Similarity — Paper 2 · IGCSE Mathematics - International 0607

8 A NOT TO SCALE D B C ADC is a straight line and angle BAC = angle DBC. (a) Complete the following statement. Triangle ACB is similar to triangle … . [1] (b) BC = 6 cm and CD = 4 cm . Calculate the length AC. AC = … cm [2]

3 marks

Mark scheme: 8(a) BCD 1 Must be that order 8(b) 9 2 x 6 M1 for = oe 6 4

This question in 0607/22 May/June 2017

14 NOT TO SCALE The two solids are mathematically similar. The larger solid has a volume of 64 cm3. The smaller solid has a volume of 8 cm3 and a height of 5 cm. Work out the height of the larger solid. … cm [3] Question 15 is printed on the next page.

3 marks

Mark scheme: 14 10 3 3  5 8 oe M2 for  =  h  64 8 or M1 for (scale factor)3 = or 64 64 or better 8

This question in 0607/23 Oct/Nov 2018

13 A P NOT TO SCALE 9 cm 8 cm B C Q R 10 cm 6 cm The diagram shows two similar triangles, ABC and PQR. (a) Find the length of PR. PR = … cm [2] (b) The triangles are the cross-sections of mathematically similar prisms. The volume of the larger prism is 500 cm3. Find the volume of the smaller prism. … cm3 [2]

4 marks

Mark scheme: 13(a) 4.8 2 10 8 M1 for = oe 6 PR 13(b) 108 2 3 3  6   10  M1 for   or   oe seen  10   6 

This question in 0607/23 May/June 2021

9 E NOT TO SCALE D F C A B ABCD is a parallelogram. EDA and EFB are straight lines. (a) Show that triangles EDF and BCF are similar. [2] (b) BC = 4 cm, DE = 5 cm and FB = 3 cm. Find EF. EF = … cm [2]

4 marks

Mark scheme: 9(a) EFD = BFC (Vert) opposite s 2 B1 for 1 pair with reason or all 3 equal angle pairs EDF = BCF Alternate s identified DEF = CBF Alternate s OR Two of the above AND 3 angles are equal, triangles are similar 9(b) 3 2 EF 5 3 oe M1 for  oe 4 3 4

This question in 0607/23 May/June 2022

8 12 cm NOT TO SCALE 18 cm The diagram shows two triangles formed by two parallel lines and two intersecting lines. (a) Use one of these words to complete the statement. alternate congruent similar cyclic parallel The triangles are … [1] (b) The area of the smaller triangle is 24 cm 2. Calculate the area of the larger triangle. … cm2 [2]

3 marks

Mark scheme: 8(a) similar 1 8(b) 54 2 2 2  18   12  M1 for   oe or   oe  12   18 

This question in 0607/23 Oct/Nov 2022

16 A NOT TO SCALE D E B C ABC is a triangle. DE is parallel to BC. (a) Show that triangle ADE is similar to triangle ABC. … … … … … [2] (b) AD : DB = 2 : 3 . Find the ratio Area of triangle ADE : Area of triangle ABC. … : … [1]

3 marks

Mark scheme: 16(a) Two from 2 B1 for 1 pair with a reason ADE = ABC Corresponding s or 2 pairs with no/incorrect reason AED = ACB Corresponding s DAE = BAC common oe [And Angles equal] 16(b) 4 : 25 1

This question in 0607/22 May/June 2023

9 NOT TO SCALE 30 cm 24 cm The two bottles are mathematically similar. The height of the large bottle is 30 cm. The height of the small bottle is 24 cm. The volume of the large bottle is 250 cm3. Calculate the volume of the small bottle. … cm3 [3]

3 marks

Mark scheme: 9 128 3 3  24  M2 for 250   oe  30   24 3  30 3 or M1 for   or   oe seen  30   24 

This question in 0607/23 Oct/Nov 2023

14 C R NOT TO SCALE A B P Q The triangles ABC and PQR are similar. The area of triangle ABC is 24 cm2. PQ 1 = AB 2 Work out the area of triangle PQR. … cm2 [2]

2 marks

Mark scheme: 14 6 2 2  1  M1 for   or 22 seen  2 

This question in 0607/22 Oct/Nov 2024

19 h NOT TO SCALE A large cone has height h. The large cone is cut parallel to its base to make a smaller cone and a frustum. 3 The height of the frustum is h . 5 Find the ratio volume of small cone : volume of frustum. … : … [3]

3 marks

Mark scheme: 19 8 : 117 3 3  2  M2 for   oe  5  or M1 for 2[ h ] 5

This question in 0607/22 Feb/March 2025

18 NOT TO F SCALE E A B C D C, E and F are points on a circle. ABCD is a tangent to the circle at C. EB is parallel to FC. (a) Show that triangle CEB is similar to triangle FCE. … … … … … [3] (b) CB = 6 cm, FE = 8 cm and EB = 5 cm. Calculate CE. … cm [2] Area of triangle CEB (c) Find . Area of triangle FCE … [1]

6 marks

Mark scheme: 18(a) BEC =ECF Alternate angle 3 B2 for 2 correct pairs of angles or one BCE =EFC Alternate Segment correct pair of angles with reason therefore similar [AA or AAA] or B1 for one correct pair of angles 18(b) 20 2 6 5 oe M1 for = oe 3 8 EC 18(c) 36 1 oe 64

This question in 0607/21 Oct/Nov 2025