IGCSE Mathematics Paper-1: Specimen Questions with Answers 78 - 81 of 324

Question 78

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Solve the equation

Explanation

Here, equation is

Question 79

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AB is a chord of a circle, O is center. Angle OAB = . Calculate angle AOB.

A circle with triangle in it

A Circle with Triangle in It

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Explanation

Here,

As we can see in the figure AB is chord and O is center, so OA and OB will be radius of the circle.

So, these radiuses will make same angle with points of chord.

So, Angle OAB = , so angle OBA =

Now, in any triangle addition of all angles will give

So, in

.

Question 80

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The population of India was 1.252 billion in 2013. It is expected that this population will increase by 30 % by the year 2015. Calculate the expected population in 2015.

Explanation

Here, Population is. (1 billion = 1000 million)

Expected population will increase by 30%.

So, increment in population will: .

So, expected population in 2015 will be

Question 81

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As shown in the diagram DE is parallel to BC. ADB and AEC are straight lines.

(a) Fill in the blanks with any of the words given: Congruent equilateral isosceles similar

Triangle ADE and triangle ABC are________.

(b) Angle What is the size of angle DBC?

Two triangles made by a middle line

Two Triangles Made by a Middle Line

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Explanation

Here,

(a) Here, Triangle ADE is similar to triangle ABC because there all three angles are same in both as below:

Angle A is common in both so it is same, angle ADB and ABC are corresponding angles and AED and ACB are also corresponding angles, so these will be also same.

While both have no equal sides, so it can’t be called as congruent triangles.

  • Two triangles are called as similartriangles:
  • If all angles are same in both OR
  • If all pairs of sides are in same proportion OR
  • If two pairs of sides are in same proportion and one angle is also same in both.
  • Two triangles are called as congruent triangles when both have all equal sides and equal angles.
  • A triangle with two equal sides and the angles opposite the equal sides are also equal is called as Isosceles.

(b) Here, angle , angle DBC =?

Now, BD is straight line, so angle

So, angle DBC =

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