O-Level E-Maths Number and Algebra: the four operations, indices and standard form, ratio and proportion, percentages and money, and algebraic manipulation

Why Number and Algebra comes first

Number and Algebra is the foundation strand of O-Level E-Maths (SEAB 4052). Every other strand, from geometry and trigonometry to statistics, leans on the ability to compute accurately, manipulate symbols and reason about proportion. The student who is fluent here loses far fewer marks elsewhere, because a single arithmetic slip or a dropped negative sign can collapse an otherwise correct multi-step answer. This overview ties the strand together and links to every dot point in the module, each with its own worked answers and practice.

See the full set of dot points at /sg-o-level/mathematics/syllabus.

The arithmetic toolkit

The strand opens with numbers and the four operations: adding, subtracting, multiplying and dividing integers, fractions and decimals, the order of operations (BIDMAS), and rounding to significant figures and decimal places with estimation as a check. These are the workhorse skills that the calculator supports but cannot replace, because markers reward shown method and exact form.

The toolkit extends to indices and standard form, where the laws of indices ($a^m \times a^n = a^{m+n}$, $a^m \div a^n = a^{m-n}$, $(a^m)^n = a^{mn}$) handle powers, and zero, negative and fractional indices extend them, with standard form $a \times 10^n$ (where $1 \le a < 10$) used to write very large or very small numbers compactly.

The language of comparison

Two dot points teach you to compare quantities. Ratio, rate and proportion covers simplifying and dividing in a ratio, rates such as speed, and the contrast between direct proportion ($y = kx$) and inverse proportion ($y = \frac{k}{x}$). Percentage and financial arithmetic applies the same proportional reasoning to money: percentage change, reverse percentages, profit and loss, discount, taxation, and the all-important distinction between simple and compound interest.

Financial arithmetic is heavily examined because SEAB sets problems in real-world contexts, including personal and household finance. Being comfortable moving between a percentage, a decimal multiplier and a fraction is what makes these questions quick.

The algebra that unlocks the rest

Algebraic manipulation and factorisation is where number becomes algebra. Expanding products, factorising by common factor and by grouping, recognising the difference of two squares $a^2 - b^2 = (a+b)(a-b)$, factorising quadratics, and simplifying algebraic fractions are the manipulations that the equations and graphs strands then build on directly.

How the strand is examined

• Show clear, structured working. A correct method with a small slip often earns more than a bare wrong answer. Lay out each step so method marks are visible.
• Give the exact form requested. A fraction in its simplest form, a value to three significant figures, or an answer in standard form: read the instruction and match it.
• Apply skills in real-world contexts. Many questions, especially on percentages and money, are set in everyday or financial settings; translate the words into the right calculation, then interpret the answer in context.

Check your knowledge

A mix of arithmetic, proportion and algebra questions covering the strand. Attempt them, then check the solutions.

1. Evaluate $\dfrac{3}{4} + \dfrac{1}{6} \times \dfrac{9}{2}$, giving your answer as a fraction in its simplest form. (2 marks)
2. Simplify $\dfrac{12a^3 b}{8a b^4}$, giving your answer with positive indices. (2 marks)
3. Write $0.000\,0408$ in standard form. (1 mark)
4. A map has a scale of $1 : 50\,000$. A road is $6\ \text{cm}$ long on the map. Find its actual length in kilometres. (2 marks)
5. A jacket is sold for \96$after a$20%$ discount. Find its original price. (2 marks)
6. Factorise completely $3x^2 - 12$. (2 marks)