Constructing Lines, Angles, and Polygons · CSEC Mathematics

53 past-paper questions on Constructing Lines, Angles, and Polygons, part of GEOMETRY AND TRIGONOMETRY, from every CSEC Mathematics paper on Quelpr.

1. 4(b)(i)4 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Using only a ruler, a pencil and a pair of compasses, construct \Delta LMN such that MN = LM = 6.0\text{ cm} and \angle LMN = 60^\circ.
2. 4(c)(i)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Construct the circle which passes through the points L, M and N.
3. 6(a)5 marks· CSEC Mathematics · 2009 (second paper) · Paper 2Using a pencil, a ruler and a protractor only, draw accurately the quadrilateral KLMN such that: KN = MN = 6\text{ cm}, \angle KNM = \angle NKL = 90^\circ, and KL = 10\text{ cm}.
4. Q521 mark · multiple choice· CSEC Mathematics · January 2011 · Paper 1What is the measure of \angle BAC?
5. Q521 mark · multiple choice· CSEC Mathematics · May/June 2011 · Paper 1What is the measure of \angle BAC?
6. Q541 mark · multiple choice· CSEC Mathematics · May/June 2012 · Paper 1Item 54 refers to the diagram below of a construction. With centre A, an arc BC is drawn. With centre B, and the same radius, the arc PCQ is drawn. What is the measure of \angle BAC?
7. 3(a)4 marks· Mathematics Q3 3(a)Using a ruler, a pencil and a pair of compasses only, construct the triangle NLM, in which LM = 12 cm, ∠MLN = 30° and ∠LMN = 90°. (Credit will be given for clearly drawn construction lines.)
8. 3(a)4 marks· Mathematics Q3 3(a)Using a ruler, a pencil and a pair of compasses, construct the right-angled triangle ABC, such that AB = 5 cm, ∠ABC = 90° and ∠BAC = 60°.
9. 3(a)4 marks· Mathematics Q3 3(a)Using a ruler, a pencil and a pair of compasses, construct the triangle ABC, such that AB = 8 cm, ∠BAC = 30° and AC = 10 cm.
10. 3(b)7 marks· Mathematics Q3 3(b)Using a ruler, a pencil and a pair of compasses, construct the trapezium ABCD with AB = 8 cm, BAD = 60°, AD = 6 cm, ABC = 90° and AB parallel to CD. (Credit will be given for clearly drawn construction lines.)
11. 3(b)6 marks· Mathematics Q3 3(b)Using a ruler, a pencil and a pair of compasses only, construct parallelogram ABCD with AB = 8 cm, AD = 6 cm and ∠DAB = 60°. Marks will be awarded for construction lines clearly shown.
12. 3(b)(i)1 mark· Mathematics Q3 3(b)(i)Using a straight edge and compasses only, construct the line representing the fence.
13. 3(b)(i)4 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 8 cm, angle PQR = 120° and QR = 5 cm.
14. 3(b)(i)4 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil, and a pair of compasses, construct the rhombus PQRS accurately.
15. 3(b)(i)4 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 5 cm, ∠ PQR = 60° and ∠ QPR = 90°.
16. 3(b)(i)5 marks· Mathematics Q3 3(b)(i)Using a ruler, pencil, a pair of compasses and a protractor, draw accurately a quadrilateral EFGH using the following measurements: EF = 8 cm, ∠EFG = 125°, FG = 4 cm, ∠HEF = 70°, EH = 7 cm.
17. 3(b)(i)3 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil and a pair of compasses, construct accurately, the square ABCD, with sides 6 cm.
18. 3(b)(i)3 marks· Mathematics Q3 3(b)(i)Construct, accurately, the triangle ABC shown below, where AC = 6 cm, ∠ACB = 60°, ∠CAB = 60°.
19. 3(b)(i)4 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil and a pair of compasses, construct accurately, the square EFGH where EF = 6 cm. (Show ALL construction lines and curves.)
20. 3(b)(i)4 marks· Mathematics Q3 3(b)(i)Using a ruler, a pencil and a pair of compasses, construct triangle ABC with AB = 9 cm, angle ABC = 90° and BC = 6 cm.
21. 3(b)(i)a)4 marks· Mathematics Q3 3(b)(i)a)Using a pair of compasses, a ruler and a pencil, construct a triangle CDE in which DE = 10 cm, DC = 8 cm and ∠CDE = 45°.
22. 3(b)(i)a)3 marks· Mathematics Q3 3(b)(i)a)a triangle PQR in which PQ = 8 cm, PR = 6 cm and angle P = 60°
23. 3(b)(i)a)7 marks· Mathematics Q3 3(b)(i)a)Using a pencil, a ruler and a pair of compasses only, construct a triangle PQR in which QR = 8.5 cm, PQ = 6 cm and PR = 7.5 cm.
24. 3(b)(i)b)2 marks· Mathematics Q3 3(b)(i)b)Using a pair of compasses, a ruler and a pencil, construct a line, CF, perpendicular to DE such that F lies on DE.
25. 3(b)(i)b)2 marks· Mathematics Q3 3(b)(i)b)the line segment RX which is perpendicular to PQ and meets PQ at X. [Note: Credit will be given for clearly drawn construction lines.]
