Mathematical Literacy - Number, Algebra and Computation
The Number, Algebra and Computation domain tests whether you can move fluently between fractions, decimals, percentages, ratios and algebraic expressions, and whether you can justify each step rather than guess. Questions are short but layered: a correct method with one sign error loses the mark.
Core rules
- Order of operations: brackets, indices, multiplication/division left to right, then addition/subtraction. Treat a fraction bar as invisible brackets.
- Percentages: 'of' means multiply; percentage change = (new − old) ÷ old × 100. A 20% increase followed by a 20% decrease does not return to the original value.
- Ratio and proportion: scale both parts by the same factor; for a ratio a:b, the fraction of the whole is a/(a+b).
- Algebra: collect like terms; when expanding, multiply every term inside the bracket; when solving, perform the same operation on both sides.
- Powers and roots: a^m × a^n = a^(m+n); (a^m)^n = a^(mn); √(ab) = √a × √b for non-negative a, b.
Worked example
Solve 3(2x − 5) = 4x + 9. Expand: 6x − 15 = 4x + 9. Subtract 4x: 2x − 15 = 9. Add 15: 2x = 24, so x = 12. Check by substitution: left side 3(24 − 5) = 57; right side 48 + 9 = 57. The check is part of the reasoning, not decoration.
Traps
- Distributing a negative incorrectly: −2(x − 3) = −2x + 6, not −2x − 6.
- Cancelling terms across a plus sign: (x + 3)/3 is not x.
- Using the wrong base in percentage change - divide by the original value, not the new one.
- Rounding intermediate values; keep exact fractions until the final step.