YEARS 1–4 · SCHOOL-ADAPTED · ONLINE

IP Math tuition.
Recognise the structure. Connect ideas. Build the argument.

We help IP learners recognise structure in unfamiliar questions, connect ideas and build mathematical arguments. We plan from the student’s school topics, recent work and current understanding.

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Live online Math lessons · Learn from home across Singapore

F9 A13–6 months

FROM OUR MATH TEACHING EXPERIENCE

Our secondary Math teaching experience includes helping students improve from F9 to A1 within 3–6 months. For G2 and IP learners, we work with the school’s grading system and the child’s own targets.

What your child is working towards.

There is no single national IP Math syllabus for every school. Published RI and RGS curricula emphasise understanding, independent thinking and application. The useful starting point is your child’s own school sequence.

Algebra & functions

Move between expressions, equations and graphs. Explain the relationships instead of relying on a remembered sequence.

Geometry & trigonometry

Read the diagram carefully, identify useful properties and build a chain of reasons that supports the solution.

Data, probability & later topics

Interpret information and test conclusions. For later-year work, discuss the calculus and other topics on the school’s current plan.

A CURRICULUM WITH A CLEAR STRUCTURE

See the chapters. Understand the learning goals.

Open a chapter group to see the learning focus and a short recap prompt. Earlier ideas return in later work, so the next topic has a stronger base. SLC’s year map is illustrative and school-dependent. We adapt the sequence, depth and practice to your child’s school topics and assessment needs.

IP Year 1 · Number, algebra and mathematical language3 chapter groups

Number and proportional reasoning
Connect factors, real numbers, estimation, ratio, rates and percentages.
Quick recap: Estimate first and explain the unit used.
Linear algebra, graphs and patterns
Use expressions, equations, simultaneous linear relationships, graphs and sequences.
Quick recap: Explain how a rule appears in both a formula and a graph.
Geometry, measurement and statistics
Build angle, polygon, area, volume and data-reading skills with clear explanations.
Quick recap: Which property makes the calculation valid?

IP Year 2 · Quadratics and geometric connections3 chapter groups

Quadratics and algebraic structure
Connect factorisation, equations, graphs, algebraic fractions and indices.
Quick recap: Match roots and turning points to the graph.
Similarity, circles and trigonometry
Connect Pythagoras, similarity, triangle trigonometry, circle properties, sectors and radian measures as the school sequence develops.
Quick recap: Read the diagram before deciding on a rule.
Probability and statistical interpretation
Use set or outcome representations and compare statistical displays and measures.
Quick recap: Explain what the data supports, using its context.

IP Year 3 · Functions, proof and trigonometric reasoning3 chapter groups

Further algebra and functions
Develop work with polynomials, surds, logarithms, graph transformations and coordinate geometry.
Quick recap: Check the domain before accepting a solution.
Geometry, matrices and representations
Link circle equations, plane-geometry reasoning, matrices and linearised relationships.
Quick recap: Explain why the chosen representation helps.
Trigonometric graphs, equations and identities
Connect graphs, special angles, identities, compound angles and equivalent trigonometric forms.
Quick recap: Track every solution in the required interval.

IP Year 4 · Calculus and connected problem solving3 chapter groups

Binomial and probability
Use expansion structure and probability representations in multi-step reasoning.
Quick recap: State the conditions before using a formula.
Differentiation, integration and motion
Connect derivatives and integrals to graphs, optimisation, area, rates and motion, including the school’s required function types.
Quick recap: What physical or geometric quantity does the answer represent?
Vectors and cumulative revision
Use vector relationships and revisit earlier algebra, geometry and trigonometry in longer solutions.
Quick recap: Compare two methods and explain which is more efficient.

A clearer path through IP Years 1–4.

These illustrative priorities guide SLC’s IP teaching. We adapt the starting point and pace to your child’s school topics and recent work.

Secondary 1 / IP Y1 in 2027

Make the move to algebra with confidence.

Connect number skills with expressions, linear equations and straight-line graphs. Use clear diagrams and explanations for geometry, measurement and introductory statistics.

