subject that they teach and are really encouraging.Mr Anthony is willing to go an extra mile to ensure that his students are crystal clear in their concepts. He also provides helpful resources (prepared by him) which enables to understand and follow what is being taught. During the class hours,he answers every question that every student asks and also repeats himself until the student understands fully and he does not leave anyone behind during the class.Also the environment there is extremely conducive to study thanks to the provision of snacks and drinks . Overall I will strongly recommend this tuition to the students
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Sim Bee Leng
2873 days ago
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Mr Anthony is truly a remarkable, excellent and awesome tuition teacher I’ve come across so far. I am glad to have made the right choices by having my daughter to be taught under him for Physics n Maths. He has been a great inspiration and motivator towards my daughter n teaches with a heart and passion. His lessons are interesting, thought provoking n engaging. His endless patience and countless encouragements has made a positive impacts on my daughter as she gains more confident with the subjects. He never fails to help whenever my daughter needs it. We are deeply grateful to him. Thank you very, very much, Mr Anthony, for being so amazing and for being a one-of-a-kind teacher who touches lives and makes a great difference.
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Goh Kh
2891 days ago
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One of the best decision I have made for my son to be tuition by Anthony for Maths and Physic. He was doing very badly in school failing his midyears until he signed up for this tuition. Anthony is very accommodating and helpful being able to identify his weaknesses quickly. Appreciate his effort and patience, would highly recommend his tuition for all
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Choong Pek San profile picture
Choong Pek San
2954 days ago
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We were very impressed with Mr Anthony when he taught my son H2 Maths for the past 2 years. He was able to motivate him. He is also very accommodating and always went the extra mile to help my boy whenever he needs help. Hopefully he will be able to help my girl next year when we enroll her for his class. Thank you Mr Anthony!
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Aishwaryaa Padmanaban
306 days ago
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Mr Anthony was my teacher for not too long. Along with Ms Agnes. Since I enrolled with him about a year before my o levels. Mr Anthony taught me math, Ms Agnes taught me physics. I really improved on both sectors after being enrolled with them, since both of them are easy going and they teach really good. I was failing math before I reached Orion, now in o levels, I pushed to a B3. My physics was the same too. In the end, Orion really has helped me out a lot and I wouldn’t be where I am without my tutors’ help.
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Winnie Teo profile picture
Winnie Teo
1360 days ago
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With less than 5 months of teaching and guidance from Mr Anthony, my boy has improved from E8 in MYE to A1 in his O-level A-Maths. His method of identifying the understandind gaps and solving techniques was impressive. I would like to thank him for his patience and encouragement for my boy despite of last lap dash to O-Level.
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Clara Lim profile picture
Clara Lim
1605 days ago
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We would like to express our gratitude to Mr. Anthony who has helped my child achieve good results in Physics and Maths A level and she was offered her desired course in local universities. She was consistently failing her subjects even up till prelims and It was pleasant surprised that she did quite well at A levels. We started Physics with Mr. Anthony quite late, and Maths only after prelims. It was very last minute but Mr. Anthony did not give up on her, and continued to encourage her and helping her, constantly adjusting his teaching style to suit my child’s needs. We are thankful that our child got the help she needed and hope other students will get the same quality mentorship from Anthony as well
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Exley Yun profile picture
Exley Yun
1778 days ago
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Have been with Orion for 3.5 years now, from Sec 3 to JC2 and the tutors here really put in the care and patience to guide every student. Would like to highlight and thank specifically Ms Agnes Chan who has been with me since 2018 to maintain a strong chemistry grade and Mr Anthony Lee who pulled me through notoriously difficult H2 Math as well as Ms Celia Chia for setting the foundations in IP math They go the extra mile by providing additional supplementary classes, exercises where requested and can text them for schoolwork questions as well which is invaluable and much appreciated. Both the secondary school/IP and JC programmes are stellar.
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ethan profile picture
ethan
1819 days ago
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Mr Anthony was the driving force for me to stay motivated and work hard for my As, pushing me to do the best I can throughout the time he taught me H1 math, and i couldn’t recommend a better tutor!
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huahuol profile picture
huahuol
1832 days ago
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great tutors that are very sincere and willing to guide you through your mistakes! it's a very conducive environment to study in and learn from your mistakes. also, the tutors go out of their way to ensure that you really really understand certain topics. i took sec school math here and I couldn't be more thankful to have such a wholesome + educational experience here
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Jenica Tan profile picture
Jenica Tan
2199 days ago
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orion was v helpful to me in 2020!! i went there for sec4 IP math and my math foundation really improved :) throughout the year, my teacher (ms celia) was soo encouraging and alw motivated me to do better- esp through the highs and lows of math exams :) throughout the covid cb period, she was very patient and skilled in explaining different math concepts, the lessons gave me more confidence for my final exams!
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Daryl Lim profile picture
Daryl Lim
2418 days ago
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Anthony is a brilliant teacher who goes all out in helping his students achieve their best results. Highly recommended if you need help with Math and/or Physics. Helped me immensely in my preparation for the A Level exams. 6/5!
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$360/Month (4 Lessons)

