Hint
Do not include a pole under any weak inequality. Inspect the original denominator.
Worked solution
(a)
\(x=10\) makes the denominator zero.
Answer: \(10\).
Answer: \(10\)
(b)
\(x=7\) makes only the numerator zero.
Answer: \(7\).
Answer: \(7\)
(c)
\(\displaystyle f(0)= \frac{7}{10}\)
Answer: \(\displaystyle \frac{7}{10}\).
Answer: \(\displaystyle \frac{7}{10}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Inspect the original denominator.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Squaring an inequality needs the sign conditions checked first.
(b) · 2 marks
- 1 mark: Set the numerator equal to zero and check the denominator.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Absolute value on the output is different from absolute value on the input.
(c) · 2 marks
- 1 mark: Substitute \(\displaystyle x=0\) without removing the sign of either factor.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Squaring an inequality needs the sign conditions checked first.
Total: 6 marks.