halve every power 1764 = 2² × 3² × 7² √1764 = 2 × 3 × 7 = 42
∛ cube root
divide every power by 3 2744 = 2³ × 7³ ∛2744 = 2 × 7 = 14
🧠 HOOKPerfect square ⇔ every power is even. Perfect cube ⇔ every power is a multiple of 3. e.g. smallest k so 72k is a square: 2³×3² → need one more 2 → k = 2.
✍ SPOT THE TYPEHCF word problems = "largest equal groups / biggest square tile". LCM word problems = "next time together / smallest common length".
E Math · Sec 1
➖
2
Integers, Rationals & Reals
N1 · number line, operations, order of operations
BIG IDEAThe number line runs from negative to positive. With signs: same signs → +, different signs → −.
Types of numbers
➕➖ Sign rules
× or ÷
(+)(+)
+
(−)(−)
+
(+)(−)
−
−3 − (−5) = −3 + 5 = 2 (−2)³ = −8 · (−2)⁴ = 16
Order of operations
Brackets
Indices (powers, roots)
Divide / Multiply — left to right
Add / Subtract — left to right
Example
10 − 2 × (3 + 1)² = 10 − 2 × 16 = 10 − 32 = −22
Inequality symbols
< less than · > greater than · ≤ at most · ≥ at least −5 < −2 (further left = smaller)
⚠ TRAP−3² = −9 but (−3)² = 9. The power only hits what it touches.
🧠 HOOKCalculator: use brackets for negatives and fractions, e.g. (−4)^2. Recurring decimal: 0.3̇ = ⅓.
E Math · Sec 1
🎯
3
Approximation & Estimation
N1 · decimal places, significant figures
BIG IDEAd.p. = digits after the decimal point. s.f. = count from the first non-zero digit.
Zeros…
Significant?
Example
between non-zero digits
YES
305 → 3 s.f.
at the front (leading)
NO
0.0047 → 2 s.f.
at the end, after a decimal point
YES
2.50 → 3 s.f.
at the end of a whole number
depends
4500 → 2, 3 or 4 s.f.
Rounding — look at the NEXT digit
Number
Round to
Answer
3.14159
2 d.p.
3.14
0.05962
2 s.f.
0.060 (keep the 0!)
30 060
3 s.f.
30 100
7.996
2 d.p.
8.00
🎯 Estimation
round every number to 1 s.f. first 39.8 × 0.51 ≈ 40 × 0.5 = 20 √(48.7) ≈ √49 = 7
Next digit rule
5–9 → round up 0–4 → keep Then fill places with 0 (whole numbers only)
⚠ TRAPExam answers: give to 3 s.f. unless told otherwise (angles to 1 d.p.). Never round in the middle of working — keep full values.
✍ WHY ESTIMATE"An estimate is a rough answer found by rounding each number (usually to 1 s.f.) to check if a calculated answer is reasonable."
BIG IDEAAn equation is a balance. Whatever you do to one side, do to the other.
2x + 3 = 11 → 2x = 8 → x = 4
Steps
① expand brackets ② collect x terms on one side ③ numbers on the other ④ divide by the coefficient 5(x − 2) = 3x + 4 5x − 10 = 3x + 4 → 2x = 14 → x = 7
BIG IDEALine = 180° · Point = 360° · Triangle = 180° · Vertically opposite angles are equal.
Parallel lines — F, Z, C
equal
equal
add to 180°
Triangles & quadrilaterals
exterior angle = sum of interior opposite angles
Special triangles
Isosceles: 2 equal sides → 2 equal base angles Equilateral: all 60° Right-angled: one 90°
Shape
Sides
Angles
Diagonals
Square
all equal
all 90°
equal, ⊥, bisect
Rectangle
opp. equal
all 90°
equal, bisect
Rhombus
all equal
opp. equal
⊥, bisect
Parallelogram
opp. equal & ∥
opp. equal
bisect
Trapezium
1 pair ∥
—
—
Kite
2 pairs adjacent equal
1 pair equal
⊥
Polygons
Formulas
interior sum = (n − 2) × 180° exterior sum = 360° regular: each exterior = 360° ÷ n interior + exterior = 180°
Example
Regular hexagon: ext = 360 ÷ 6 = 60° → int = 120° Each int = 156° → ext = 24° → n = 360 ÷ 24 = 15 sides
✍ REASONSAlways give the reason: "alt. ∠s, AB ∥ CD", "∠s on a str. line", "vert. opp. ∠s", "∠ sum of △", "base ∠s of isos. △".
🧠 HOOKConstructions: use a ruler + compasses, keep the construction arcs, label everything.
E Math · Sec 1
📦
9
Mensuration
G5 · area, prisms, cylinders, conversions
BIG IDEAPrism or cylinder: Volume = cross-section area × length. Surface area = add up the faces of the net.
parallelogram b × h
trapezium ½(a + b)h
triangle ½ × b × h
circle πr² · 2πr
Prisms & cylinders
cylinder + its net
Solid
Volume
Surface area
Prism
cross-section × length
sum of all faces
Cylinder
πr²h
2πr² + 2πrh
Cuboid
l × b × h
2(lb + bh + lh)
Unit conversions
Area
1 m² = 100 × 100 = 10 000 cm² 1 cm² = 100 mm²
Volume
1 m³ = 1 000 000 cm³ 1 litre = 1000 cm³
⚠ TRAPSquare the conversion for area, cube it for volume. Composite shapes: split into simple shapes, then add or subtract.
E Math · Sec 1
📊
10
Data Handling
S1 · tables, pictograms, bar & line graphs, pie charts
BIG IDEAChoose the chart that fits the data, and watch for charts that mislead.
Pictogram
Bar graph
Line graph
Pie chart
Chart
Best for
Watch out
Pictogram
eye-catching, simple counts
needs a key; part-symbols are hard to read
Bar graph
comparing categories
bars must have equal widths
Line graph
change over time
only for continuous/time data
Pie chart
parts of a whole
hard to compare small sectors
🥧 Pie chart angle
angle = (frequency ÷ total) × 360° 12 of 40 students → 12/40 × 360 = 108°
⚠ SPOT ITMisleading graphs: y-axis not starting at 0, uneven scale, 3-D effects, pictures of different sizes.
✍ WRITE THIS"The graph is misleading because the vertical axis does not start from zero, so the difference between the bars looks bigger than it really is."
E Math · Sec 1
💰
11
Money Maths & Real-World Graphs
Interest, GST, exchange, bills, travel graphs
BIG IDEAReal-world questions are just percentage and rate in disguise. Read units carefully.
Topic
Formula / method
Example
Simple interest
I = PRT ÷ 100
$2000 at 3% for 4 yrs → I = 2000×3×4÷100 = $240
Compound interest (Sec 3)
A = P(1 + r/100)ⁿ
given in the formula list
GST (9% in Singapore)
price × 1.09
$50 meal → 50 × 1.09 = $54.50
Discount
price × (1 − d%)
20% off $80 → 80 × 0.8 = $64
Money exchange
multiply / divide by rate
S$1 = RM3.45 → S$200 = RM690
Utilities bill
units used × rate (+ GST)
350 kWh × $0.30 = $105
Instalments
deposit + (monthly × months)
$300 + 12 × $80 = $1260
💱 Exchange trick
Write it as a ratio and keep units: S$1 : RM3.45 RM100 → 100 ÷ 3.45 = S$28.99
Which is the better buy?
work out the price per unit (per 100 g, per litre) and compare
Distance–time & speed–time graphs
distance–time: gradient = speed, flat = stopped
speed–time: gradient = acceleration, area = distance