O-LevelMathematicsGeometry4024/22 · May/June 2016 · Q411 Marks
Triangle ABC has sides AB = 8 cm, AC = 7 cm and BC = 12cm. Use a ruler and compasses to construct triangle ABC. Side AB has been drawn for you. [Figure 4.1]
- (a)(i)Triangle ABC has sides AB = 8 cm, AC = 7 cm and BC = 12cm. Use a ruler and compasses to construct triangle ABC. Side AB has been drawn for you. [Figure 4.1][2]
- (a)(ii)Measure BẬC.[1]
- (b)Calculate the interior angle of a regular 12-sided polygon.[2]
- (c)(i)The diagram shows a hexagon with two parallel sides and one horizontal line of symmetry. [Figure 4.2] Calculate p.[1]
- (c)(ii)Calculate q.[2]
- (d)Trapezium PQRS is similar to trapezium ABCD. AB is parallel to DC and ABC = 90°. DC=2AB, BC = ½AB and PQ = ⅔ DC. Given that BC = x cm, find an expression, in terms of x, for the area of PQRS. [Figure 4.3][3]
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Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [2] (a)(i) Correct triangle with arcs shown
- [2] (a)(i) B1 for correct triangle with no arcs
- [2] (a)(i) or triangle with one side correct length with arcs
- [2] (a)(i) or triangle with BC = 7 and AC = 12 with arcs (reflection)
- [1] (a)(ii) 104 to 108
- [2] (b) 150°
- [2] (b) M1 for 180-(360 ÷ 12)
- [2] (b) or (180 × (12-2)) ÷ 12
- [1] (c)(i) 110°
- [2] (c)(ii) 165°
- [2] (c)(ii) ft their p provided p < 120 and p ≠ 90
- [2] (c)(ii) B1 for 30, 15 or 75 seen
- [3] (d) 27/4 x² final answer
- [3] (d) EITHER B2 for ½ (6x + 3x) 3x/2 oe
- [3] (d) or B1 for PQ = 3x
- [3] (d) OR B1 for 3x² (area of small trapezium)
- [3] (d) B1 for their 3x² × (3/2)² oe
- [3] (d) OR If AB = x used SC2 for 27/16 x² or SC1 for 27/16
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