AC9M9N01

Elaborations

• AC9M9N01_E1investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
• AC9M9N01_E2using a real number line to indicate the solution interval for inequalities of the form ax+b<c ; for example, 2x+7<0, or of the form ax+b>c; for example, 1.2x-5.4>10.8
• AC9M9N01_E3using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting
• AC9M9N01_E4solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula A=πr^2 and specifying the answer in terms of π as an exact real number; for example, the circumference of a circle with diameter 5 units is 5π units, and the exact area is π(5/2)^2=25/4π square units which rounds to 19.63 square units, correct to 2 decimal places
• AC9M9N01_E5investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, √(2) is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square