26. 3(b)(i)b)1 mark· Mathematics Q3 3(b)(i)b)Construct a line PT such that PT is perpendicular to QR and meets QR at T.
27. 3(b)(ii)2 marks· Mathematics Q3 3(b)(ii)Complete the diagram to show the kite, ABCD, in which AD = 5 cm.
28. 3(b)(ii)2 marks· Mathematics Q3 3(b)(ii)Construct, as an extension of your drawing in (b)(i), the trapezium DABQ so that ∠ABQ = 120°. [Note: Credit will be given for clearly drawn construction lines.]
29. 3(b)(iii)2 marks· Mathematics Q3 3(b)(iii)On your diagram in (b)(i), construct the point S, such that PQRS forms a parallelogram.
30. 3(b)(iii)2 marks· Mathematics Q3 3(b)(iii)On the diagram, show the point D such that ABCD is a parallelogram.
31. 4(a)4 marks· Mathematics Q4 4(a)Using a ruler, a pencil and a pair of compasses, construct the triangle ABC in which AB = 8 cm, ∠BAC = 60°, and AC = 5 cm (Credit will be given for a neat, clear diagram)
32. 4(a)6 marks· Mathematics Q4 4(a)Using a ruler, a pencil and a pair of compasses only, construct the rectangle PQRS in which PQ = 8 cm and PS = 6 cm. Measure and state the length of the diagonal, in centimetres.
33. 4(a)(i)3 marks· Mathematics Q4 4(a)(i)Using a pencil, ruler and a pair of compasses only, construct Δ ABC with BC = 6 cm and AB = AC = 8 cm. All construction lines must be clearly shown.
34. 4(a)(ii)2 marks· Mathematics Q4 4(a)(ii)Draw a line segment AD such that AD meets BC at D and is perpendicular to BC.
35. 4(b)(i)5 marks· Mathematics Q4 4(b)(i)Use a ruler and a protractor to draw accurately the quadrilateral PQRS shown below. PQ = 8 cm, QR = 4 cm, PS = 6.5 cm, angle PQR = 125° and angle QPS = 70°.
36. 4(b)(i)5 marks· Mathematics Q4 4(b)(i)Using only a pair of compasses, a ruler and a pencil, construct parallelogram ABCD in which AB = AD = 7 cm and the angle BAD is 60°.
37. 4(b)(i)5 marks· Mathematics Q4 4(b)(i)Using a ruler, a pencil and a pair of compasses, construct triangle EFG with EG = 6 cm, ∠FEG = 60° and ∠EGF = 90°.
38. 4(b)(i)4 marks· Mathematics Q4 4(b)(i)Using a pencil, ruler and a pair of compasses only, construct a triangle LMN with angle LMN = 60°, MN = 9 cm and LM = 7 cm. ALL construction lines MUST be clearly shown.
39. 4(d)2 marks· Mathematics Q4 4(d)Draw on your diagram the line CD which is perpendicular to AB and meets AB at D.
40. 5(a)(i)4 marks· Mathematics Q5 5(a)(i)Using a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 8 cm, ∠PQR = 60° and ∠QPR = 45°.
41. 5(a)(i)3 marks· Mathematics Q5 5(a)(i)Using a ruler, a pencil and a pair of compasses, construct triangle ABC with BC = 10 cm, AB = 6 cm and AC = 8 cm.
42. 5(a)(iii)2 marks· Mathematics Q5 5(a)(iii)Complete the diagram to show a quadrilateral, CABD, such that CD = CA and BD = BA.
43. 5(b)5 marks· Mathematics Q5 5(b)Using a ruler, a pencil, and a pair of compasses, construct the parallelogram KLMN, in which KL = 8 cm, KN = 6 cm, and ∠LKN = 60°.
44. 5(b)(ii)4 marks· Mathematics Q5 5(b)(ii)Using a ruler and a pair of compasses, draw the line RM on the scale drawing.
45. 5(b)(iii)1 mark· Mathematics Q5 5(b)(iii)Mark and name the angle in the scale drawing that measures 120°.
46. 6(a)2 marks· Mathematics Q6 6(a)Draw a cross-sectional view of the container showing the measurements of the inner and outer radii.
47. 6(a)6 marks· Mathematics Q6 6(a)Using a ruler, a pencil and a pair of compasses only, construct the rectangle.
48. 6(b)(i)5 marks· Mathematics Q6 6(b)(i)Using a ruler, a pencil and a pair of compasses, construct parallelogram WXYZ in which WX = 7.0 cm, WZ = 5.5 cm and angle XWZ = 60°.
49. 6(b)(i)6 marks· Mathematics Q6 6(b)(i)Draw the mirror line and label it M.
50. 8(a)3 marks· Mathematics Q8 8(a)Using ruler and compasses only, construct triangle PVY where each side is of length 6 cm.
51. 8(b)2 marks· Mathematics Q8 8(b)Draw lines on your diagram to sub-divide triangle PVY into nine identical equilateral triangles.
52. 11(a)1 mark· Mathematics Q11 11(a)Copy and label the diagram.
53. 11(b)(i)2 marks· Mathematics Q11 11(b)(i)Copy the diagram in your answer booklet and show the points M and N.