ATD Level II
Business Mathematics and Statistics cheat sheet
Every chapter's key points, formulas and definitions on one page, for the last week before the exam. Each heading links to the chapter that explains it.
Algebra and relationships
- An inequality is solved like an equation, except that multiplying or dividing both sides by a negative number reverses the inequality sign.
- Simultaneous equations are solved for the one set of values that satisfies all of them at once: by elimination, by substitution, or graphically where the lines intersect.
- A quadratic ax² + bx + c = 0 is solved by factorisation where possible, otherwise by the quadratic formula x = (-b ± √(b² - 4ac)) / 2a.
- The 2×2 matrix [[a, b], [c, d]] has determinant ad - bc, and it has an inverse only when that determinant is not zero.
- A logarithm finds an unknown power, which is how the time for a sum to grow is found: KES 100,000 at 8% compound interest doubles in n = ln(2) / ln(1.08), about 9 years.
Key terms
- The number line
- An ordered visual line representing every real number, negative numbers to the left of zero and positive numbers to the right, used to reason about order, magnitude and distance between values.
- Known and unknowns (variables)
- A known is a fixed value already given in a problem; an unknown (variable), conventionally a letter such as x, represents a value still to be found.
- Algebraic terms and expressions operation
- A term is a single number, variable, or product of numbers and variables (e.g. 5x); an expression combines terms with addition or subtraction. Like terms (same variable, same power) can be added or subtracted directly; unlike terms cannot.
- Factorisation
- Rewriting an expression as a product of its factors, the reverse of expanding brackets, most often used to simplify an expression or to solve a quadratic equation by setting each factor to zero.
- Simplification of algebraic expressions using BODMAS
- BODMAS (Brackets, Orders/indices, Division and Multiplication, Addition and Subtraction) fixes the order operations must be carried out in, so an expression evaluates to one, unambiguous value.
- Simplification of fractions
- An algebraic fraction is simplified by factorising numerator and denominator and cancelling any factor common to both.
The rest of the sheet covers
- Sequences, series and calculus
- Commercial mathematics
- Descriptive statistics and data presentation
- Probability
- Worked examples
- Exam technique and revision
- Glossary