Higher November 2020 Paper 4 Q20
20 Solve.
\[x^2 + y^2 = 34\]\[y = x + 2\]Show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(x\) =] −5 [\(y\) =] −3 [\(x\) =] 3 [\(y\) =] 5 with some algebraic working | 6 | M1 for \(x^2 + (x + 2)^2 = 34\) M1 for expanding their square term e.g. \(x^2 + 4x + 4\) M1 for simplifying their quadratic expression e.g. \(2x^2 + 4x + 4 = 34\) or better M1 for correctly factorising their quadratic expression \(ax^2 + bx + c = 0\) e.g. \((x + 5)(x - 3)\) or \((2x + 10)(x - 3)\) or use of quadratic formula with no more than two errors B1FT for either one correct point or two correct \(x\) values B1FT for the other correct point or two correct \(y\) values If insufficient working B2 for 4 correct answers or B1 for 2 correct answers | e.g. \(x^2 + 2x - 15 = 0\) \(a, b, c \ne 0\) Alternative : M1 for \((y - 2)^2 + y^2 = 34\) or better M1 for \(y^2 - 4y + 4\) M1 for \(2y^2 - 4y + 4 = 34\) or better M1 for \((y - 5)(y + 3)\) or use of quadratic formula with no more than two errors Both B1s are strict FT from their method to solve their quadratic equation e.g. they must FT correctly from their factorisation |