All notes · HSC

1 chapter · 10 notes · all free

1. Real Numbers and Subsets of Real NumbersIs 0 a natural number? Is 0.5454... rational? Drop a number and see which box it lands in.
2. Axioms of Real NumbersIs ℕ closed under subtraction? Draw members and hunt for a counter-example, then find a minimum from a square.
3. Intervals, Bounds and CompletenessThe supremum of (−1, 1) is 1, yet 1 is not in the set. How? Drag m and see.
4. Axioms of Inequalities2 < 3, yet −8 > −12. Drag c and see why multiplying by a negative flips the sign.
5. Absolute Value−4 and 4 are different numbers with the same absolute value. Why, and when does |a + b| equal |a| + |b|?
6. Inequalities of One Variable and Their SolutionDoes −2x > 4 give x > −2 or x < −2? Drag the handles and see when the sign turns.
7. Quadratic and Rational Inequalities: Sign-Table Methodx(x+1)/(x−2) > 0? Cut the line at the critical values, then just count signs.
8. Absolute Value Inequalities|x − 3| < 5 just says x is less than 5 away from 3. Drag the centre and the distance and see.
9. Solving a One-Variable Inequality by GraphTurn both sides into graphs. Whichever is on top is your answer.
10. Linear Inequalities of Two Variables and Their GraphsWhich side of the line is 2x − y − 6 > 0? Substitute one point and you know.

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