IGCSE Mathematics Paper-1: Specimen Questions with Answers 36 - 38 of 324

Question 36

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Essay▾

In the diagram, AB is a diameter of the circle, center O. DBE is the tangent at the point B. The line DCA cuts the circle at C. Angle BAC = .

Geometrical image showing angle DAB

Geometrical Image Showing Angle DAB

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(a) Write down the size of angle ACB.

(b) Calculate the size of angle CBA.

(c) Calculate the size of angle ADB.

Explanation

Here,

(a) Angle BAC = is given,

  • As we know, the triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle.
  • So, angle ACB =

(b) Now, in triangle ABC,

(c) In triangle ABD,

So,

Question 37

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Short Answer▾

The net of a solid is drawn accurately below.

Six squares making a solid

Six Squares Making a Solid

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Write down the special name for

(a) The squares shown on the net,

(b) The solid.

Explanation

Here,

(a) The squares shown on the net are equal squares, which have equal lengths of edges.

(b) The solid of net image will called as cube.

  • A cube is made by four equal squares which have six faces, eight vertices and twelve edges.

Question 38

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Write in Short

Short Answer▾

The diagram shows a pole of length l centimeters.

A pole of length l centimeters

A Pole of Length L Centimeters

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(a) Mita says that l = 88.2. Round this to nearest whole number.

(b) If the pole has a length 86 cm, to the nearest centimeter. What can be said about l.

Explanation

Here,

(a) Mita says that l = 88.2 cm.

So, for round this to the nearest whole number we need to see the digit after decimal point, if this digit is 5 or more than 5 then the digit before decimal point will increase by 1.

Here, the digit after decimal point is 2 which is less than 5, so digit 8 which is before decimal point will remain same.

So, length will be: 88 cm after rounding up.

(b) In fact the pole has a length 86 cm, to the nearest centimeter.

Then the nearest length can be:

(I) Less than 86 but more than 85.4: these all will round up and be 86 because digit after decimal point is 5 or more than 5.

(II) More than 86 can be: these all will also round up and be 86 because digit after decimal point is less than 5.

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