Netherlands VWO 2 (onderbouw) Mathematics

Chapters: 4

1. Numbers and quantities

Calculating with numbers and quantities · Algebraic expressions and scientific notation

Ratio and Proportion – A ratio a : b compares two amounts of the same kind. Divide both parts by the same number to simplify it. To share an amount in a ratio, add the parts, find one part, then multiply. Two quantities are in direct proportion when y = k·x (double one, double the other) and in inverse proportion when x·y = k (double one, halve the other).
Algebraic Expressions: Variables, Terms and Simplifying – An algebraic expression uses letters (variables) and numbers joined by +, −, × and ÷, like 3x + 2. A variable stands for a number that can change. An expression is made of terms (3x and 2). In 3x, 3 is the coefficient; a term with no letter, like 2, is the constant. Like terms have exactly the same letter part (3x and 5x) and can be added; unlike terms (3x and 2, or x and x²) cannot. Substitution means putting a number in place of the letter to find the value. Expanding removes brackets: a(b + c) = ab + ac. Factorising is the reverse: take out the common factor. A formula is an expression that gives one quantity from others, and an identity is true for every value of the letter.

Patterns and relations · Formulas and functions

Sequences and Progressions – A sequence is a list of numbers in a fixed order. We can describe it with a recursive rule (how to get the next term from the last one) or an explicit rule (a formula for term n). In an arithmetic progression (AP) we add the same number every time. In a geometric progression (GP) we multiply by the same number every time. Fractals and the Tower of Hanoi are fun patterns that hide these rules.
Linear Functions – A linear function adds the same amount to y every time x goes up by 1. Its rule is y = mx + c (also written f(x) = mx + b). m is the slope: rise ÷ run, the change in y for each 1 step in x. c is the y-intercept: the value of y when x = 0. Its graph is always a straight line.

2D and 3D space · Angles and right triangles

Coming soon

Mathematical language and representations · Measuring and digital tools

Mathematical Communication: Saying Maths Clearly – Mathematical communication means sharing maths ideas so that another person can follow and check them. The same situation can be shown in words, symbols (a formula), a table or a graph; each one is good for a different job. Clear working writes one step per line with correct symbols and units. A good communicator also judges graphs critically and presents results with a question, method, results and conclusion.
Measurement and Units: How We Measure Anything – To measure something is to compare it with a fixed amount called a unit. Every measurement has a number and a unit. Scientists everywhere use the SI system, with seven base units such as the metre, kilogram and second. Prefixes like kilo (×1000), centi (÷100) and milli (÷1000) make units bigger or smaller. A good measurement starts at zero, is read with the eye straight above the mark, and is only as accurate as the smallest division (least count). Rounded values hide a small range, given by upper and lower bounds.