Hint
Use the stated units and precision. Collect coefficients of identical variable terms, or substitute the stated inputs into the whole simplified expression.
Worked solution
(a)
Collect the x terms, then the y terms, retaining the constant: \(8 x + 7 y + 109\).
Answer: \(8 x + 7 y + 109\)
(b)
Substitute into the collected expression: \((8)(5)+(7)(3)+109\) = \(170\).
Answer: \(170\)
(c)
Collect coefficients of identical variable terms, or substitute the stated inputs into the whole simplified expression.
\(109\)
Answer: \(109\)
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 only like terms, retaining the signs of all coefficients.
- 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 input into the complete expression and calculate consistently.
- 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: Collect coefficients of identical variable terms, or substitute the stated inputs into the whole simplified expression.
- 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.