IGCSE Mathematics Paper-1: Specimen Questions with Answers 92 - 93 of 324

Question 92

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Write in Short

Short Answer▾

Factorize completely

Explanation

Here,

  • Factoring is the decomposition of an object into a product of other objects or factors, which gives the original equation when multiplied together.

So,

Question 93

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Essay▾

Diagram shows a triangle ABC and a rectangle ABDF. Angle and AB = 5 cm, AF = 9 cm and BC = 12.5 cm.

A triangle and Rectangle set into each other

A Triangle and Rectangle Set into Each Other

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(a) (i) Write down the size of angle AEF.

(ii) Write down the size of angle BCA and EAF.

(b) Complete the statement: Triangle ABC is ________ to triangle AFE.

(c) AB = 5 cm, AF = 9 cm and BC = 12.5 cm. Calculate the length of EF.

Explanation

(a) (i) Here, in angles BAC and AEF are alternate interior angles which will be similar.

So, .

(ii) For :

Here, both triangles are right-angled triangles, so

Now, in any triangle addition of all angles will be

So, in

So, in , will also be , as and are alternate interior angles.

(b) Here, Triangle ABC is similar to triangle AFE because there all three angles are same in both.

  • Two triangles are called as congruent triangles when both have all equal sides and equal angles.
  • Two triangles are called as similartriangles:

o If all angles are same in both.

o If all pairs of sides are in same proportion.

o If two pairs of sides are in same proportion and one angle is also same in both.

(c) Here, AB = 5 cm, AF = 9 cm and BC = 12.5 cm are given,

So, formula for similar triangles for side:

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