GST absorbed with no hidden costs nor deposits.

Optimal class ratio

Average class size of 8

Beyond class
consultation

Our tutor regularly takes the initiative to clarify doubts via Zoom and Whatsapp.

Revision Summary (Online)

Hundreds of bite sized summary lessons and guided practice for our registered students to facilitate their revision.

How we teach

How we teach IP Math Trigonometry Identities: every line has a reason

Our IP Math tuition in Toa Payoh and Yishun teaches trigonometry identities line by line. In class, the tutor reveals each worked example one line at a time and explains the reason for every step. Some examples are printed, so students focus on the reasoning. Others are left blank, so students write them out once they understand the flow, which strengthens it in their mind.

1Tutor clicks and explains. One line at a time, with the reason for each step.
APrinted examples. Students focus on the reasoning and the flow.
BBlank examples. Students write it out once the flow is clear.

This is the screen students see in class. Click Next to try it.

0 / 0
Download IP Math trigonometry worked examples (PDF) Sample worked examples from our IP Math notes, for reference only.
Read all 5 worked solutions as text

Example 1: Prove an identity

Question. Prove that sec x − cos x ≡ sin x tan x.

  • Count the terms. Left side: 2 terms. Right side: 1 term. So we combine the left side first.
  • LHS = 1/cos x − cos x (sec x = 1 ÷ cos x)
  • = (1 − cos² x)/cos x (2 terms on the left, 1 on the right: combine into 1 term (common denominator).)
  • = sin² x/cos x (1 − cos²x = sin²x)
  • = sin x × sin x/cos x
  • = sin x tan x (= RHS, shown)

Example 2: Prove, then "hence"

Question. (a) Prove the identity (1 + cos x)/sin x + sin x/(1 + cos x) ≡ 2/sin x.

Question. (b) Hence, find all the angles between 0° and 360° for which (1 + cos x)/sin x + sin x/(1 + cos x) = 3.

  • (a) Count the terms. Left side: 2 terms. Right side: 1 term. Combine the left side.
  • LHS = (1 + cos x)/sin x + sin x/(1 + cos x)
  • = ((1 + cos x)² + sin² x)/(sin x(1 + cos x)) (2 terms on the left, 1 on the right: combine into 1 term (common denominator).)
  • = (1 + 2cos x + cos² x + sin² x)/(sin x(1 + cos x)) (expand (1 + cos x)²)
  • = (2 + 2cos x)/(sin x(1 + cos x)) (sin²x + cos²x = 1)
  • = (2(1 + cos x))/(sin x(1 + cos x)) (factorise the top)
  • = 2/sin x (= RHS, shown)
  • (b) By (a), the equation becomes 2/sin x = 3.
  • sin x = 2/3
  • Basic angle α = 41.8°. sin x is positive: 1st and 2nd quadrants.
  • x = 41.8°, 138.2°

Example 3: Solve in radians (Pythagorean identity)

Question. Find all the angles between 0 and π inclusive which satisfy the equation 2cos² x + 3sin x = 3.

