G3 Sec 1 · Number and algebra
Use primes, factors and signed numbers accurately. Make sense of ratio, percentage and speed, then connect expressions and linear equations to straight-line graphs.
SECONDARY 1–2 · G3 & G2 · ONLINE
Lower Secondary Math tuition.
Turn number reasoning into algebra and geometry.
We help Sec 1–2 learners turn arithmetic reasoning into algebraic models and justify geometric steps. Students learn to form the relationship, choose a method and explain their working.
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.
Build the foundations that upper secondary will use.
The Sec 1–2 topic map moves from number sense to algebra, graphs and geometric reasoning. We follow the child’s G2 or G3 school sequence and choose a useful starting point.
G3 Sec 1 · Geometry and data
Reason with angles and polygons, measure composite shapes and solids, and read tables and graphs with care. Explain the choice of method as well as the answer.
G3 Sec 2 · Equations and relationships
Extend algebra through expansion, factorisation, fractions and changing the subject of a formula. Connect simultaneous equations and quadratic graphs, and interpret direct or inverse proportion.
G3 Sec 2 · Shape, statistics and chance
Apply similarity, Pythagoras and right-angled trigonometry. Work with solids, averages and simple probability while keeping diagrams, units and explanations clear.
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. The year map follows G3; G2 topic timing is shown in the subject-level comparison below. Lessons follow the student’s subject level and school sequence.
G3 Secondary 1 · Number, algebra and graphs7 chapter groups
Primes, factors and multiples
Use prime factorisation, HCF and LCM to organise number relationships.
Quick recap: Is the question asking for a shared factor or a shared multiple?
Signed numbers, estimation and accuracy
Calculate with signed numbers, order values and use rounding and significant figures meaningfully.
Quick recap: Check the sign and the expected size of the answer.
Ratio, percentage, rate and speed
Interpret comparisons, reverse percentages and compound units in everyday situations.
Quick recap: Name the starting quantity and keep units consistent.
Expressions, patterns and linear equations
Translate words into algebra, simplify, form equations and express a pattern using a general term.
Quick recap: Substitute the solution back into the original equation.
Straight-line graphs
Connect coordinates, intercept and gradient to a relationship between two quantities.
Quick recap: Explain the gradient with the quantities and their units.
Angles, polygons and measurement
Use angle facts, shapes, area and the surface area or volume of appropriate solids.
Quick recap: Which lengths are needed before using the formula?
Tables, charts and data interpretation
Read scales and compare representations, including recognising a misleading display.
Quick recap: Does the graph’s scale change the impression it gives?
G3 Secondary 2 · Extend and connect the foundations7 chapter groups
Proportion and scale
Connect direct and inverse proportion with scale drawings and quantities.
Quick recap: Which product or ratio stays constant?
Algebraic identities and fractions
Expand, factorise, change the subject of a formula and operate on algebraic fractions.
Quick recap: Factorise before deciding what can be cancelled.
Simultaneous and quadratic equations
Solve simultaneous equations and factorisable quadratics; connect roots to quadratic graphs and inequalities to a number line.
Quick recap: Check each root in the original equation.
Congruence and similarity
Match corresponding sides and angles before using a proportion.
Quick recap: Write the matching order before forming a ratio.
Pythagoras and right-angled trigonometry
Identify the hypotenuse and choose a useful ratio for an acute angle.
Quick recap: Label opposite and adjacent for the chosen angle.
Solids and mensuration
Work with pyramids, cones and spheres, and distinguish surface area from volume.
Quick recap: Are the required units squared or cubed?
Statistics and simple probability
Interpret diagrams, use mean, median and mode, and list outcomes to calculate a simple probability.
Quick recap: What is the complete set of possible outcomes?
The right syllabus. Appropriate challenge.
Both G2 and G3 learners practise understanding, method selection and explanation. We adjust prerequisites, scaffolding, pace and question complexity to the student’s subject requirements and demonstrated readiness.
Understand
Make sense of the quantities, representations and conditions.