Secondary 2 / IP Y2 in 2027

Bring equations and graphs together.

Link quadratic equations to their graphs, work confidently with algebraic fractions and extend geometry through similarity and trigonometry. Build meaning behind each method before adding speed.

Secondary 3 / IP Y3 in 2027

Connect a wider range of ideas.

Deepen algebra through polynomials, surds and logarithms. Read function transformations, develop coordinate-geometry reasoning and connect trigonometric graphs, equations and identities.

Secondary 4 / IP Y4 in 2027

Use earlier learning in longer problems.

Consolidate trigonometry alongside calculus, probability and vectors. Practise choosing methods across topics, showing a complete argument and checking a solution against its conditions.

SLC WORKED EXAMPLES

See the connection that unlocks the problem.

Two SLC IP examples connect geometric proof, trigonometry and calculus with clear reasons at each step.

SLC IP Y2–Y3 · SIMILARITY & PROOF

In trapezium $ABCD$ , $AB\parallel CD$ , $AB=8\text{ cm}$ and $CD=12\text{ cm}$ . The diagonals $AC$ and $BD$ meet at $O$ .

Prove $AO:OC=BO:OD=2:3$ . State the triangles you use and justify the correspondence.
Using part 1, prove that triangles $AOD$ and $BOC$ have equal areas. Do not argue from the appearance of the diagram.
If $[AOB]=20\text{ cm}^2$ , find $[AOD]$ , $[BOC]$ , and $[COD]$ .

Teacher’s original trapezium ABCD, with AB parallel to CD, AB 8 cm, CD 12 cm and diagonals meeting at O. — Diagram not to scale.

Show the thinking

The key idea

Similarity → ratios → areas

Solution steps

1. Diagonal ratio

Because $AB\parallel CD$ ,

\angle ABO=\angle CDO,\qquad \angle BAO=\angle DCO.

Also, $\angle AOB=\angle COD$ because they are vertically opposite. Therefore

\triangle AOB\sim\triangle COD\quad\text{(AA)}.

Corresponding sides are proportional:

\frac{AO}{OC}=\frac{BO}{OD}=\frac{AB}{CD}=\frac{8}{12}=\frac23.

Thus

AO:OC=BO:OD=2:3.

2. Equal areas, proved by ratios

Triangles $AOD$ and $AOB$ use bases $OD$ and $OB$ on the same line $BD$ , and have the same altitude from $A$ . Hence

\frac{[AOD]}{[AOB]}=\frac{OD}{OB}=\frac32.

Triangles $BOC$ and $AOB$ use bases $OC$ and $OA$ on the same line $AC$ , and have the same altitude from $B$ . Hence

\frac{[BOC]}{[AOB]}=\frac{OC}{OA}=\frac32.

Both areas are therefore $\tfrac32[AOB]$ , so

[AOD]=[BOC].

This equality follows from two common-altitude/base ratios, not from the drawing's appearance.

3. Numerical areas

[AOD]=20\times\frac32=30\text{ cm}^2, \qquad [BOC]=20\times\frac32=30\text{ cm}^2.

For $COD$ , use both corresponding-side ratios, or multiply the two area factors:

\frac{[COD]}{[AOB]}=\frac{OC}{OA}\cdot\frac{OD}{OB} =\frac32\cdot\frac32=\frac94.

Therefore

[COD]=20\times\frac94=45\text{ cm}^2.

Verify your answer:

In the exact coordinate model $A=(0,0)$ , $B=(8,0)$ , $D=(-2,12.5)$ , $C=(10,12.5)$ , $O=(4,5)$ , direct determinant areas are $[AOB]=20$ , $[AOD]=30$ , $[BOC]=30$ , $[COD]=45$ cm². Their sum is $125$ cm², matching $\tfrac12(8+12)(12.5)$ .

Try a similar question

In trapezium $PQRS$ , $PQ\parallel SR$ , $PQ=9\text{ cm}$ , $SR=15\text{ cm}$ , and diagonals meet at $X$ . If $[PXQ]=18\text{ cm}^2$ , prove the corresponding diagonal ratio and find $[PXS]$ , $[QXR]$ , and $[SXR]$ .

