Higher June 2024 Paper 5 Q21
21 Work out the coordinates of the intersection of the graphs of \(y = 5 - 2x\) and \(y = 3x^2\).
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\left(-\frac{5}{3}, \frac{25}{3}\right)\) oe and (1, 3) with correct working | 6 | Accept ( –1.67 or –1.666 to –1.667 , 8.33[3]…) Correct working requires evidence of at least M2M2 | |
| M2 for \(3x^2 + 2x - 5\) [= 0] or M1 for \(3x^2 = 5 - 2x\) | For M2 accept e.g. \(5 - 2x - 3x^2\) [= 0] | ||
| M2 for \((3x + 5)(x - 1)\) [= 0] or M1 for \((3x + a)(x + b)\) where \(ab = -5\) or \(3b + a = 2\) or for correct partial factors \(3x(x - 1) + 5(x - 1)\) or \(x(3x + 5) - [1](3x + 5)\) | Strict FT their 3-term quadratic equation or expression e.g.If M2 awarded for \(5 - 2x - 3x^2\) [= 0] then factors should be correct for this equation for M2 or M1 Accept correct use of quad formula or completing the square, M2 if completely correct, M1 if one error in substitution in formula or \((x + a)^2\) correct if completing the square | ||
| A1dep on M2M2 for either pair of coordinates correct or for both \(x\) values correct or both \(y\) values correct If 0, 1 or 2 scored, instead award SC3 for answers \(\left(-\frac{5}{3}, \frac{25}{3}\right)\) oe and (1, 3) If 0 or 1 scored, instead award SC2 for answer \(\left(-\frac{5}{3}, \frac{25}{3}\right)\) oe or for both \(x\) values correct or both \(y\) values correct If 0 scored, SC1 for one answer (1, 3) | If A1 for correct \(x\)–values or \(y\) – values after correct partial factorisation award M2 for factors See AG for work with equations in terms of \(y\) | ||
Additional guidance: Question 21
A few may choose to work in terms of \(y\)
If working in terms of \(y\)
| M2 for \(3y^2 - 34y + 75\) [ = 0] or M1 for \(\frac{5 - y}{2} = \sqrt{\frac{y}{3}}\) oe or better | accept \(-75 + 34y - 3y^2\) [= 0] |
| M2 for \((3y - 25)(y - 3)\) [= 0] | accept equivalent negative version factors \(-(3y - 25)(y - 3)\) [= 0] oe |
| or M1 for \((3y + a)(y + b)\) where \(ab = 75\) or \(3b + a = -34\) | accept equivalent negative version factors \(-(3y + a)(y + b)\) Allow M1 for factors that when expanded give one other term correct as well as ‘\(3y^2\)’ |
| or for correct partial factors \(3y(y - 3) - 25(y - 3)\) or \(y(3y - 25) - 3(3y - 25)\) | accept equivalent negative version partial factors |
If A1 for correct \(y\) values after correct partial factors award M2 for factors