HSC Mathematics Standard 1 study plan

HSC Mathematics Standard 1 · Give each week a clear focus.

8 weeks · About 6 hours per week

Week 1

Algebra

Simplify algebraic expressions and expand and factorise binomial products without errors
Rearrange linear equations and formulas to solve for any nominated variable
Solve linear equations and inequalities and represent solution sets on a number line
Set up and solve simultaneous linear equations from short worded contexts

A 20-question self-marked algebra test, with every error logged and reworked to a correct full solution

Week 2

Substitute into and interpret linear, quadratic and exponential models drawn from practical contexts
Sketch and read off key features of linear and simple quadratic graphs, including intercepts and gradient
Solve quadratic equations by factorising and by substitution into the standard formula
Translate short real-world statements into algebraic models and justify the chosen model

A one-page modelling summary sheet with five worked context problems, each showing the model, the solution and a written interpretation

Week 3

Convert fluently between metric units of length, area, volume and mass
Calculate perimeter and area of composite shapes by decomposing them into standard figures
Apply Pythagoras' theorem to find unknown sides and to test for right angles
Compute surface area and volume of prisms, cylinders and composite solids

A formula-and-conversion reference card plus 15 fully worked measurement problems covering every formula on the card

Week 4

Interpret and use scale drawings, plans and maps to find real dimensions
Apply trigonometry in right-angled triangles to find sides and angles in practical situations
Calculate perimeter, area and volume problems involving circles and sectors
Solve multi-step practical measurement problems and round answers appropriately with units

A timed 45-minute measurement practice paper scored out of 30, with a correction sheet listing every lost mark and its cause

Week 5

Calculate weekly, fortnightly and monthly pay from hourly rates, including overtime and penalty rates
Deduce gross pay, taxable income, deductions and net pay from a set of payslip figures
Compute simple interest and apply it to savings and loan scenarios
Interpret common deductions and entitlements such as tax withheld and superannuation contributions

A completed personal-budget spreadsheet for a hypothetical worker showing gross pay, each deduction, net pay and a simple-interest savings projection

Week 6

Apply compound interest and depreciation formulas to growth and decay problems
Compare simple and compound interest outcomes over the same period and explain the difference
Solve problems involving credit cards, flat-rate loans and reducing-balance loans
Interpret tables and statements to extract the figures needed for a financial calculation

A comparison report of at least 300 words contrasting two loan options over five years, with all calculations shown and a justified recommendation

Week 7

Classify data as categorical or numerical and choose an appropriate display for each
Construct and interpret frequency tables, histograms, stem-and-leaf plots and dot plots
Calculate mean, median, mode, range and interquartile range and explain what each measures
Identify outliers and describe the shape and spread of a distribution from its display

A statistical report on a self-collected dataset of at least 30 values, including one display, a five-number summary and a written interpretation

Week 8

Complete full-length mixed papers under timed conditions across all four domains
Diagnose recurring error patterns and rework every incorrect question to a correct solution
Recall all key formulas and conversions from memory without a reference sheet
Prioritise remaining revision time toward the weakest domain identified by practice scores

Two timed full-length practice papers, each scored and fully corrected, with a final one-page formula sheet written from memory

Week 2: Score at least 75% on a self-set 20-question algebra test and show a corrected solution for every missed question

Week 4: Score at least 70% on the timed 45-minute measurement paper and correctly state every conversion and formula from memory

Week 6: Produce a loan comparison in which all interest figures are independently recalculated and verified

Week 8: Average at least 75% across both full-length practice papers, with no domain below 65%