General Mathematics flashcards

What this deck covers

• Topic 1: Modelling with Linear Relationships (20 cards, 4 dot points)

  • Linear functions and modelling (SACE Stage 2 General Mathematics) (5)
  • Linear programming (SACE Stage 2 General Mathematics) (4)
  • Piecewise-linear models (SACE Stage 2 General Mathematics) (5)
  • Simultaneous equations and break-even (SACE Stage 2 General Mathematics) (6)
• Topic 2: Modelling with Matrices (14 cards, 3 dot points)

  • Matrix applications and networks (SACE Stage 2 General Mathematics) (4)
  • Matrix operations (SACE Stage 2 General Mathematics) (6)
  • Transition matrices (SACE Stage 2 General Mathematics) (4)
• Topic 3: Statistical Models (14 cards, 3 dot points)

  • Bivariate data and correlation (SACE Stage 2 General Mathematics) (5)
  • Least-squares regression (SACE Stage 2 General Mathematics) (4)
  • The normal distribution and z-scores (SACE Stage 2 General Mathematics) (5)
• Topic 4: Financial Models (16 cards, 3 dot points)

  • Compound interest and annuities (SACE Stage 2 General Mathematics) (5)
  • Depreciation (SACE Stage 2 General Mathematics) (6)
  • Reducing-balance loans (SACE Stage 2 General Mathematics) (5)
• Topic 5: Discrete Models (13 cards, 3 dot points)

  • Assignment problems (SACE Stage 2 General Mathematics) (4)
  • Critical path analysis (SACE Stage 2 General Mathematics) (5)
  • Shortest path and network flow (SACE Stage 2 General Mathematics) (4)

Sample cards from this deck

1. Definition

   Linear functions and modelling (SACE Stage 2 General Mathematics)

   Define Gradient and intercept

   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.

2. Definition

   Matrix applications and networks (SACE Stage 2 General Mathematics)

   Define Adjacency matrix

   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 $j$.

3. Definition

   Bivariate data and correlation (SACE Stage 2 General Mathematics)

   Define Form

   Form is the pattern roughly linear, or curved?

4. Definition

   Depreciation (SACE Stage 2 General Mathematics)

   Define Flat-rate depreciation

   The asset's value decreases by a constant amount each period, producing a straight-line graph. The annual loss is often quoted as a percentage of the original purchase price, so the dollar loss stays the same every year.

5. Definition

   Assignment problems (SACE Stage 2 General Mathematics)

   Define Assignment problem

   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.

6. Definition

   Linear programming (SACE Stage 2 General Mathematics)

   Define Feasible region

   The feasible region is the set of all points $(x, y)$ that satisfy every constraint at once.

7. Definition

   Matrix operations (SACE Stage 2 General Mathematics)

   Define Conformable for an operation

   Two matrices are conformable for addition or subtraction only if they have the same order.

8. Definition

   Least-squares regression (SACE Stage 2 General Mathematics)

   Define Residual

   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.

9. Definition

   Reducing-balance loans (SACE Stage 2 General Mathematics)

   Define Reducing-balance loan

   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.

10. Definition

    Critical path analysis (SACE Stage 2 General Mathematics)

    Define Critical path

    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.