CIE Mathematics Paper-1: Specimen Questions 36 - 37 of 175

Question number: 36

Essay Question▾

Describe in Detail

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 = 650 .

Geometrical image showing angle DAB

Geometrical image showing angle DAB

Find the below given angles by using triangular formulas

(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 = 650 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 = 900.

(b) Now, in triangle ABC, ∠ACB+∠CAB+∠ABC=1800

∴900+650+∠ABC=1800

→1550+∠ABC=1800

→∠ABC=250

(c) In triangle ABD, ∠BAD=650,∠ABD=900(∵AB⊥DE)

So, ∠BAD+∠ABD+∠ADB=1800

→650+900+∠ADB=1800

→ 1550+∠ADB=1800

→∠ADB=250

Question number: 37

Short Answer Question▾

Write in Short

The net of a solid is drawn accurately below.

Six squares making a solid

Six squares making a solid

Find below mentioned names of squares and solid

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.
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