SACE General Mathematics exam 2026Exam: Mon 2 Nov · SACE Board timetable

The gradient $m$ is the constant rate of change: $m = \dfrac{\text{change in } y}{\text{change in } x} = \dfrac{y_2 - y_1}{x_2 - x_1}$. The vertical intercept $c$ is the value of $y$ when $x = 0$, the starting amount.

A breakpoint is an $x$-value where the model switches from one linear rule to the next. A model is continuous if the two pieces give the same $y$-value at the breakpoint, so the graph has no jump.

The feasible region is the set of all points $(x, y)$ that satisfy every constraint at once. It is the overlap of all the shaded half-planes and is usually a polygon.

The break-even point is the production level $x$ at which total cost equals total revenue, $C = R$, so the profit $P = R - C$ is zero. Below it the business makes a loss; above it, a profit.

For a network with vertices labelled $1, 2, \dots, n$, the adjacency matrix $A$ is the $n \times n$ matrix whose entry $a_{ij}$ is the number of edges joining vertex $i$ to vertex $j$.

The state vector $S_n$ is a column listing the amount in each category after $n$ steps. The transition matrix $T$ holds the step-to-step proportions, with columns summing to 1. The recurrence is $S_{n+1} = T S_n$, and after $n$ steps $S_n = T^n S_0$.

Two matrices are conformable for addition or subtraction only if they have the same order. They are conformable for multiplication $AB$ only if the number of columns of $A$ equals the number of rows of $B$.

The explanatory (independent) variable is the one used to explain or predict; it goes on the horizontal axis. The response (dependent) variable is the one being explained or predicted; it goes on the vertical axis.

where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. A positive $z$ is above the mean, a negative $z$ is below.

A residual is the vertical gap between an observed data point and the value the line predicts: $\text{residual} = y_{\text{actual}} - y_{\text{predicted}}$. The least-squares line minimises the sum of the squared residuals.

where $V_0$ is the initial value, $r$ is the annual depreciation rate as a decimal, and $n$ is the number of years. This is the compound interest formula with a negative growth rate.

A loan on which interest is charged each period on the outstanding balance only. Because the balance reduces with every repayment, the interest charged shrinks over time, so a growing share of each fixed repayment goes towards the principal.

The interest earned is $A - P$.

A network in which each edge is labelled with a numerical weight such as distance, time or cost. The length of a path is the sum of the weights of its edges, and the shortest path is the path of least total length between two chosen vertices.

A problem of matching $n$ agents to $n$ tasks one-to-one so that the total cost (or time) is minimised. Each row of the cost matrix is an agent, each column a task, and a complete allocation chooses exactly one entry from each row and each column.

The critical path is the longest path through the activity network from start to finish. Its total duration is the minimum possible project completion time, because every activity on it must be done in sequence with no spare time.