Hint
Use the stated units and precision. Factor the difference of squares, cancel the nonzero common factor and preserve the original exclusion.
Worked solution
(a)
\(x^2-16=(x-4)(x+4)\). Cancel x−4 only when it is nonzero.
Answer: \(F(x)=x+4,\quad x\ne 4\)
(b)
Factor the difference of squares, cancel the nonzero common factor and preserve the original exclusion.
\(4\)
Answer: \(4\)
(c)
Factor the difference of squares, cancel the nonzero common factor and preserve the original exclusion.
\(13\)
Answer: \(13\)
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) · 3 marks
- 1 mark: Factor the numerator before cancellation.
- 1 mark: Retain the original excluded input after simplifying.
- 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: Factor the difference of squares, cancel the nonzero common factor and preserve the original exclusion.
- 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: Factor the difference of squares, cancel the nonzero common factor and preserve the original exclusion.
- 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: 7 marks.