TOPIC 4: INEQUALITIES

Question 1

4 Ways to solve non-linear inequalities

Answer 1

1. Algebraic - Factorise
2. Algebraic - Completing the square
3. Graphic - Draw left and right side of inequality on GC
4. Graphic - Equate RHS to 0, draw on GC

Question 2

Number line of repeated linear factors

Answer 2

odd integer: + - or - +
even integer: + + or - -

Question 3

When can multiply to remove denominator for inequalities?

Answer 3

If 100% the denominator is positive, can multiply over

But if unsure if denominator is positive or negative, CANNOT, because won’t know if need to change direction of < > or not

Question 4

6 Steps for solving inequalities questions

Answer 4

1. Rewrite as f(x) >/< 0
2. Factorise both numerator and denominator
3. If cannot factorise, complete the square to prove ≥ 0
4. Draw number line
5. Take note if open circle or closed circle
6. Solve inequality