Hint
Use the stated units and precision. Multiply or divide numerical coefficients, then add or subtract the exponents of each separate variable.
Worked solution
(a)
The coefficient is \(\displaystyle \frac{25}{2}\). The x exponent is \(3+4-4=3\) and the y exponent is \(5-4=1\).
Answer: \(\displaystyle \frac{25 x^{3} y}{2}\), \(\displaystyle x\ne 0\) and \(\displaystyle y\ne 0\).
(b)
Multiply or divide numerical coefficients, then add or subtract the exponents of each separate variable.
\(3\)
Answer: \(3\)
(c)
Multiply or divide numerical coefficients, then add or subtract the exponents of each separate variable.
\(1\)
Answer: \(1\)
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: Combine numerical coefficients independently of variable powers.
- 1 mark: Apply the correct exponent law to each base and preserve original exclusions.
- 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: Multiply or divide numerical coefficients, then add or subtract the exponents of each separate variable.
- 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: Multiply or divide numerical coefficients, then add or subtract the exponents of each separate variable.
- 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.