O-LevelMathematicsGeometry4024/21 · May/June 2023 · Q37 Marks

PQ is parallel to RS. ABCD is a straight line. BE = CE and ABE = 110°. Calculate ECQ, giving a reason for each step of your working. [Figure 3.1]

(a)PQ is parallel to RS. ABCD is a straight line. BE = CE and ABE = 110°. Calculate ECQ, giving a reason for each step of your working. [Figure 3.1][3]
(b)U, V, W, X and Y are points on the circumference of a circle, centre O. UY is a diameter of the circle and ZX is a tangent to the circle at X. VÛX = 35°, XŻY = a° and VŴY = b°. Find an expression for b in terms of a. Give your answer in its simplest form. [Figure 3.2][4]

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Mark scheme

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[3] (a) ∠ECQ = 40 and correct reasons for each step eg B1 for ∠ECQ = 40 B1 for one correct angle with reason ∠ CBE = 70 sum of angles on a straight line equal 180 ∠BCE = 70 base angles in an isosceles triangle are equal ∠BCQ=110 corresponding angles are equal oe
[4] (b) [b =] 100 + a/2 or [b =] (200+a)/2 final answer B2 for ∠ XUO = 45 – a/2 oe or ∠ UXO = 145 – b oe or M1 for OXZ = 90 soi or ∠XUO=145-b oe M1 for b + 35 + their (45-a/2) = 180 oe or 2 × their (145 – b) + 90 + a = 180 oe

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