Mathematical requirements
- Syllabus
- 9701–2028–2029
- Topic
- —
- Level
- A2
Learning objectives
—M.1—Arithmetic, rounding, percentages, means and significant figuresPerform addition, subtraction, multiplication and division; understand integers; estimate numerical expressions; round numbers correctly; give answers to appropriate significant figures; calculate percentages, convert fractions and percentages, and calculate arithmetic means.—M.2—Unit conversions, standard form, logs and algebraConvert cm3, dm3 and m3; nm and m; Pa and kPa; seconds and minutes; mg, g, kg and tonne; Celsius and Kelvin; J and kJ. Use standard form, logarithms for pH, powers, roots and reciprocals; rearrange formulae; substitute quantities with consistent units; solve simple algebraic equations.—M.3—Graphs, proportionality, gradients and interceptsTest direct proportionality by graph or constant ratio; choose variables and scales; plot linear graphs of y = mx + c; determine and interpret gradient and intercept; choose best-fit lines or curves; use plotted points marked as crosses or circled dots.—M.4—Curves, models, logarithms and core chemical formulaeInterpret tangent gradients as rates of change and areas under curves where physically meaningful; estimate orders of magnitude; set up simple algebraic models such as rate equations and identify limitations; use log x and ln x; calculate density, concentration and number of moles.—M.5—Key quantities, symbols and unitsUse key quantities, symbols and units correctly, including mass, length, time, current, temperature, amount of substance, Avogadro constant, potential difference, charge, Faraday constant, half-life, Kw, R, Ar, Mr, E standard, enthalpy change and volume.
Calculate, estimate and report precision honestly
Perform the required arithmetic, estimate the expected order of magnitude, calculate percentages or arithmetic means where needed, and round only the final answer to an appropriate number of significant figures.
The mean of 2.10, 2.20 and 2.30 is 2.20. Keep guard digits during working, then report a precision supported by the least precise supplied measurement and include the unit.
Extra calculator digits do not add accuracy. A percentage change is relative to the original value, whereas a percentage-point change is the difference between two percentages.
Convert units and rearrange before substituting
Convert cm3/dm3/m3, nm/m, Pa/kPa, s/min, mg/g/kg/tonne, degrees Celsius/K and J/kJ as required. Express values in standard form, rearrange the formula symbolically, then substitute quantities with consistent units.
| Conversion or operation | Result |
|---|---|
| 250 cm3 | 0.250 dm3 |
| 101 kPa | 101000 Pa |
| 27 degrees Celsius | approximately 300 K |
| pH = 3.00 | [H+] = 10^-3.00 mol dm-3 |
Use powers, roots, reciprocals and logarithms when the chemistry requires them, and solve only the resulting simple algebraic equation. A temperature difference has the same numerical size in degrees Celsius and kelvin, so do not add 273 to a difference.
Use graphs to test proportionality and extract gradient and intercept
Choose the variables and scales from the model, fill the available grid, plot each point as a cross or circled dot, and draw a justified best-fit line or curve. For y = mx + c, determine and interpret m and c with units.
Direct proportionality requires a constant ratio y/x and a straight-line graph through the origin. A straight line with a non-zero intercept is linear but not directly proportional.
Use a large triangle on the best-fit line for a gradient; do not automatically join point to point or use two close raw points when the model calls for a best fit.
Interpret curves, models and core chemical formulae within their limits
A tangent gradient gives an instantaneous rate of change; an area under a curve represents an accumulated quantity only when the axes and units justify that meaning. Estimate the order of magnitude before accepting a result.
Set up simple models such as rate equations, use log x or ln x consistently where linearisation is appropriate, and state the measured range over which the model is supported.
n=Mrm,c=Vn,ρ=Vm
A tangent gradient is not the total change, and a straight transformed graph supports a model only over the tested range; it does not prove universal validity.
Keep chemical quantities, symbols and units consistent
| Quantity | Typical symbol/unit |
|---|---|
| mass, volume, amount | m in g or kg; V in dm3 or m3; n in mol |
| temperature, time, current | T in K; t in s; I in A |
| charge, potential difference | Q in C; E in V |
Use N_A, F, R, K_w, A_r, M_r, E standard and enthalpy change with their defined meanings and compatible units. Write units beside intermediate results so dimensional inconsistencies remain visible.
Similar-looking symbols are not interchangeable: E standard is an electrode potential, enthalpy change is an energy change, and half-life is a time. Let the equation and units identify the intended quantity.