  • We need one trig function only. There is a cos² x, so use the Pythagorean identity.
  • 2cos² x + 3sin x = 3
  • 2(1 − sin² x) + 3sin x = 3 (cos²x = 1 − sin²x)
  • 2sin² x − 3sin x + 1 = 0 (collect on one side: a quadratic in sin x)
  • (2sin x − 1)(sin x − 1) = 0 (factorise)
  • sin x = 1/2 gives x = π/6 or π − π/6 = 5π/6. sin x = 1 gives x = π/2.
  • x = π/6, π/2, 5π/6

Example 4: Changed angle

Question. Find all the angles between 0° and 360° which satisfy each of the following equations.

Question. (a) cos(x + 30°) = −0.3

Question. (b) sin 2x = 0.866

  • (a) Change the range first: 0° ≤ x ≤ 360° gives 30° ≤ x + 30° ≤ 390°.
  • Basic angle α = cos⁻¹(0.3) = 72.5°. cos is negative: 2nd and 3rd quadrants.
  • x + 30° = 180° − 72.5°, 180° + 72.5°
  • x + 30° = 107.5°, 252.5°
  • x = 77.5°, 222.5° (Answer a)
  • (b) Change the range first: 0° ≤ x ≤ 360° gives 0° ≤ 2x ≤ 720°.
  • Basic angle α = sin⁻¹(0.866) = 60°. sin is positive: 1st and 2nd quadrants, then add 360°.
  • 2x = 60°, 120°, 420°, 480°
  • x = 30°, 60°, 210°, 240° (Answer b)

Example 5: Prove, then find exact angles

Question. (a) Prove the identity (cos x + sin x)(1 − cos x sin x) ≡ cos³ x + sin³ x.

Question. (b) Hence, find all the angles between −π and π which satisfy the equation (cos x + sin x)(1 − cos x sin x) = 0, giving your answers in an exact form.

  • (a) Left side is a product, right side is a sum. Expand the left side.
  • LHS = (cos x + sin x)(1 − cos x sin x)
  • = cos x − cos² x sin x + sin x − cos x sin² x (expand)
  • = cos x(1 − sin² x) + sin x(1 − cos² x) (factorise in pairs)
  • = cos x × cos² x + sin x × sin² x (1 − sin²x = cos²x and 1 − cos²x = sin²x)
  • = cos³ x + sin³ x (= RHS, shown)
  • (b) By (a), the equation becomes cos³ x + sin³ x = 0.
  • sin³ x = −cos³ x
  • tan³ x = −1 (divide both sides by cos³x)
  • tan x = −1
  • tan x is negative: 2nd and 4th quadrants. Basic angle α = π/4.
  • x = −π/4, 3π/4

Register your Interest for IP Math

Nov to Mar
First lesson is a trial.

If your child doesn’t continue, the lesson fee is waived.

Apr to Oct
3-Lesson Trial Pack

Try our class with a 3-Lesson Trial Pack.

A Level: $315IP: $240

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    IP Maths tuition by level: IP1 to IP4

    IP Mathematics is a progressive subject. The concepts introduced in IP3 are the direct foundations for IP4, and IP4 is the foundation for H2 Mathematics at IP5/IP6 and A-Level.

    1-21-to-1 coaching

    IP1 and IP2 Maths

    For IP1 and IP2, we offer 1-to-1 coaching. The earlier a student joins, the more time there is to build strong foundations without pressure.

