N(A)-Level Mathematics Number and Algebra: the four operations, ratio and rate, percentage and money, and algebraic manipulation

Why Number and Algebra comes first

Number and Algebra is the foundation strand of N(A)-Level Mathematics (SEAB 4045, Mathematics Syllabus A). Every other strand, from mensuration and trigonometry to statistics, leans on the ability to compute accurately, compare quantities and manipulate simple algebra. A 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-n-level/mathematics/syllabus.

The arithmetic toolkit

The strand opens with numbers and the four operations: adding, subtracting, multiplying and dividing integers, fractions and decimals, working with negative numbers, applying the order of operations (BIDMAS), and rounding the final answer sensibly. The same-sign and different-sign rule for multiplying negatives ($(-) \times (-) = (+)$ and $(-) \times (+) = (-)$) and the trick of dividing fractions by multiplying by the reciprocal are the workhorse skills the calculator supports but cannot replace, because markers reward shown method.

The language of comparison

Two dot points teach you to compare quantities. Ratio, rate and proportion covers simplifying a ratio like a fraction, sharing a quantity in a given ratio (add the parts, find one part, then multiply), working with rates such as speed where $\text{speed} = \dfrac{\text{distance}}{\text{time}}$, and solving direct proportion by the unitary method. Percentage and money applies proportional reasoning to money: finding a percentage of a quantity, expressing one amount as a percentage of another, percentage change, and the everyday contexts of discount, profit and loss, and simple interest.

Money problems are heavily examined because SEAB sets questions in real-world settings, 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. Collecting like terms (only terms with the same letters and powers combine), expanding single brackets by multiplying every inside term by the outside term, expanding double brackets with FOIL, and factorising (the reverse of expanding) by taking out the highest common factor are the manipulations that the equations and graphs strands then build on directly. Always watch the sign on a negative bracket, and check a factorisation by expanding it again.

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 a given unit: read the instruction and match it.
• Apply skills in real-world contexts. Many questions, especially on percentage and money, are set in everyday 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 $\dfrac{2}{3} + \dfrac{1}{4} \times \dfrac{8}{3}$, giving your answer as a fraction in its simplest form. (2 marks)
2. Evaluate $-6 + (-4) \times (-3)$. (1 mark)
3. Divide \240$in the ratio$3 : 5$. (2 marks)
4. A jacket costing \80$is sold at a$15%$ discount. Find the selling price. (2 marks)
5. Expand and simplify $3(2x - 1) - (x - 4)$. (2 marks)
6. Factorise completely $6x^2 + 9x$. (1 mark)