Geometrical terms — Paper 2 · IGCSE Mathematics 0580

17 For Examiner's Use A B C AB is the diameter of a circle. C is a point on AB such that AC = 4 cm. (a) Using a straight edge and compasses only, construct (i) the locus of points which are equidistant from A and from B, [2] (ii) the locus of points which are 4 cm from C. [1] (b) Shade the region in the diagram which is • nearer to B than to A and • less than 4 cm from C. [1]

4 marks

Mark scheme: 17 (a) 2 B1 for correct line, on each side of AB (longer than dash at C) B1 for 2 pairs of intersecting arcs R 1 Intention to draw a full correct circle (b) 1 R shaded must be a closed region 7 84

This question in 0580/21 Oct/Nov 2012

19 For Examiner′s C Use D B c b E A O OABCDE is a regular polygon. (a) Write down the geometrical name for this polygon. Answer(a) … [1] (b) O is the origin. = b and = c. Find, in terms of b and c, in their simplest form, (i) , Answer(b)(i) = … [1] (ii) , Answer(b)(ii) = … [2] (iii) the position vector of E. Answer(b)(iii) … [1] _____________________________________________________________________________________ Question 20 is printed on the next page.

5 marks

Mark scheme: 19 (a) hexagon 1 (b) (i) −b + c 1 (ii) b − 12 c 2 B1 for OB + BA or any correct route (iii) −b + c 1FT = their (b)(i) √

This question in 0580/23 May/June 2013

11 B A C (a) Using compasses and a straight edge only, construct the bisector of angle BAC. [2] (b) Complete the statement. The bisector of angle BAC is the locus of points that are … … [1]

3 marks

Mark scheme: 11 (a) Accurate angle bisector with correct 2 B1 for accurate angle bisector arcs or correct arcs with no/wrong line (b) Equidistant (oe) from AB and AC 1

This question in 0580/22 Oct/Nov 2016

3 C N L A B M In the diagram, BL is the bisector of angle ABC and MN is the perpendicular bisector of AB. Complete the statement. The shaded region contains the points, inside triangle ABC, that are • nearer to B than to A and • nearer to … than to … [1]

1 marks

Mark scheme: 3 BC AB oe 1

This question in 0580/22 Oct/Nov 2017

13 A B C The diagram shows a triangle ABC and an arc with centre C and radius 6.5 cm. (a) Using a straight edge and compasses only, construct the locus of points inside the triangle that are equidistant from BA and BC. [2] (b) Shade the region inside the triangle that is • more than 6.5 cm from C and • nearer to BA than to BC. [1]

3 marks

Mark scheme: 13(a) Correct angle bisector at B with two 2 B1 for accurate with no/wrong arcs or for pairs of correct arcs reaching AC two pairs of correct arcs with no or wrong line or short line 13(b) Correct region shaded 1

This question in 0580/21 Oct/Nov 2018

4 Complete each statement. (a) A quadrilateral with only one pair of parallel sides is called a … . [1] (b) An angle greater than 90° but less than 180° is called … . [1]

2 marks

Mark scheme: 4(a) Trapezium 1 4(b) Obtuse 1

This question in 0580/22 May/June 2019

12 A regular polygon has an interior angle of 176°. Find the number of sides of this polygon. … [3]

3 marks

Mark scheme: 12 90 3 M2 for 360 ÷ (180 – 176) oe or M1 for 180(n – 2) = 176n oe or 180 – 176

This question in 0580/22 Oct/Nov 2019

6 A NOT TO 58° SCALE 82° B C The diagram shows triangle ABC. The triangle is reflected in the line BC to give a quadrilateral ABDC. (a) Write down the mathematical name of the quadrilateral ABDC. … [1] (b) Find angle ACD. Angle ACD = … [2]

3 marks

Mark scheme: 6(a) Kite 1 6(b) 80 2 M1 for (180 – 82 – 58) or better

This question in 0580/23 Oct/Nov 2020

19 A B NOT TO SCALE X P Q In the diagram, AB is parallel to PQ. AQ and PB intersect at X with AX = XQ . Complete the following statements. In triangles ABX and QPX, AX = XQ is given information. Angle BAX = Angle … because … Angle AXB = Angle … because … Triangle ABX is congruent to triangle QPX because of the congruency criterion … PX = … because the triangles are congruent. [4]

4 marks

Mark scheme: 19 PQX and alternate 4 B2 for lines 1 and 2 correct PXQ and [vertically] opposite oe or B1 for line 1 or 2 correct, or both angles correct ASA XB B1 for line 3 correct B1 for line 4 correct

This question in 0580/21 May/June 2022

17 A NOT TO SCALE B D C In triangle ABC, AC = AB. D is the point on BC such that AD is perpendicular to BC. Complete the following statements to show that triangle ACD and triangle ABD are congruent. AD is perpendicular to BC so that Angle … = Angle … = … ° AC = AB is given information. Side … is common to both triangles. Triangle ACD is congruent to triangle ABD because of the congruency criterion … [3]

3 marks

Mark scheme: 17 ADC and ADB and 90 3 B1 for each correct line AD RHS

This question in 0580/23 May/June 2022

5 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about centre M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. … [1] (b) Find angle BAD. Angle BAD = … [2]

3 marks

Mark scheme: 5(a) Parallelogram 1 5(b) 68 2 M1 for 180 – 112 oe or for 180 − 112 − 44

This question in 0580/23 Oct/Nov 2023

3 A quadrilateral has one line of symmetry. The diagonals of the quadrilateral cross at right angles. Write down the mathematical name of the quadrilateral. … [1]

1 marks

Mark scheme: 3 Kite 1

This question in 0580/22 Feb/March 2025