    3Content accelerates

    IP3 Maths

    IP3 is where the mathematical content accelerates noticeably. Students move from structured, guided problem-solving in lower secondary to more open-ended mathematical reasoning. The jump in abstraction, particularly in Functions and early Calculus, catches many students off guard even when they did well in Sec 1 and Sec 2. Students who join in IP3 have ample time to consolidate understanding before H2 Maths in IP5/IP6.

    FunctionsEarly Calculus
    4Leads into H2 level

    IP4 Maths

    IP4 Maths content, particularly Further Trigonometry and early Integration, introduces ideas that students will meet again at H2 level. Students who join in IP4 can still benefit significantly, with our focus on the high-value foundational topics that recur throughout the IP and A-Level syllabus.

    Further TrigonometryEarly Integration

    Frequently Asked Questions


    The Integrated Programme (IP) is a six-year direct-entry pathway to Junior College offered at schools like Raffles Institution, Raffles Girls’ School, Nanyang Girls’ High, and others. IP students bypass the O-Level examinations and proceed directly to the A-Level curriculum.

    This means the mathematical content taught in IP schools is accelerated, deeper, and often uniquely sequenced per school. Unlike mainstream O-Level or A-Level tuition, IP Maths tuition must align with your child’s specific school syllabus — because the pace, topic order, and assessment style differs between IP schools.

    At Orion, Mr Anthony and Ms Celia are experienced with this school-by-school variation and tailor the programme accordingly.

    This is a question that comes up frequently among parents whose child has been placed in an IP school. The short answer is that IP Maths and O-Level A Maths cover overlapping content but are different in difficulty and pace.

    O-Level A Maths is examination-driven with a clear ceiling of difficulty. The syllabus is standardised across all schools and assessed through a single national examination at the end of Secondary 4, which means students can prepare methodically using past-year papers i.e. the “ten years series”.

    IP Maths, by contrast, has no standardised national examination. Each IP school — including CHIJ St Nicholas Girls’ School, Raffles Girls’ School, Raffles Institution, and others — designs its own curriculum. Content, depth, and assessment style vary between schools. IP Maths typically moves faster, introduces topics like Calculus and Functions earlier, and expects students to apply concepts in less structured ways than O-Level A Maths does.

    For this reason, generic O-Level tuition materials are often unsuitable for IP students. At Orion, our IP Maths classes are specifically designed for the IP context — built around each school’s own curriculum and internal assessment expectations, not a standardised national syllabus.

    IP Mathematics at Orion is taught by Mr Anthony Lee and Ms Celia Chia — and together they bring a depth of IP-specific teaching experience that is genuinely unusual in Singapore’s tuition landscape.

    Mr Anthony leads the programme and brings over 20 years of teaching experience across IP Mathematics, H2 Mathematics, and H2 Physics. His own academic journey — from the EM3 stream in primary school to the NUS Dean’s List — gives him a distinctive perspective on mathematical learning. He has worked with IP students from a range of schools over many years, including Raffles Institution, Hwa Chong Institution, Nanyang Girls’ High School, National Junior College, and others, and is well acquainted with the way different IP schools sequence and assess their Mathematics curriculum.

    Ms Celia Chia is a dedicated full-time tutor who joined Orion since 2016 and has built a strong reputation among IP Maths students and parents for her exceptional patience in explaining complex concepts simply. Students who found certain IP Maths topics overwhelming — particularly in Functions, Trigonometry, and early Calculus — consistently describe how Ms Celia’s explanations made things click in a way nothing else had.

    Both tutors share the same core teaching philosophy: never assume a student is ready for the current level of content on day one. Regular assessments are conducted throughout the programme, serving two purposes: to give students near-term goals that keep them motivated and on track, and to allow the tutor to structure revision more efficiently based on each student’s progress.

    Our IP students come from CHIJ St Nicholas Girls’ School, Raffles Girls’ School, Raffles Institution, and other IP schools across Singapore.

