Higher June 2025 Paper 1R Q23
23
Diagram NOT accurately drawn
\(PTR\) and \(QTS\) are chords of a circle.
\(PT = (3y - 5)\) cm \(QT = (y + 3)\) cm \(RT = 4x\) cm \(ST = (x + 2)\) cm
Find an expression for \(y\) in terms of \(x\)
(5)
| Scheme | Marks |
|---|---|
eg \((y + 3)(x + 2) = 4x(3y - 5)\) or \(\dfrac{3y - 5}{x + 2} = \dfrac{y + 3}{4x}\) or \(\dfrac{x + 2}{3y - 5} = \dfrac{4x}{y + 3}\) or \(\dfrac{3y - 5}{y + 3} = \dfrac{x + 2}{4x}\) or \(\dfrac{4x}{x + 2} = \dfrac{y + 3}{3y - 5}\) | M1 |
| eg \(xy + 2y + 3x + 6 = 12xy - 20x\) oe | M1 |
| eg \(20x + 3x + 6 = 12xy - xy - 2y\) oe or \(23x + 6 = 11xy - 2y\) oe | M1ft |
| eg \(23x + 6 = y(11x - 2)\) or \(20x + 3x + 6 = y(12x - x - 2)\) | M1ft |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{23x + 6}{11x - 2}\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for correct use of intersecting chords theorem to form an equation
M1: for expanding the brackets or for removing the fractions and expanding the brackets, allow one error in one term we can ft \(4x(y + 3) = (x + 2)(3y - 5)\) oe for the 2nd, 3rd and 4th method marks
M1ft: dep on previous M1 for correctly collecting all the \(y\) terms on one side and non-\(y\) terms on the other side
M1ft: dep on 2nd M mark for factorising, for \(y\), an equation in the form \(ax + b = cxy + dy\) (may not be simplified) the factorisation must be correct
A1: oe