CAIE IGCSE Mathematics Extended E3.4 Length…point

Covered syllabus points

E3.4.1 Calculate the length of a line segment.E3.4.2 Find the coordinates of the midpoint of a line segment.

[Maximum number: 3]

16 A is the point (7,2) and B is the point (-5,8).

Calculate the length of AB.

13.4 or 13.41 to 13.42

M2 for $\sqrt{(-5-7)^2+(8-2)^2}$ oe.
M1 for $(-5-7)^2+(8-2)^2$ oe.

[Maximum number: 5]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. $O B=6 \mathrm{~cm}, B C=2 \mathrm{~cm}$ , obtuse angle $A O C=135^{\circ}$ and angle $B C O=90^{\circ}$ .

C is the midpoint of OD.
Calculate AD.

16.1 or 16.10 to 16.13
M2 for $2\times\sqrt{6^2-2^2}$ oe or $2\times6\cos19.5$ oe
or M1 for $OC^2+2^2=6^2$ oe or $6\cos19.5$ or better
AND M2 for $\sqrt{6^2+\text{their }OD^2-2\times6\times\text{their }OD\times\cos135}$
or M1 for expression under the square root
A1 for 259 to 260

[Maximum number: 4]

9 A is the point (0,2), B is the point (3,3) and C is the point (4,0).

Determine if triangle ABC is scalene, isosceles or equilateral. You must show all your working.

$[AB^2=](3-0)^2+(3-2)^2$ oe or better, or $\begin{pmatrix}3\\1\end{pmatrix}$ oe
$[AC^2=](4-0)^2+(0-2)^2$ oe or better
$[BC^2=](4-3)^2+(0-3)^2$ oe or better
Triangle is isosceles [with 10, 10, 20]

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CAIE IGCSE Mathematics Extended E3.4 Length and Midpoint Topic Practice

Covered syllabus points

Question 1

Question 2

Question 3