    This is more common than parents expect — and it is not a sign of long-term academic failure. IP schools attract Singapore’s top primary school performers, which means the peer group is highly competitive from day one.

    The IP also emphasises independent, self-directed learning rather than the structured exam drilling that produced strong PSLE results. Students who thrived through rote learning often find the IP’s open-ended, concept-heavy approach unsettling at first.

    Add to this a faster curriculum pace and higher-order problem-solving expectations, and it becomes clear why many capable students need structured support to find their footing. Orion’s IP Maths classes provide the scaffolding that lets students build genuine understanding without the chaos of trying to figure it out alone.

    Our IP Maths students come from a range of IP schools across Singapore, including Raffles Institution, CHIJ St Nicholas Girls’ School, Nanyang Girls’ High School, National Junior College, Raffles Girls’ School, Temasek Junior College, and others.

    Because each IP school designs its own mathematics curriculum, we take time to understand each student’s school-specific syllabus and pace before structuring their support.

    This is why our classes are kept small — to allow genuine personalisation that a large lecture-style tuition group simply cannot provide.

    While the specific topic sequencing differs across IP schools, the areas that consistently cause the most difficulty for IP3 and IP4 students are Logarithm, Trigonometry, and the introduction of Differentiation and Integration.

    For students at CHIJ St Nicholas Girls’ School, the challenge is often the transition from structured, guided problem-solving in lower secondary to the more open-ended mathematical reasoning that IP3 Maths demands. The jump in abstraction — particularly in Functions and early Calculus — catches many students off guard even when they did well in Sec 1 and Sec 2.

    For students at Raffles Girls’ School, the IP Maths syllabus moves at a particularly brisk pace in IP3, and internal assessments require students to apply concepts in unfamiliar combinations. Students who keep up comfortably in class often find school tests harder than expected, because the application demands exceed what lectures alone prepare them for.

    For students at Raffles Institution, the pace is similarly fast, and the content in IP4 Maths — particularly Further Trigonometry and early Integration — introduces ideas that students will encounter again at H2 level. Students who build genuine understanding here consistently find the H2 Maths transition smoother.

    At Orion, Mr Anthony and Ms Celia structure IP Maths classes around the specific syllabus and assessment style of each student’s school, ensuring lessons are always relevant to what your child is currently covering.

    This is the core strategic purpose of Orion’s IP Maths programme. The mathematical foundations built in IP3 and IP4 — particularly in Advanced Trigonometry, Functions, Differentiation, and Integration — are the exact building blocks for H2 Mathematics at IP5/IP6 and A-Level.

    Our tutors, having extensive A-Level teaching experience, know precisely which IP concepts are prerequisites for which H2 Maths topics. This means we place deliberate, heavier emphasis on foundational areas that will matter most later — not just what is tested in the next school exam.

    Students who go through Orion’s IP programme consistently find the transition to H2 Maths more manageable than their peers.

    “Generally doing okay” in an IP school often masks gaps that only surface later in IP5/IP6 or at A-Level. IP assessments within school are designed to stretch students, but they don’t always reveal whether foundational understanding is truly solid or whether the student is getting by on short-term memorisation.

    If your child can explain concepts back clearly, apply them to unfamiliar problems without prompting, and maintains consistent results — they may be fine without tuition.

    But if they struggle to articulate why an approach works, or if their grades fluctuate significantly between topics, targeted support now prevents much more costly remediation later.

    Yes — and this is a concern many parents raise, particularly when their child is joining mid-year or is significantly behind their school cohort.

    Our IP Maths students come from CHIJ St Nicholas Girls’ School, Raffles Girls’ School, Raffles Institution, and other IP schools. They join at different points in the year, with different levels of foundational strength, and from schools that sequence their IP curriculum differently.

    What makes this work is Orion’s consistent starting point: we never assume a student is ready for the current level of content on day one. Regardless of which school a student attends or how well they have been doing, Mr Anthony begins by identifying where each student’s foundational gaps are — in algebra, in mathematical reasoning, or in specific topics covered earlier in the IP programme.

