Higher June 2023 Paper 1 Q11
11 Write \(\dfrac{(6x^5y^3)^2}{3x^2y^7 \times 4xy^{-3}}\) in the form \(ax^by^c\) where \(a\), \(b\) and \(c\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(3x^7y^2\) | M1 | for full evaluation of numerator or denominator with at least 2 of 3 terms correct in a product, eg \(36x^{10}y^6\) or \(12x^3y^4\) or full evaluation of \(\dfrac{6x^5y^3}{3x^2y^7}\) or \(\dfrac{6x^5y^3}{4xy^{-3}}\) with at least 2 of 3 terms correct in a product, eg \(2x^3y^{-4}\) or \(1.5x^4y^6\) |
| M1 | for correct evaluation of numerator and denominator, eg \(36x^{10}y^6\) and \(12x^3y^4\) or for full evaluation of numerator and denominator with no more than one error and a final answer of the form \(ax^by^c\) with two of \(a\), \(b\) and \(c\) correct or for correct evaluation of \(\dfrac{6x^5y^3}{3x^2y^7}\) and \(\dfrac{6x^5y^3}{4xy^{-3}}\) eg \(2x^3y^{-4}\) and \(1.5x^4y^6\) or for full evaluation of \(\dfrac{6x^5y^3}{3x^2y^7}\) and \(\dfrac{6x^5y^3}{4xy^{-3}}\) with no more than one error and a final answer of the form \(ax^by^c\) with two of \(a\), \(b\) and \(c\) correct | |
| A1 | for \(3x^7y^2\) oe |
Additional guidance
Accept \(a = 3\), \(b = 7\), \(c = 2\)