Foundation November 2022 Paper 2 Q23
23.
(a) Solve \(5x + 4 = 2x + 6\). [2]
(b) Solve \(4x - 3 \gt 17\). [2]
(c)
Solve the following simultaneous equations. Use an algebraic (not graphical) method.
\[\begin{aligned} 5x - 2y &= 16 \\ x - y &= 5 \end{aligned}\]You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(5x - 2x = 6 - 4\) or \(3x = 2\) oe | B1 | |
| (\(x\) =) \(\dfrac{2}{3}\) oe, ISW | B1 | Allow 0.67 or 0.666 but not 0.66 FT from \(ax = 2\), \(a \ne 1\) or \(3x = b\) accept \(\dfrac{2}{a}\) or \(\dfrac{b}{3}\) but if on FT either simplifies to an integer the answer must be given as an integer. Correct answer implies first B1 unless incorrect working seen. Maximum of 1 mark if not fully correct |
| Scheme | Marks | Comments |
|---|---|---|
| \(4x \gt 17 + 3\) oe | M1 | |
| \(x \gt 5\) | A1 | Mark final answer; no marks for use of “=”, unless finally replaced to give \(x \gt 5\) then award M1 A1. |
| Scheme | Marks | Comments |
|---|---|---|
| No marks for T&I; no marks for an unsupported answer. | ||
| Method to eliminate an unknown e.g. equal coefficients and subtraction or rearranges one equation and substitutes into the other | M1 | Allow one error in one term, not in the equated coefficients if appropriate |
| Finds one unknown | A1 | CAO; \(x = 2\), \(y = -3\) |
| Finds the other unknown | A1 | FT ‘their x’ or ‘their y’ used in one of their equations |
| (7) |