Hint
Use the stated units and precision. Check which integer under a root is not a perfect square.
Worked solution
(a)
Check which integer under a root is not a perfect square.
The first root simplifies to \(7 \sqrt{2}\), which is irrational. The other numbers are integers or fractions.
Answer: \(\sqrt{98}\)
(b)
Multiply a by itself.
\(49\)
Answer: \(49\)
(c)
Solve \(\displaystyle (-a)r=1\).
\(\displaystyle - \frac{1}{7}\)
Answer: \(\displaystyle - \frac{1}{7}\)
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: Check which integer under a root is not a perfect square.
- 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: Multiply a by itself.
- 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: Solve \(\displaystyle (-a)r=1\).
- 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.