CAIE IGCSE Mathematics Extended E4.4 Similarity

Covered syllabus points

E4.4.1 Calculate lengths of similar shapes.E4.4.2 Use the relationships between lengths and areas of similar shapes and E4.4.3 Solve problems and give simple explanations involving similarity

[Maximum number: 4]

Figure for Question 1 — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

Triangle ABC and triangle PQR are mathematically similar.

(a)

Calculate the length of PR.
P R= cm

[ 2 ]

8

M1 for $\frac{9}{6}=\frac{12}{P R}$ oe

(b)

Triangle ABC and triangle PQR are the cross-sections of two prisms.

These prisms are mathematically similar.
The volume of the smaller prism is $1120 \mathrm{~cm}^{3}$ .
Calculate the volume of the larger prism. $\mathrm{cm}^{3}$

[ 2 ]

3780

M1 for $\frac{6^{3}}{1120}=\frac{9^{3}}{V}$ or better or $1120 \times\left(\frac{9}{6}\right)^{3}$ oe
or for $\left(\frac{9}{6} \times \sqrt[3]{1120}\right)^{3}$

[Maximum number: 3]

A sector of a circle has radius 8 cm and area 160 cm^2.

A mathematically similar sector has radius 20 cm .
Calculate the area of the larger sector.
cm^2
[3]

1000 cao
M2 for $160\times\left(\frac{20}{8}\right)^2$ or $160\div\left(\frac{8}{20}\right)^2$ oe
or M1 for $\left(\frac{20}{8}\right)^2$ or $\left(\frac{8}{20}\right)^2$ oe

[Maximum number: 7]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

[ 7 ]

(i)

Explain why triangle PQR is similar to triangle PUT.

Give a reason for each statement you make.

[ 3 ]

(ii)

$\quad P T: T R=4: 3$
(a) Find the ratio P U: P Q.:
(b) The area of triangle PUT is $20 \mathrm{~cm}^{2}$ .

Find the area of the quadrilateral QRTU. $\mathrm{cm}^{2}$

[ 4 ]

(a) 4:7 oe
(b) 41.25 oe
M2 for $20\times\left(\frac{7}{4}\right)^2$ oe or $20\times\frac{7^2-4^2}{4^2}$ oe, or M1 for $\left(\frac{7}{4}\right)^2$ , $\left(\frac{4}{7}\right)^2$ , $\frac{7^2-4^2}{4^2}$ , or $\frac{4^2}{7^2-4^2}$ .

[Maximum number: 2]

Figure for Question 4 — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

Triangle ABC and triangle PQR are mathematically similar.

Calculate the length of PR.
P R= cm

8

M1 for $\frac{9}{6}=\frac{12}{P R}$ oe

[Maximum number: 3]

Figure for Question 5 — CAIE IGCSE Mathematics Extended

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

Explain why triangle PQR is similar to triangle PUT.

Give a reason for each statement you make.

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CAIE IGCSE Mathematics Extended E4.4 Similarity Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question 5