Check the answer

The same AA argument gives $PX:XR=QX:XS=PQ:SR=9:15=3:5$ . The common-altitude/base ratios give

[PXS]/[PXQ]=XS/XQ=5/3, \qquad [QXR]/[PXQ]=5/3,

so $[PXS]=[QXR]=18\times5/3=30\text{ cm}^2$ . Finally

[SXR]/[PXQ]=(5/3)^2=25/9,

so $[SXR]=18\times25/9=50\text{ cm}^2$ . This is independently recomputed from the follow-up values, not copied from the main answer.

SLC IP Y4 · TRIGONOMETRY & CALCULUS

A rectangular panel is placed in the corner of a quarter-circle. One vertex is at the centre O of the quarter-circle, two adjacent sides lie along the perpendicular radii, and the opposite vertex P lies on the arc. The radius is 12 m. Let $\theta$ be the angle between $OP$ and the horizontal radius.

The mechanism permits only

\frac{\pi}{6}\leq \theta\leq\frac{5\pi}{12}.

Using the geometry, construct a trigonometric model for the panel's area $A(\theta)$ . Then find the maximum possible area.

Rectangle inside a quarter-circle, with corner O at the centre and opposite corner P on the arc. OP is 12 metres and makes angle theta with the horizontal. — Diagram not to scale.

Show the thinking

The key idea

CONSTRUCTION → TEST

Solution steps

1. Area model

Let the rectangle's width be $x$ and height be $y$ . The radius triangle gives

x=12\cos\theta,\qquad y=12\sin\theta.

Therefore

A(\theta)=xy=144\sin\theta\cos\theta.

2. Differentiate

Differentiate with respect to $\theta$ (in radians):

A'(\theta)=144(\cos^2\theta-\sin^2\theta)

A'(\theta)=144\cos(2\theta).

For a stationary point,

144\cos(2\theta)=0

\cos(2\theta)=0.

Within $\pi/6\leq\theta\leq5\pi/12$ , the only solution is

\theta=\frac{\pi}{4}.

3. Compare

Now test the stationary point and both endpoints:

A\left(\frac{\pi}{6}\right)=144\left(\frac12\right)\left(\frac{\sqrt3}{2}\right)=36\sqrt3\approx62.35\text{ m}^2.

A\left(\frac{\pi}{4}\right)=144\left(\frac{\sqrt2}{2}\right)^2=72\text{ m}^2.

A\left(\frac{5\pi}{12}\right)=144\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{5\pi}{12}\right)=72\sin\left(\frac{5\pi}{6}\right)=36\text{ m}^2.

Since $72>36\sqrt3\approx62.35$ and $72>36$ , the maximum is

\boxed{72\text{ m}^2=72.00\text{ m}^2}

\boxed{\theta=\frac{\pi}{4}=45^\circ}.

Verify your answer:

at $\theta=\pi/4$ , $x=y=12/\sqrt2$ , so $xy=(12/\sqrt2)^2=72\text{ m}^2$ , agreeing with the model.

Try a similar question

A similar panel has radius $15$ m and the mechanism permits $\pi/3\leq\theta\leq5\pi/12$ . Construct the area model, check whether any stationary point is admissible, test both endpoints, and state the maximum area exactly.

Check the answer

$A(\theta)=225\sin\theta\cos\theta$ , with derivative $225\cos(2\theta)$ . The stationary solution $\theta=\pi/4$ is outside the permitted interval and must be rejected. At the endpoints, $A(\pi/3)=225\sqrt3/4\approx97.43\text{ m}^2$ and $A(5\pi/12)=225/4=56.25\text{ m}^2$ . Thus the maximum is $225\sqrt3/4\text{ m}^2$ at $\theta=\pi/3$ . Alternatively, $2\theta$ lies between $2\pi/3$ and $5\pi/6$ , where cosine is negative, so the area decreases throughout the interval. This tests why the unrestricted square solution is not always admissible.

