Hint
Use the stated units and precision. Express the central angle as a fraction of a full turn.
Worked solution
(a)
Express the central angle as a fraction of a full turn.
Divide \(72\) by 360 to obtain \(\displaystyle \frac{1}{5}\).
Answer: \(\displaystyle \frac{1}{5}\)
(b)
Apply the angle fraction to circumference.
The circle circumference coefficient 8 is multiplied by \(\displaystyle \frac{1}{5}\).
Answer: \(\displaystyle \frac{8}{5}\)
(c)
Apply the angle fraction to circle area.
The circle area coefficient 16 is multiplied by \(\displaystyle \frac{1}{5}\).
Answer: \(\displaystyle \frac{16}{5}\)
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: Express the central angle as a fraction of a full turn.
- 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.
(b) · 2 marks
- 1 mark: Apply the angle fraction to circumference.
- 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: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Apply the angle fraction to circle area.
- 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.