Choose
Compare possible methods and decide which fits.
Explain
Justify key steps and check the conclusion in context.
How the syllabuses differ.
Topic timing differs; understanding and reasoning matter at both levels. This comparison follows MOE’s content-by-level tables. The chapter map follows G3.
| Topic / scope | G3 | G2 |
|---|---|---|
| Straight-line graphs and gradients | Sec 1 | Sec 2 |
| Quadratic graphs and equations | Sec 2 | Sec 3–4 |
| Right-angled trigonometry | Sec 2 | Sec 3–4 |
Choose the stage your child is in.
All year levels below refer to 2027.
Secondary 1 in 2027
Settle into algebra and mathematical language. Learn to label a diagram, form an equation and explain what the answer means.
Secondary 2 in 2027
Build similarity, Pythagoras, statistics and algebra skills. G3 also includes quadratic equations and right-angled trigonometry at this stage; G2 develops these in upper secondary.
SLC WORKED EXAMPLES
Understand the relationship. Choose the method.
From a price flow to similar triangles, see how the first useful step changes the problem.
G3 SEC 1 / G2 SEC 2 · PERCENTAGES & ALGEBRA
In a hypothetical town with an 8% sales tax, two shops sell the same type of backpack. The stated tax is part of this model, not a claim about Singapore’s current GST rate.
At Shop A, the marked price is unknown. A customer receives 15% off the marked price, then uses a $7 voucher. Sales tax of 8% is added to the reduced price after the voucher. The final receipt total is $120.96.
At Shop B, the backpack has a marked price of $160. Shop B gives 12% off, then adds the same 8% sales tax.
- Find the marked price at Shop A.
- Find the final receipt total at Shop B.
- Which shop is cheaper, and by what percentage is the cheaper receipt below the other receipt? Use the Shop B receipt as the comparison base. Give the percentage to 1 decimal place.
- Marked price?
- 15% discount
- $7 voucher off
- 8% sales tax
- $120.96
Show the thinking
The key idea
Apply each change to the current price, in the stated order.
Solution steps
1. Shop A marked price
Let be the marked price at Shop A, in dollars.
A 15% discount leaves 85%:
After the $7 voucher:
Adding 8% sales tax multiplies this current amount by . The receipt therefore gives the linear equation:
Divide by :
Add 7:
Divide by :
So the Shop A marked price is $140.00.
2. Shop B receipt
A 12% discount leaves 88% of $160:
The 8% tax is applied to $140.80:
Rounded to the nearest cent, the Shop B receipt is $152.06.
3. Comparison
Shop A is cheaper. The saving is:
The question specifies Shop B’s receipt as the base, so:
To 1 decimal place, the Shop A receipt is 20.5% below Shop B’s receipt.
Answer: Shop A is cheaper by $31.10 when the receipts are rounded to cents, which is 20.5% of the Shop B receipt.
Verify your answer:
Substitute into the original ordered model: . Both receipt totals are positive, and the comparison denominator $152.064 is non-zero.
Try a similar question
A third retailer marks the backpack at $170, gives a 25% discount, then applies an 8% tax. Its receipt is compared with Shop A’s $120.96 receipt. Find the third retailer’s receipt and state the percentage by which Shop A is cheaper, using the third retailer’s receipt as the base. (Calculator permitted; round money to the nearest cent and the percentage to 1 decimal place.)
Check the answer
The third receipt is . Saving relative to that receipt is , so Shop A is cheaper by 12.2%. This transfers the same ordered-multiplier model while changing both the discount and the comparison base.
SEC 2 · G2/G3 · SIMILARITY & PYTHAGORAS
In the diagram, ABC is a right-angled triangle with ∠ACB = 90°. D lies on AB, and CD ⟂ AB. The lengths are AD = 36 cm and DB = 64 cm.
(a) Explain why the two smaller triangles formed by CD are similar, and state the corresponding order of their vertices.
(b) Use the similarity to find CD.
