Essential Mathematics 40S: Core Topics and Problem-Solving Strategies
Overview of the Course
Essential Mathematics 40S is a senior applied mathematics course built around practical, real-world numeracy. Because the exam does not publish a fixed domain list, candidates should expect questions drawn from a consistent cluster of topic areas: personal finance (wages, deductions, budgeting, credit, loans, and investments), measurement and geometry (perimeter, area, volume, surface area, and unit conversion), proportional reasoning (ratios, rates, scale, and percent), statistics and probability (data displays, measures of central tendency, and simple probability), and linear relationships (interpreting graphs, slope as a rate, and using formulas).
Concepts You Must Understand
Know how to move between units within and across the metric and imperial systems, and how to choose the correct conversion factor. Understand gross versus net pay, including common deductions and overtime rules. Be comfortable with simple and compound interest formulas, and with reading a budget or a loan schedule. For geometry, distinguish perimeter, area, volume, and surface area, and match the correct formula to the shape. For statistics, know when mean, median, or mode best describes a data set and how outliers distort the mean.
Common Traps
Watch for unit mismatches (mixing centimetres and metres, or hours and minutes) and for percent problems where the base changes. Read carefully whether a question asks for gross or net, before or after tax, or total cost versus unit price. In geometry, do not confuse square units with cubic units. In statistics, remember that adding a value changes the mean but not necessarily the median.
Worked Example
A worker earns $18.50 per hour for 40 hours and time-and-a-half for 6 overtime hours. Gross pay = (40 × 18.50) + (6 × 18.50 × 1.5) = 740 + 166.50 = $906.50. If 22% is deducted, net pay = 906.50 × 0.78 ≈ $707.07.
Rule of Thumb
Always write the units beside every number, convert to one system before calculating, and check that your answer is reasonable in size.