Skip to content

Finance and economics, grade 12 (3 units)

Twelfth-grade finance and economics, 3 study units.Subjects

The topics, in order:

  • economic processes in a quadratic model: revenue and profit as a parabola, the price that gives the greatest revenue and the greatest profit;
  • linear programming: variables and constraints, the feasible region and its corner points, the objective function and the best plan;
  • analytic geometry: the distance between two points, the midpoint of a segment, a line’s slope and equation, parallel lines and where lines meet – on a city map and on delivery routes;
  • the normal distribution in economics: salaries, sales, a machine’s filling weight, delivery times – the 34/13.5/2.5 rule, the standard score and quality control.

Two kinds of lessons:

  • learning lessons – an explanation, solved examples and a few questions to try;
  • practice lessons – questions only.

How the page works: Using a page.

  1. Revenue: price times quantityLearningWhen raising the price drives customers away, the revenue is a product of two linear expressions – a parabola opening downwards: the revenue rises, reaches a peak and falls.
  2. The price for the greatest revenueLearningThe greatest revenue is at the parabola's vertex, x=-b/2a; the revenue is 0 where the parabola meets the x-axis, and the vertex is halfway between those points; and when the quantity falls in a straight line, the best price is half the price at which nobody buys.
  3. Profit as a parabolaLearningThe profit is the revenue minus the cost: when the quantity falls with the price, the profit is a parabola too – at its vertex the most profitable price, and where it meets the x-axis the break-even prices, with a profit between them and a loss outside them.
  4. Practice: a quadratic model of revenue and profitPracticeRevenue as a product of price and quantity, the price for the greatest revenue and the greatest profit, the prices at which the revenue is 0, and the break-even prices of the profit.
  5. Constraints: inequalities in two variablesLearningLinear programming starts from the variables and the constraints: each limit of time or material is an inequality in two variables, and its solutions are a half-plane – one side of a line.
  6. The feasible region and its corner pointsLearningThe plans that keep all the constraints together are the feasible region – a polygon in the plane; its corner points are where boundary lines meet, found on the graph and by a system of equations.
  7. The objective function and the best planLearningThe objective function gives each plan its profit or its cost; its greatest or least value in the feasible region is at one of the corner points, so you work it out at the corners and choose.
  8. Practice: linear programmingPracticeConstraints as inequalities, checking a plan, the corner points on the graph and by a system of equations, the objective function at the corners, the greatest profit and the least cost.
  9. The distance between two points and the midpointLearningPoints on a city map in a coordinate system: the straight-line distance between two points by Pythagoras' theorem, the distance along the streets, and the midpoint of a segment – a warehouse halfway between two shops.
  10. The slope and the equation of a line through two pointsLearningA straight road on a city map: the slope from two points, the equation y=mx+b of the line through two points, checking whether a point is on the line, and a price that grows linearly as a line through two points.
  11. Parallel lines and the meeting point of two linesLearningParallel streets are lines with the same slope; a parallel line through a point; a junction of two roads is the meeting point of two lines – on a graph and by a system of equations; and two parallel lines have no meeting point.
  12. Practice: analytic geometryPracticeThe distance between two points and the midpoint on a map, a delivery drone's route, the equation of a line through two points, a parallel line through a point, the meeting point of two lines and price plans that cross.
  13. The normal distributionLearningSalaries, sales and delivery times are often spread in a bell shape around the mean: the 34/13.5/2.5 rule, the percent above a value, below it and between two values, and the number of cases out of all of them.
  14. The standard score and quality controlLearningThe standard score says how many standard deviations a value is from the mean: comparing values from two distributions, a value from a percent, and quality control – a pack beyond two standard deviations leaves the line.
  15. Practice: the normal distributionPracticeThe 34/13.5/2.5 rule in salaries, sales and delivery times, the number of cases out of all of them, the standard score and comparing distributions, a value from a percent and quality control.
  16. Review: finance and economics, grade 12PracticeQuestions from every topic: revenue and profit as a parabola, linear programming, analytic geometry and the normal distribution.
Last updated on