    This allows students from different schools and different starting points to improve together effectively. Rather than pitching classes at the strongest students and leaving others behind, Orion builds everyone to the required level before advancing. Parents consistently tell us this is the part of Orion’s approach that made the biggest difference for their child.

    Our IP Maths classes are kept deliberately small — typically around 8 to 10 students. This is essential for IP tuition because each student’s school may be at a different point in the curriculum.

    A smaller class allows Mr Anthony or Ms Celia to provide genuinely personalised pacing: if one student needs more time on Differentiation while another is ahead on Trigonometry, the class structure accommodates this in a way that a large group tuition session cannot.

    Beyond class, students can reach their tutor via WhatsApp or Zoom for follow-up questions at any time.

    The earlier a student joins, the more time there is to build strong foundations without pressure. That said, the most common entry point at Orion is IP3 or IP4 — when the mathematical content accelerates noticeably and school assessments become more demanding.

    Students who join in IP3 have ample time to consolidate understanding before the curriculum pushes into H2 Maths territory in IP5/IP6.

    Students who join in IP4 or even later can still benefit significantly, especially with our focus on the high-value foundational topics that recur throughout the IP and A-Level syllabus.

    Yes — and this is something we specifically design for. Because IP schools have autonomy over their curriculum, topic sequences do vary between institutions. 

    Our tutors are familiar with this variation and adapt lessons to match where each student’s school currently sits in the curriculum. For students from schools with less common sequences, we may provide targeted supplementary materials to bridge any short-term gaps.

    The goal is always to ensure your child is supported at their actual current level — not a generic approximation of it.

     

    No — and this is a conscious decision that reflects how we think about effective learning.

    IP Mathematics is a progressive subject. The concepts introduced in IP3 are the direct foundations for IP4, and IP4 is the foundation for H2 Mathematics at IP5/IP6 and A-Level. This progression cannot be shortcut. A student who does not genuinely understand Functions in IP3 will not meaningfully benefit from three days of intensive IP4 content during a school holiday — they will be covering advanced material on a shaky base, which produces confusion rather than clarity.

    The marketing around holiday crash courses tends to be especially intense during the break periods before major school assessments — creating real pressure on parents who are worried about their child’s progress. We understand that pressure. But in our view, the students who most need intensive support are those who are significantly behind in IP Maths, and these are also the students for whom a crash course is least likely to help and most likely to create false confidence.

    At Orion, school holiday periods are used differently. Our existing IP Maths students receive extended consultation access with Mr Anthony and Ms Celia, additional targeted revision on topics identified as weak, and personalised practice sets designed around their specific school’s upcoming assessments. Our tutors’ time goes to the students who have built a learning relationship with us over time — because that consistency is what produces real improvement.

    If you are looking for IP Maths support for your child, the most effective step is to start a structured weekly programme early — ideally at the beginning of an IP year, not in the final weeks before an examination.

    Yes — and for IP Maths, a trial lesson is especially valuable because of how much the programme varies between students.

    Unlike O-Level tuition, where the syllabus is standardised, IP Maths students come from schools with different curricula, different pacing, and different assessment styles. A trial lesson gives Mr Anthony or Ms Celia the chance to understand exactly where your child’s school currently is in its programme, identify any foundational gaps from earlier IP years, and begin planning how to structure the support. By the time your child attends their first regular lesson, the class is already personalised to their specific situation.

    The trial policy is the same across all Orion programmes: if your child attends the trial and decides not to continue, the trial fee is fully waived — no questions asked. If your child chooses to enrol, the trial lesson is counted as the first lesson of the programme.

    Trial lessons are typically offered at the beginning of the year or when a new class is forming — this minimises disruption to ongoing classes and ensures the trial is as representative of a real lesson as possible.