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VCE General Mathematics formula sheet: the short sheet, and what your bound reference must add

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Formula sheet

The card below opens today's Year 12 Statistics paper with the sheet in a drawer. The contents follow in our own layout. The VCAA published the sheets for all VCE mathematics exams in August 2024 in a redesigned layout, and the sheet is on the VCAA General Mathematics pages. Check any line against it before you rely on it.

Formula sheet

Year 12 Statistics (Standard & General Maths)

Open formula sheet

Data analysis

z=\frac{x-\overline{x}}{s_x}standardised score
\text{lower fence}=Q_1-1.5\times IQRlower fence in a boxplot
\text{upper fence}=Q_3+1.5\times IQRupper fence in a boxplot
y=a+bx,\quad b=r\frac{s_y}{s_x},\quad a=\overline{y}-b\overline{x}least squares line of best fit
\text{residual value}=\text{actual value}-\text{predicted value}residual value
\text{seasonal index}=\frac{\text{actual figure}}{\text{deseasonalised figure}}seasonal index

Recursion and financial modelling

u_0=a,\quad u_{n+1}=Ru_n+dfirst-order linear recurrence relation
r_{effective}=\left[\left(1+\frac{r}{100n}\right)^n-1\right]\times100\%effective rate of interest for a compound interest loan or investment

Matrices

\det A=ad-bcdeterminant of a 2 by 2 matrix A with first row a, b and second row c, d
A^{-1}=\frac{1}{\det A}\left(\text{first row }d,\ -b;\ \text{second row }-c,\ a\right)inverse of that matrix, where det A is not zero
S_0=\text{initial state},\quad S_{n+1}=TS_n+Brecurrence relation
S_0=\text{initial state},\quad S_{n+1}=LS_nLeslie matrix recurrence relation

Networks and decision mathematics

v+f=e+2Euler's formula

How the two exams work with the sheet

The VCAA's 2025 General Mathematics papers give these conditions for both exams:

ItemExamination 1Examination 2
Reading time15 minutes15 minutes
Writing time1 hour 30 minutes1 hour 30 minutes
Content40 multiple-choice questions, 40 marks18 questions, 60 marks
NotesOne bound reference that may be annotatedOne bound reference that may be annotated
TechnologyOne approved CAS calculator or CAS software, and one scientific calculatorThe same
Formula sheetSuppliedSupplied

This is the opposite of Methods and Specialist Exam 1: both General Maths exams allow technology and a bound reference. See how South Australia handles it in our SACE General Maths guide, and compare the QCE and WACE sheets. Our VCE Maths Methods guide covers the other stream.

What is not on the VCE General Maths formula sheet

  • All geometry and measurement. No area, volume, perimeter or Pythagoras, and no sector or segment formulas.
  • Trigonometry. No sine rule, cosine rule, area of a triangle or right-angled ratios.
  • Financial formulas beyond the effective rate. No compound interest, annuity or loan formula: you use the recurrence relation, or the finance solver on your CAS.
  • Sequence formulas. No arithmetic or geometric nth term or sum.
  • Statistics beyond a few lines. No mean, standard deviation, quartile or correlation formula, and no normal distribution rule.
  • Network algorithms. Euler's formula is there, but not the shortest path, spanning tree or critical path methods.
  • Linear programming and time series smoothing. Not on the sheet.

How to use the sheet in the exam

  1. During reading time, find the matrices and recursion lines, which are not obvious from other states' sheets.
  2. Write the formula from the sheet, then substitute, and let the CAS do the arithmetic.
  3. For the recurrence relation, write down the first terms by hand to check the pattern before you use the solver.
  4. In multiple-choice Exam 1, use the sheet to check answers quickly.

Example 1: a standardised score

A mark of 72 in a set with mean 65 and standard deviation 4. The standardised score line gives:

z=\frac{x-\overline{x}}{s_x}=\frac{72-65}{4}=1.75

The mark is 1.75 standard deviations above the mean.

Example 2: the effective rate of interest

A loan has a nominal rate of 6% a year, compounding monthly, so r = 6 and n = 12. The effective rate line gives:

r_{effective}=\left[\left(1+\frac{6}{100\times12}\right)^{12}-1\right]\times100\%=6.17\%

That is the rate to compare with a loan that compounds yearly. Note that the sheet writes r as a percentage, not a decimal.

Example 3: a recurrence relation

A balance starts at $2000 and follows u₀ = 2000 and uₙ₊₁ = 1.03uₙ − 150, with R = 1.03 and d = −150. The first two steps give:

u_1=1.03\times2000-150=1910,\qquad u_2=1.03\times1910-150=1817.30

A negative d means a repayment is taken off each period. Practise related ideas in the Probability course.

Example 4: a 2 by 2 inverse

For A with first row 2, 1 and second row 5, 3, the determinant is 2 × 3 − 1 × 5 = 1, and the inverse line gives:

A^{-1}=\frac{1}{1}\left(\text{first row }3,\ -1;\ \text{second row }-5,\ 2\right)

Because the determinant is 1, the inverse entries are whole numbers.

Practise with the sheet open

Our Year 12 Statistics (Standard and General Maths) daily paper is a short timed paper of 8 questions worth 25 to 35 marks. It is not a VCAA paper. Sit it with your calculator and a bound reference of your own.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. They show which line of the sheet each question wanted. We do not publish official answers, past paper answers or leaked papers.

Common questions

Do you get a formula sheet in VCE General Maths?
Yes. The VCAA supplies the same formula sheet with Examination 1 and Examination 2.
Can I bring notes into VCE General Maths?
Yes. Both exams allow one bound reference that may be annotated.
Can I use a CAS in General Maths?
Yes. One approved CAS calculator or CAS software, and one scientific calculator, are approved in both exams.
Are finance formulas on the sheet?
Only the effective rate of interest and a recurrence relation.
How long are the exams?
Each has 15 minutes of reading time and 1 hour 30 minutes of writing time.

Revision cards

Say the answer first, then flip the card to check it.

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Australia · VCEVCE General Maths: Exam 1, Exam 2, SACs and PracticeVCE General Mathematics explained: Exam 1 (40 multiple choice), Exam 2 (60 marks), the bound reference, study score weighting and worked questions.