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
15 \(A\), \(B\) and \(C\) are points on a circle, centre \(O\)
Diagram NOT accurately drawn
Angle \(BAO = 36^\circ\) Angle \(BCO = 21^\circ\)
Work out the size of angle \(ACO\)
(3)
Mark scheme
Scheme
Marks
\(ABC = 21 + 36\;(= 57)\) or angle \(ABO = 36\) and angle \(CBO = 21\) and \(21 + 36\;(=57)\) or (reflex) \(AOC = 360 - (21 + 21 + 36 + 36)\;(= 246)\) or (obtuse) \(AOC = 2 \times (21 + 36)\;(=114)\)
or \(BAX = 90 - 36\;(= 54)\) with the tangent at \(A\) drawn oe or \(BCY = 90 - 21\;(= 69)\) with the tangent at \(C\) drawn oe or angle \(ADB = 180 - 90 - 36\;(= 54)\) OR eg \(x\) = angle \(ACO\) and \(y = ABC\) and \(x + x + 2y = 180\) oe and \(y + (x + 36) + (x + 21) = 180\) oe
Correct answer only scores full marks (unless from obviously incorrect working) Answer: 33
A1
(3)
(3 marks)
Notes
M1: for a method to find one of the angles on the scheme; for this mark, values and calculations must be linked to the correct angle by notation or by being marked on the diagram. May also be awarded for a correct method to set up and solve an equation to find one of these angles; the variable must be clearly defined
where \(X\) is a point on the tangent at \(A\) where \(Y\) is a point on the tangent at \(C\) where \(AD\) is a diameter OR for any correct pair of simultaneous equations with clearly defined variables one of which must be angle \(ACO\)
or any correct equation in terms of \(ACO\) only
M1: for a complete method to find angle \(ACO\) OR forms a correct equation in terms of \(ACO\) only and solves to get a value (condone arithmetic errors)
implies the 1st M mark (provided no incorrect working seen)