(c) Use Pythagoras to find AC.
(d) Find BC, giving your answer in centimetres.
Show the thinking
The key idea
ACD ~ CBD: corresponding right triangles.
Solution steps
(a) AA similarity
(a) Both △ACD and △CBD have a right angle because CD ⟂ AB: ∠ADC = ∠CDB = 90°. Also, ∠CAD and ∠BCD are each complementary to the corresponding acute angle of the large right triangle ABC, so ∠CAD = ∠BCD. Therefore, by AA similarity,
△ACD ∼ △CBD.
The correspondence is A ↔ C, C ↔ B, D ↔ D.
(b) Use the similarity to find CD.
(b) Under that correspondence, corresponding sides first give the explicit proportion
AD / CD = CD / DB.
Therefore the altitude relationships give the geometric-mean result for the segment CD:
CD² = AD × DB
CD² = 36 × 64 = 2304
CD = 48 cm, since a length is positive.
(c) Use Pythagoras to find AC.
(c) In right triangle ACD,
AC² = AD² + CD²
AC² = 36² + 48²
AC² = 1296 + 2304 = 3600
AC = 60 cm.
(d) Find BC.
(d) First find the hypotenuse of the large triangle:
AB = AD + DB = 36 + 64 = 100 cm.
In right triangle ABC,
BC² = AB² − AC²
BC² = 100² − 60²
BC² = 10000 − 3600 = 6400
BC = 80 cm.
The positive root is selected because BC is a length. The answers are therefore:
- (a)
△ACD ∼ △CBD, withA ↔ C,C ↔ B,D ↔ D. - (b)
CD = 48 cm. - (c)
AC = 60 cm. - (d)
BC = 80 cm.
Verify your answer:
60² + 80² = 3600 + 6400 = 10000 = 100², so AC, BC, and AB satisfy Pythagoras in the large right triangle. Also, 36:48:60 and 48:64:80 are both scaled 3:4:5 right triangles, consistent with the similarity.
Try a similar question
A right triangle PQR has ∠Q = 90°. The altitude from Q meets hypotenuse PR at S, with PS = 9 cm and SR = 16 cm. Without using trigonometry, find QS, PQ, and QR. State the two similar smaller triangles in corresponding order and justify your correspondence.
Check the answer
QS² = PS × SR = 144, so QS = 12 cm. PR = 25 cm; then PQ² = PS × PR = 225, so PQ = 15 cm, and QR² = SR × PR = 400, so QR = 20 cm. A valid correspondence is △PQS ∼ △QRS (P ↔ Q, Q ↔ R, S ↔ S), justified by the right angles and the acute angles inherited from △PQR.
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.
Keeps making algebra slips
Locate the line where the reasoning changes, then practise that skill in a short sequence before returning to the full question.
Can calculate, cannot interpret
Label what each number means. Use a diagram, variable or table to organise the information.
Runs out of time
Build fluency with focused practice, then use mixed questions to improve method selection and checking.
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.
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 →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.
Questions parents ask.
Choose the subject and stage that fit your child.
Is Lower Secondary Math the same as E Math tuition?
This page focuses on Sec 1–2 foundations. Our E Math page focuses on Sec 3–4 and SEC Mathematics preparation. Both pathways help students connect concepts, show working and solve independently.
Do you support both G2 and G3 learners?
Yes. Share the child’s subject level and current topics. We adapt explanations, pace and practice to their schoolwork and learning needs.
Can my child join when algebra starts to feel difficult?
Yes. Tell us which step feels difficult: forming an expression, solving an equation, reading a graph or choosing a method. This gives us a practical starting point.
Are the lessons online?
Yes. All SLC Math lessons are online. Choose a year level and subject on this page to prepare a short WhatsApp enquiry.
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: lower-secondary algebra, graphs, geometry and data. Lessons follow your child’s G2 or G3 school topics. Reviewed 12 November 2026.
Sources checked 12 November 2026: MOE G2/G3 Mathematics: content by level