ZIMSEC O Level Mathematics Bearings and Scale Drawing questions

Question 1

Answer the whole of this question on a sheet of plain paper. Use ruler and pair of compasses only for all constructions and show all the construction lines and arcs. (a) Construct on a single diagram (i) quadrilateral ABCD in which AB = 8 cm, angle ABC = 90 degrees, angle BCD = 120 degrees, BC = 10 cm, and CD = 5 cm, [6] (ii) the locus of points equidistant from B and C, [2] (iii) the locus of points equidistant from DC and DA. [2] (b) (i) Mark and label the point P which is equidistant from B and C and equidistant from DC and DA. [1] (ii) Draw a circle with centre P and radius PC. [1] (iii) Measure and write down the length of PC. [1]

Accepted Answer

(a)(i) quadrilateral ABCD with AB = 8 cm, angle ABC = 90 degrees, BC = 10 cm, angle BCD = 120 degrees, CD = 5 cm; (ii) the perpendicular bisector of BC; (iii) the bisector of angle ADC; (b)(i) P is where the two loci cross, (ii) the circle centre P through C, (iii) PC = 5,2 cm

Question 2

Answer the whole of this question on a sheet of plain paper. Use ruler and compasses only and show clearly all construction lines and arcs. (a) On a single diagram, construct (i) quadrilateral ABCD in which AB = 9 cm, BC = 6 cm, AD = 7.3 cm, DC = 5.5 cm and angle BAD = 45 degrees, (ii) the locus of points equidistant from A and B, (iii) the locus of points 5.7 cm from B. [7] (b) Measure and write down the size of angle ADC. [1] (c) Point P is inside the quadrilateral and is such that it is equidistant from A and B and is 5.7 cm from B. Measure and write down the distance of P from D. [1]

Accepted Answer

(a)(i) quadrilateral ABCD with AB = 9 cm, BC = 6 cm, AD = 7,3 cm, DC = 5,5 cm and angle BAD = 45 degrees; (ii) the perpendicular bisector of AB; (iii) a circle of radius 5,7 cm with centre B; (b) angle ADC = 141 degrees; (c) PD = 1,8 cm

Question 3

Answer the whole of this question on a sheet of plain paper. Use ruler and pair of compasses only for all constructions and show clearly all the construction lines and arcs. (a) On a single diagram, construct (i) trapezium ABCD in which AB = 8,5 cm, angle ABC = 120 degrees, BC = 6 cm, CD = 12 cm and AB is parallel to DC, (ii) the locus of points which are equidistant from C and D, (iii) the circle of which CD is the diameter. [7] (b) Measure and write down angle CBD. [1] (c) CD satisfies a certain locus. Describe this locus fully. [2]

Accepted Answer

(a)(i) trapezium ABCD with AB = 8,5 cm, angle ABC = 120 degrees, BC = 6 cm, CD = 12 cm and AB parallel to DC; (ii) the perpendicular bisector of CD; (iii) the circle on CD as diameter; (b) angle CBD = 90 degrees; (c) DC is the locus of points 5,2 cm from the line AB, on the same side of AB as C and D

Question 4

Answer the whole of this question on a sheet of plain paper. Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. (a) On a single diagram, construct (i) quadrilateral WXYZ in which WX = 5,3 cm, angle WXY = 120 degrees, XY = 5 cm, YZ = 9,1 cm and WZ = 8,5 cm, (ii) the locus of points which are equidistant from 1. W and Y, 2. X and Z. [7] (b) Mark and label clearly, the point O, inside the quadrilateral WXYZ, which is equidistant from W, X, Y and Z. [1] (c) (i) Draw a circle centre O and radius OX. (ii) Measure and write down the radius of the circle. [2] (d) State the special name given to quadrilateral WXYZ. [1]

Accepted Answer

(a)(i) quadrilateral WXYZ with WX = 5,3 cm, angle WXY = 120 degrees, XY = 5 cm, YZ = 9,1 cm, WZ = 8,5 cm; (ii)1. the perpendicular bisector of WY, 2. the perpendicular bisector of XZ; (b) O is where those two perpendicular bisectors cross; (c)(ii) radius = 5,1 cm; (d) a cyclic quadrilateral

Question 5

Answer the whole of this question on a sheet of plain paper. Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be done on a single diagram. (a) Construct a quadrilateral ABCD in which AB = 8,5 cm, AD = 7 cm, DC = 5 cm, angle ADC = 90 degrees and angle BAD = 60 degrees. [6] (b) Measure and write down the length of BC. [1] (c) Construct the locus of a point (i) that is 4,5 cm from B, (ii) X, on the same side of AD as C, such that the area of triangle ACD = area of triangle AXD. [3] (d) Mark and label X1 and X2, the points that are 4,5 cm from B and are such that the area of triangle AX1D = the area of triangle AX2D. [2]

Accepted Answer

(a) quadrilateral ABCD with AB = 8,5 cm, AD = 7 cm, DC = 5 cm, angle ADC = 90 degrees, angle BAD = 60 degrees; (b) BC = 3,6 cm; (c)(i) a circle of radius 4,5 cm with centre B, (ii) the line through C parallel to AD; (d) X1 and X2 are the two points where that parallel line cuts the circle

Bearings and Scale Drawing Questions and Answers

Test yourself on this topic

Questions on this topic

More topics in this subject

Practise this topic in the app