Find the part that needs attention.

Two students with the same mark may need very different support. Tell us what happens when your child works independently.

Understands examples, gets stuck alone

Compare a familiar question with a changed version. Identify what stays the same and what needs a new idea.

Finishes quickly, loses explanation marks

Slow down at the key reasoning step and make the argument clear enough for another person to follow.

School pace feels demanding

Choose the prerequisite concept that will make the next school topic easier to approach.

RESEARCH-INFORMED LEARNING

Learn it clearly. Recall it later. Use it independently.

Short recaps bring earlier ideas back, so your child can use them again in a new question.

01
Learn with a worked example
Connect a diagram, the method and the reason behind it.
02
Recall after a short gap
Try a short question from memory, then check the key idea.
03
Revisit in a later lesson
Bring an earlier skill back alongside current school topics.
04
Mix, correct and apply
Choose a method, repair an error and solve a fresh version.

Spaced repetition

Key concepts return over several lessons and practice sets, with short recaps that keep earlier learning active.

Retrieval practice

Students recall a rule, explain a step or attempt a question before checking notes. This also helps locate the gap that needs attention.

Worked examples to independent attempts

A clear model leads to a partly completed question, then an independent solution as understanding becomes more secure.

Interleaved practice

Once a method is understood, mix familiar question types so students practise deciding which approach fits.

Feedback and a fresh attempt

Identify the step that went wrong, correct the reasoning and return to a related question later.

Explain with words and diagrams

Connect a calculation to a model or graph and explain why the step works.

The right kind of practice makes a difference.

SLC’s existing BBTP and CBC pathways give us two ways to approach the next learning goal.

BBTP

Build the strategy.

Topic-by-topic work on understanding a question, choosing a strategy and solving it independently. Useful when your child needs a clearer way to begin.

Explore BBTP →

CBC

Practise the performance.

Timed drills, mixed-topic practice and review of more demanding questions. Useful when your child needs to apply learning more consistently in an assessment.

Explore CBC →

Need both? Let’s plan the balance.

Discuss how topical work and exam practice can fit together around your child’s current needs.

Discuss a Math plan →

Questions parents ask.

A few useful answers before choosing a class.

Does every IP school teach the same Math syllabus?

No. Schools set their own sequences and assessment tasks. Share the school, year and current topics so we can discuss suitable support.

Is IP Math tuition just harder E Math and A Math?

There is overlap, but useful IP support also develops explanations, connections and flexible thinking around the school’s work. We plan from that work rather than applying one exam template to everyone.

Can my child prepare for IP Year 1 after PSLE?

Yes. Ask about a transition plan that connects primary problem solving to algebra, notation and explaining a method. Tell us the school and that your child will enter Y1 in 2027.

Are these Math lessons online?

Yes. SLC’s Math lessons are online. Tell us the year level, subject and learning concern on WhatsApp to discuss a suitable class.

Tell us where your child needs a hand.

Choose the year and learning focus, then add context in WhatsApp.

What to share

When you message us, share your child’s recent exam results and any teacher feedback, if available.

How this helps

We use the year, subject and learning context to discuss a suitable starting point and whether topical teaching, exam practice or a combination would be more useful.

Explore another Math pathway.

Find the subject that matches your child’s school journey.

Learning focus reviewed 12 November 2026. We use your child’s school topics and recent work to plan the next step.

Sources checked 12 November 2026: RI Mathematics curriculum · RGS Mathematics curriculum

IP Math tuition.Recognise the structure. Connect ideas. Build the argument.

What your child is working towards.

Algebra & functions

Geometry & trigonometry

Data, probability & later topics

See the chapters. Understand the learning goals.

Number and proportional reasoning

Linear algebra, graphs and patterns

Geometry, measurement and statistics

Quadratics and algebraic structure

Similarity, circles and trigonometry

Probability and statistical interpretation

Further algebra and functions

Geometry, matrices and representations

Trigonometric graphs, equations and identities

Binomial and probability

Differentiation, integration and motion

Vectors and cumulative revision