Number and Operations
Core content
Candidates should move fluently among integers, fractions, decimals, percentages, ratios, radicals, and scientific notation. Know place value and rounding, divisibility tests, prime factorisation, greatest common divisor and least common multiple, order of operations, absolute value, and the laws of exponents. Proportional reasoning is central: distinguish part-to-part from part-to-whole ratios and identify the base in percentage change. Estimation and number sense should be used to judge whether an answer is reasonable.
Trap watch
Negative signs inside powers, subtraction of negatives, and division by zero cause many errors. A 20% increase followed by a 20% decrease does not return to the original value. When comparing fractions, cross-multiply or use a common denominator rather than comparing numerators alone. In word problems, convert units before calculating and avoid rounding intermediate results. Remember that sqrt(a+b) is not sqrt(a)+sqrt(b), and (a+b)^2 is not a^2+b^2. In LCM and GCF problems, decide whether the question asks for a shared cycle or a shared partition.
Worked example
A jacket costs AED 80 and is marked up to AED 92. The increase is 12/80 = 0.15, or 15%. If the new price is then reduced by 15%, the result is 92 x 0.85 = AED 78.20, not AED 80, because the second percentage uses a different base.
Rule of thumb: name the whole, write the relationship as an equation, then substitute with units attached.