Hint
Use the stated units and precision. Substitute the line into the curve, solve both quadratic factors and find the matching ordinate from the line.
Worked solution
(a)
Equating the two y-rules gives \(\left(x - 10\right) \left(x - 7\right)=0\). Thus \(\displaystyle x=7\) or 10. Substitution into the line gives the two matching ordinates.
Answer: \(\left\{\left( 7, \ 26\right), \left( 10, \ 35\right)\right\}\)
(b)
At \(\displaystyle x=7\), both y-rules give \(26\). At \(\displaystyle x=10\), both give \(35\).
Answer: \(\left\{\left( 7, \ 26\right), \left( 10, \ 35\right)\right\}\)
(c)
Average the two x-coordinates and separately average the two y-coordinates.
Answer: \(\displaystyle \left( \frac{17}{2}, \ \frac{61}{2}\right)\)
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: Substitute the linear equation into the quadratic and solve the resulting equation.
- 1 mark: Find both matching y-values and retain complete coordinate pairs.
- 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: Substitute each recovered pair into both original equations.
- 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: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use coordinate averages for the same two endpoints.
- 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.
Total: 7 marks.