Hint
Use the stated units and precision. Interpret the included left endpoint and excluded right endpoint before listing or counting values.
Worked solution
(a)
The left equality is allowed and the right equality is excluded. All real points strictly between the boundaries are included.
Answer: \(-6\le x<6\); filled at -6, open at 6, connected between them.
(b)
Start at the included lower integer and stop one integer below the excluded upper boundary.
Answer: \(\left\{-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5\right\}\)
(c)
Interpret the included left endpoint and excluded right endpoint before listing or counting values.
\(12\)
Answer: \(12\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Place the two boundaries and use the correct open/closed endpoint symbols.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Check both endpoint conventions and list every integer once.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Interpret the included left endpoint and excluded right endpoint before listing or counting values.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.