WACE Mathematics Applications exam 2026Exam: Fri 6 Nov · SCSA timetable

$v - e + f = 2$, where $v$ is the number of vertices, $e$ the number of edges, and $f$ the number of faces (including the outer face).

Recursive: $t_{n+1} = t_n + d$, with first term $t_1 = a$.

Explicit: $t_n = a + (n-1)d$.

Sum of the first $n$ terms: $S_n = \dfrac{n}{2}\big(2a + (n-1)d\big) = \dfrac{n}{2}(a + t_n)$.

Recursive: $t_{n+1} = R\,t_n$, with first term $t_1 = a$.

Explicit: $t_n = a R^{n-1}$.

Common ratio from a percentage change: $R = 1 + \dfrac{\text{percentage}}{100}$ (growth) or $R = 1 - \dfrac{\text{percentage}}{100}$ (decay).

The explanatory variable always goes on the horizontal axis and the response variable on the vertical axis. Getting this round the wrong way changes the least-squares line you fit later.

$A_{n+1} = R A_n$ (recurrence), $A_n = A_0 R^n$ (explicit), where $A_0$ is the starting value and $R$ is the common ratio.

• Growth of $r\%$ per period: $R = 1 + \dfrac{r}{100}$ (so $R > 1$).
• Decay of $r\%$ per period: $R = 1 - \dfrac{r}{100}$ (so $0 < R < 1$).

$A_{n+1} = R A_n + d$, with $R = 1 + i$ and $i$ the per-period rate.

• Draw-down annuity (pension, payout): $d$ negative (a withdrawal). The balance falls towards zero.
• Annuity-investment (superannuation, savings plan): $d$ positive (a deposit). The balance grows.

The maximum flow from the source to the sink equals the capacity of the minimum cut (the cut with the smallest total forward capacity).

$A_{n+1} = R A_n - d$, with $R = 1 + i$, $i$ the per-period rate, $d$ the regular repayment and $A_0$ the amount borrowed. The loan is repaid when the balance first reaches zero.