Higher November 2018 Paper 3 Q9
9
(a) Expand and simplify \((x - 2)(2x + 3)(x + 1)\) (3)
\(\dfrac{y^4 \times y^n}{y^2} = y^{-3}\)
(b) Find the value of \(n\). (2)
(c) Solve \(5x^2 - 4x - 3 = 0\)
Give your solutions correct to 3 significant figures. (3)
Give your solutions correct to 3 significant figures. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(2x^3 + x^2 - 7x - 6\) | M1 | for a method to find the product of two linear expressions eg 3 correct terms out of 4 terms or 4 terms ignoring signs |
| M1 | for a complete method to obtain all terms, half of which are correct (ft their first product) eg \(2x^3 - x^2 - 6x + 2x^2 - x - 6\) | |
| A1 | cao |
Additional guidance
Note that (eg) \(-x - 6\) in expansion of \((x - 2)(2x + 3)\) is to be regarded as 3 correct terms.
First product must be quadratic but need not be simplified or may be simplified incorrectly
| Answer | Mark | Mark scheme |
|---|---|---|
| \(-5\) | M1 | for beginning to combine indices eg \(4 + n\) or \(y^{-3+2}\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 1.27 and \(-0.472\) | M1 | for substitution into the formula |
| M1 | for simplifying to the form \(\dfrac{-b \pm \sqrt{N}}{k}\) eg \(\dfrac{4 \pm \sqrt{76}}{10}\) or 1.27 to 1.28 or \(-0.48\) to \(-0.47\) | |
| A1 | for 1.27 to 1.28 and \(-0.48\) to \(-0.47\) |
Additional guidance
Condone one sign error in the substitution
Accept \(-4^2\) or \((-4)^2\)