# IGCSE Mathematics Paper-1: Specimen Questions with Answers 166 - 168 of 324

## Question 166

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Essay▾

Simplify

(a)

(b) ,

(c)

### Explanation

Here,

(a) Because 0 powers always gives value 1 and minus power of denominator will become plus when denominator multiply by its numerator.

(b) Because division of two terms with same base will subtract denominator’s exponent from numerator’s exponent.

(c) Because it is an exponent expression that is raised to a power, so we can multiply the exponent and power which is second exponent rule.

## Question 167

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### Write in Short

The area of a square is 42.25 . Find length of one side of the square.

### Explanation

Here, formula for area of a square = where, a is side of square.

• So, here,

## Question 168

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### Describe in Detail

Essay▾

In the diagram AC is the diameter of a circle, center O. The length of AC is 12 cm.

(a) Write down the size of angle ABC.

(b) Angle BAC = 40°. Calculate the length of BC.

(c) Calculate the area of the circle.

### Explanation

Here, AC is the diameter of a circle which is of 12 cm and O is center.

(a) Size of

Here, edge AC of triangle is diameter of the circle which will be diagonal of triangle ABC.

So, we can see in the figure, it is a right angled triangle, so

• The triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle.

(b) Here, Angle BAC = 40° and length of AC is 12 cm.

So, using cosine formula of triangle:

(C) Area of circle = , where r = radius of circle.

So, here diameter AC = 12 cm, so radius = .

So, area of circle = .