June 2016 Paper 2 Q10
10
(a) Simplify \(\quad \dfrac{x^2 - 7x + 10}{x^2 - 2x - 15}\) [2 marks]
(b) Factorise fully \(\quad w^5x^3y^2 + w^2x^6y^3\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x - 5)(x - 2)\) or \((x - 5)(x + 3)\) or \((5 - x)(2 - x)\) or \((5 - x)(-x - 3)\) | M1 | oe factorisation |
| \(\dfrac{x - 2}{x + 3}\) or \(\dfrac{2 - x}{-x - 3}\) | A1 | oe numerator and denominator both linear |
Additional guidance
| Correct answer followed by incorrect further work | M1 A0 |
| \(\dfrac{x - 2}{x + 3}\) or \(\dfrac{2 - x}{-x - 3}\) from incorrect method | M0 A0 |
| Allow fraction with correct factorisations and common factors crossed out | M1 A1 |
| Allow \(\ x - 2 \,/\, x + 3\) | M1 A1 |
| Answer | Mark | Comments |
|---|---|---|
| \(w^2x^3y^2(w^3 + x^3y)\) | B2 | B1 A correct partial factorisation with at least one variable fully factorised eg1 \(y^2(w^5x^3 + w^2x^6y)\) eg2 \(w^2x(w^3x^2y^2 + x^5y^3)\) or a correct partial factorisation with all three variables as factors eg \(wxy(w^4x^2y + wx^5y^2)\) or full common factor with one term in brackets correct \(w^2x^3y^2(w^3 + \ldots)\) or \(w^2x^3y^2(\ldots + x^3y)\) Must be two terms in each bracket |
Additional guidance
| Allow multiplication signs and 1s and unnecessary brackets for B2 and B1 | |
| Use of negative or fractional or zero powers is a maximum of B1 | |
| \(w^2x^3y^2(w^3 + x^3y)\) followed by incorrect further work | B1 |
| Answer line incorrect, check working lines for possible B1 |