Hint
Use the stated units and precision. Combine the horizontal components with their signed scalar multipliers.
Worked solution
(a)
Combine the horizontal components with their signed scalar multipliers.
Twice 9 minus 2 times 8 is \(2\).
Answer: \(2\)
(b)
Combine the vertical components, preserving a negative component if present.
Twice 12 minus 2 times 2 is \(20\).
Answer: \(20\)
(c)
Use Pythagoras on the two components.
\(\displaystyle \sqrt{81+144}=15\).
Answer: \(15\)
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: Combine the horizontal components with their signed scalar multipliers.
- 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: Combine the vertical components, preserving a negative component if present.
- 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: Use Pythagoras on the two components.
- 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.