Higher June 2024 Paper 2 Q14
14
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| \((3y)(2y + 5) = 6y^2 + 15y\) \((3y)(y + 7) = 3y^2 + 21y\) \((2y + 5)(y + 7) = 2y^2 + 14y + 5y + 35\) \((= 2y^2 + 19y + 35)\) | M1 |
| \((6y^2 + 15y)(y + 7) = 6y^3 + 42y^2 + 15y^2 + 105y\) \((3y^2 + 21y)(2y + 5) = 6y^3 + 15y^2 + 42y^2 + 105y\) \(3y(2y^2 + 19y + 35) = 6y^3 + 57y^2 + 105y\) | M1 |
| working required Answer: \(6y^3 + 57y^2 + 105y\) | A1 |
| (3) |
Notes
M1: An expansion with only one error. Do not award this mark for \(6y^2 + 15y + 3y^2 + 21y\)
M1: ft dep on M1
allow one further error
A1: cao (terms may be in any order but must be simplified) dep on M1
accept \(a = 6\), \(b = 57\), \(c = 105\)
M2 for 3 (out of a maximum of 4) of
\(6y^3 + 42y^2 + 15y^2 + 105y\)
(M1 for 2 correct out of a maximum of 4)
| Scheme | Marks |
|---|---|
eg \(\dfrac{4(2x + 3) + 5(6x - 5)}{20}(= 1.63)\) oe or \(\dfrac{40x + 60}{100}(+)\dfrac{150x - 125}{100}\left(= \dfrac{163}{100}\right)\) oe \(4(2x + 3) + 5(6x - 5) = 1.63 \times 5 \times 4\) oe | M1 |
eg \(8x + 12 + 30x - 25 = 32.6\) or \(40x + 60 + 150x - 125 = 163\) or \(\dfrac{190x - 65}{100} = \dfrac{163}{100}\) or \(\dfrac{38x - 13}{20} = \dfrac{163}{100}\) oe | M1 |
| \(8x + 30x = 32.6 - 12 + 25\) or oe eg \(38x = 45.6\) or \(190x = 228\) | M1 |
| working required Answer: 1.2 | A1 |
| (4) | |
| (7 marks) |
Notes
M1: Writing fractions over a common denominator(can be 2 fractions) or for a method to remove the denominator by multiplying each term by eg 20 or 100 etc
(if expanded numerator, allow one error) or
\(20(2x + 3) + 25(6x - 5) = 163\) (could all be written over 100)
M1: Removing brackets and fractions on the LHS in an equation with no more than one error from expanding on the numerator
or
an equation with terms on numerator of fraction simplified with no more than one error from expanding on the numerator
M1: Terms in \(x\) on one side and number terms the other in a correct equation.
A1: oe dep on M1