Hint
Use the stated units and precision. Apply the integer power rule to the highest-power term.
Worked solution
(a)
Apply the integer power rule to the highest-power term.
The power rule multiplies 3 by 4, giving 12.
Answer: \(12\)
(b)
Differentiate both the linear term and the constant correctly.
The derivative of the linear term is -3 and the original constant differentiates to zero.
Answer: \(-3\)
(c)
Evaluate the derivative rather than the original function.
\(12 x^{3} - 3\) at the stated input is \(321\).
Answer: \(321\)
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: Apply the integer power rule to the highest-power term.
- 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: Differentiate both the linear term and the constant correctly.
- 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: Evaluate the derivative rather than the original function.
- 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.