Higher June 2021 Paper 1 Q9
9
| Scheme | Marks |
|---|---|
| \(5a^4c^3(5c^4d + 9a^5h)\) | B2 |
| (2) |
Notes
B2: If not B2 then award B1 for any correct factorisation with at least 2 of: the 5, a term in \(a\), a term in \(c\), outside the bracket
eg \(5ac(5a^3c^6d + 9a^8c^2h)\)
or \(a^2c(25a^2c^6d + 45a^7c^2h)\) (NB: not just \(a^4\) etc as we want to know students have considered more than just one letter or the number)
or
the correct common factor and a 2 term expression inside the bracket eg \(5a^4c^3(5c^4 + 9a^5)\) (this is missing \(d\) in first term and \(h\) in the second but the common factor is correct)
| Scheme | Marks |
|---|---|
| \(4x^2 + 10x + 10x + 25 = 4x^2 - 2x + 6x - 3\) \(4x^2 + 20x + 25 = 4x^2 + 4x - 3\) | M1 |
| \(10x + 10x - 6x + 2x = -3 - 25\) or \(3 + 25 = -16x\) or \(16x = -28\) oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working eg -1.75 oe from \(2x^2 + 20x + 25 = 2x^2 + 4x - 3\) scores M2A0) Answer: −1.75 | A1 |
| (3) | |
| (5 marks) |
Notes
M1: Correct expansion of \((2x + 5)^2\) or \((2x + 3)(2x - 1)\) or expansion of both sets of brackets with at least 3 of 4 terms correct in both (NB: if written as a 3 term quadratic (and not seen as 4 terms) then the middle term must be correct as it is equivalent to 2 correct terms) (eg (RHS) \(4x^2 + 4x + 3\) has 1 error, \(2x^2 + 4x - 3\) has 1 error, \(4x^2 + 10x - 3\) has 2 errors)
M1: ft if previous mark awarded. For terms in \(x\) on one side and number terms on the other side in a correct ft equation dependent on a linear equation
A1: or \(-1\dfrac{3}{4}\) or \(-\dfrac{7}{4}\) or \(-\dfrac{28}{16}\) or \(-1\dfrac{12}{16}\) oe