Higher June 2022 Paper 3 Q23
23 Here are two simultaneous equations.
\(y = x^2 + 7x - c\)
and
\(y = 3x + d\)
There is a solution when \(\quad x = 5\)
Work out the value of \(\quad c + d\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(5^2 + 7 \times 5 - c\) or \(60 - c\) and \(3 \times 5 + d\) or \(15 + d\) | M1 | oe |
| \(25 + 35 - c = 15 + d\) or \(60 - c = 15 + d\) or \(c = 60 - y\) and \(d = y - 15\) and \(c + d = 60 - y + y - 15\) | M1dep | oe equation with squaring and multiplications correctly completed |
| 45 | A1 | |
| Alternative method 2 | ||
| \(x^2 + 7x - c = 3x + d\) or \(x^2 + 7x - c - (3x + d) = 0\) or \(x^2 + 7x - c - 3x - d = 0\) or \(3x + d - (x^2 + 7x - c) = 0\) or \(3x + d - x^2 - 7x + c = 0\) | M1 | oe |
| (\(c + d\) =) \(x^2 + 7x - 3x\) or (\(c + d\) =) \(x^2 + 4x\) and substitutes \(x = 5\) | M1dep | oe |
| 45 | A1 | |
Additional guidance
| Once \(c + d = 45\) is seen, ignore further attempts to find values for \(c\) or \(d\) | |
| 45 on answer line with no working or no incorrect working | M1M1A1 |