IP Maths Notes (Lower Sec, Year 1-2): 01) Number Systems & Indices

Study guide16 Nov 2025, 00:00 ZUpdated 30 Nov 2025

Master integer, fractional, and decimal conversions, index laws, and significant figure rounding for Year 1 IP maths.

Download PDF Join our Telegram study group

Q: What does IP Maths Notes (Lower Sec, Year 1-2): 01) Number Systems & Indices cover?
A: Master integer, fractional, and decimal conversions, index laws, and significant figure rounding for Year 1 IP maths.

The core idea is simple: Number sense prevents algebra mistakes later.

Use it as a working check: Convert fractions, decimals, and percentages fluently, then apply index laws step by step. Keep bases consistent before combining powers.

Then go one layer deeper: Work through the examples to practise conversion, ordering, negative indices, fractional indices, surds, and rounding without relying on calculator prompts.

Number sense underpins every algebraic manipulation you will meet from Year 2 onward. This guide cleans up conversion fluency, index laws, surds, and estimation so you never lose calculator-free marks.

These notes align with MOE Lower Secondary Mathematics syllabus used in IP pathways (aligned to O-Level Mathematics 4052 foundations).

Status: MOE Lower Secondary Mathematics syllabus (latest release) checked 2025-11-30 - scope unchanged; remains the reference for these lower-sec notes.

New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.

Learning targets

Convert between fractions, decimals, and percentages without a calculator.
Apply the five index laws, including negative and fractional indices.
Standardise answers to the correct number of significant figures.
Present surds in rationalised form.

Choosing the first move

Mixed number questions become easier when you identify the structure before calculating. Use this map to choose the first tool, then show one clean line of working for that choice.

Question cue	First move	What to check
Fraction, decimal, or percentage conversion	Move everything into one form first.	Simplify fractions and keep recurring decimals clearly marked.

Reviewed by

Marcus Pang·Managing Director (Maths)

Sources

SEAB - Mathematics (4052) GCE O-Level 2026 syllabus (PDF)

Expression type	First rewrite	Law to use after rewriting	Common trap
$8^2 \times 4^3$	$(2^3)^2 \times (2^2)^3$	Power of a power, then product law.	Adding exponents before making both bases $2$ .
$\dfrac{27^2}{9^3}$	$\dfrac{(3^3)^2}{(3^2)^3}$
$16^{\frac{3}{4}}$	$(2^4)^{\frac{3}{4}}$
$5^{-2}$	$\dfrac{1}{5^2}$	Negative index means reciprocal.	Making the answer negative.

Original number	Decimal move to make $1 \leq a < 10$	Power of ten	Common trap
$45600$	Move decimal 4 places left to get $4.56$ .	$10^4$	Writing $10^{-4}$ because the decimal moved left.
$0.0032$	Move decimal 3 places right to get $3.2$ .	$10^{-3}$	Writing $10^3$ because the decimal moved right.
$7.8$	Decimal is already after the first non-zero digit.	$10^0$	Forcing a power of ten when standard form is already reached.

Denominator type	Multiplier to use	Why it works	Common trap
Single surd, such as $\sqrt{3}$	Multiply top and bottom by the same surd.	$\sqrt{3}\times\sqrt{3}=3$ .	Multiplying only the denominator and changing the value of the fraction.
Whole-number multiple, such as $2\sqrt{5}$	Multiply top and bottom by $\sqrt{5}$
Binomial surd, such as $2-\sqrt{5}$	Multiply top and bottom by the conjugate $2+\sqrt{5}$

IP Maths Notes (Lower Sec, Year 1-2): 01) Number Systems & Indices

Learning targets

Choosing the first move

Sources

1 Number systems refresher

1.1 Fraction-decimal-percentage triad

1.2 Ordering rational and irrational numbers

2 Index laws

Same-base index checkpoint

Worked example 1 - Mixed indices

Worked example 2 - Fractional indices & surds

3 Standard form & significant figures

Standard-form direction checkpoint

4 Rationalising simple surds

Rationalising denominator checkpoint

Practice Quiz

Try it yourself

Exam watchpoints

Related Posts